Atoms, Molecules & Nuclei

Atoms, Molecules & Nuclei19

COMPREHENSIVE REVIEW

Atomic Physics

1. Thomson's model of the atom

In 1898, Sir J.J. Thomson postulated thefollowing model of the atom.

a) The atom consists of a cloud of +VE charge.See fig. 1.1 below.

b) The size of the +VE cloud is of the order of10–10 m.

c) The electrons are embedded in the +VEcloud in the same way as the seeds areembedded in the water melon

d) Total +VE charge in the cloud is equal tothe total –VE charge on the electrons.

e) The electrons are distributed in the +VEcloud so as to provide stability to the system.

Fig. 1.1

Drawbacks of the Thomson's model

Although, apparently, the Thomson's modelappears to be plausible, yet it suffers from thefollowing drawbacks.

a) Electrostatically the model cannot be stable.Slight disturbance of the structure will setthe electrons into oscillations and as a resultenergy should be radiated out of the atomas em waves.

b) It cannot explain the origin of spectral linesobserved in the spectrum of hydrogen andother atoms.

c) It fails to explain the scattering of -particlesas observed by Rutherford.

Because of these drawbacks, theThomson's model of the atom is rejected.

ATOMS, MOLECULES & NUCLEI ( 275 )

2. Scattering of -particles

a) The scattering of -particles from the thinmetallic sheets was observed by Rutherfordin 1906. He found that when a beam of-particles was incident on a photographicplate a sharp image is obtained. But whenthe same beam passes through a thin metalfoil, the image becomes diffuse. He sugge-sted that this happens due to the scatteringof -particles.

b) In 1911, Rutherford successfully explainedthe scattering of -particles on the basis ofnuclear model of atom.

c) Number of -particles scattered throughangle is given by,

2

4 2

ZN( )

sin ( / 2)K

where K is the kinetic energy of the -particleand Z is the atomic number of the metal.

3. Rutherford's Model of the Atom

On the basis of his study of the scatteringof -particles, Rutherford postulated the follo-wing model of the atom.

a) Atom is sphere of diameter about 10–10 m.Whole of its +VE charge and most of itsmass is concentrated in the central partcalled the nucleus.

b) The diameter of the nucleus is of the orderof 10–14 m. See fig. below.

Fig. 3.1

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c) The space around the nucleus is virtuallyempty with electrons revolving around thenucleus in the same way as the planetsrevolve around the sun.

d) The electrostatic attraction of the nucleusprovides centripetal force to the orbitingelectrons.

e) Total +VE charge in the nucleus is equalto the total –VE charge of the orbitingelectrons.

Drawbacks of the Rutherford's model of the

atom. Rutherford's model suffers from thefollowing drawbacks :

a) Stability of the atomic model.

The electron orbiting around thenucleus radiates energy. As a result, theradius of the electron orbit shouldcontinuously decrease and ultimately theelectron should fall into the nucleus. See fig.below However, nothing of this sort seemto take place within the atom.

Fig. 3.2

b) Nature of energy spectrum.

According to the Rutherford's model,the electrons can revolve around the nucleusin all possible orbits. Hence, the atom shouldemit radiations of all possible wavelengths.However, in practice, the atoms are foundto have line spectrum, or discrete spectrum.

4. Bohr's model of the atom

To account for the drawbacks of the Rutherford'smodel of the atom, Danish physicist, NielsHenrick David Bohr (1885-1962), modified theRutherford's model of the atom as follows :

In his model, Bohr retained the following :features of Rutherford's model :

a) Atom consists of positively charged nucleusaround which electrons revolve in circularorbitals.

b) Majority of the mass and whole of the +VEcharge of the atom is concentrated in thenucleus.

c) Size of the nucleus is very very small ascompared to the size of the atom.

5. Bohr's postulates

Bohr added following postulates to theRutherford's model of the atom.

a) The electrons revolve around the nucleusonly in certain permitted orbits, in which theangular momentum of the electron is an

integral multiple of h

,2

where 'h' is the

Planck's constant.

b) The electrons does not radiate energy whilerevolving in the permitted orbits. That is, thepermitted orbits are stationary, non-radiatingorbits.

c) The energy is radiated only when theelectron jumps from an outer permitted orbitto some inner permitted orbit. (Absorptionof energy makes the electron jump frominner orbit to outer orbit).

d) If energy of the electron in nth and mth orbitsbe E

n and E

m respectively, then, when the

electron jumps from nth to mth orbit, theradiation frequency is emitted, such that :

En – E

m = h

This is called Bohr's frequency equation.

e) The orbital radius of the electron is :

2 2

n 0 2 2

n hR 4

4 me

f) The orbital velocity of electron is :

2

n

0

1 2 e

4 nh

Orbital frequency is given by :

4

2 3 30

1 mef

T 2 r 4 n h

g) The total energy of the orbital electron is :

24

2 20

1 2 me 1E

4 h n





4

2 2 20

meK.E.

8n h

;

4

2 2 20

meP.E.

4n h

h) The velocity of the orbital electron may bewritten as :

2 2

n

0 0

1 2 e 1 c 1 2 e

4 h n n 4 ch

c

n

Here 2

0

1 2 e

4 eh

is called structure

constant. It is a dimensionless quantity.

The value of a comes out to be 1

137 = 0·0073.

i) The kinetic, potential and total energies ofthe electron with r as the radius of the orbitare as follows :

2

0

1 1 eK.E.

2 4 r

,

2

0

1 eP.E.

4 r

&2

0

1 1 eE

2 4 r

Therefore, they are related to each other asfollows :

K.E. = – E. And P.E. = 2E

For example, in the ground state ofhydrogen atom we have E

1 = – 13.6 eV,

P.E. = – 27 eV and K.E. = + 13.6 eV.

6. Energy level diagram

The diagramatic description of the energy of theelectron in different orbits around the nucleus iscalled energy level diagram.

The energy of the orbital electron in the nthorbit is given by :

n 2

13.6E eV

n

Accordingly, the energy associated with thedifferent orbits is as follows :

1 2

13.6E eV 13.6 eV

1

2 2

13.6E eV 3.4 eV

2

3 2

13.6E eV 1.51 eV

3

4 2

13.6E eV 0.85 eV

4

5 2

13.6E eV 0.54 eV

5

& 2

13.6E 0

We find that as n increases En decreases.

So, that when n is large the values of En become

very very close to each other.

a) Excitation energy & excitation potential

The excitation energy is defined as

the energy required to take the electron

from ground level orbit to any higher

order orbit.

Suppose, the electron goes from the

ground state (n = 1) to pth (n = p) orbit. Then,excitation energy is given by :

E p 1 H 2 2

1 1E E E hcR

1 p

It is clear that the excitation energydepends on the higher state to which the

orbital electron jumps. For example, theenergy of the orbital electron in the groundstate is –13.6 eV and that in the first excitedstate (n = 2) is –3.4 eV. Therefore, theexcitation energy for the first excited stateis –3.4 eV – (–13.6) eV = 10.2 eV.

Excitation potential. The potential through

which an electron need to be acceleratedso that it acquires energy equal to theexcitation energy is called excitation

potential. If the excitation energy is 10.2 eVthen excitation potential will be 10.2 V.





b) Ionisation energy and potential

The energy required to ionise an

atom is called ionisation energy. It is theenergy required to make the electron jumpfrom the present orbit to the infinite orbit.Suppose. the electron is in the nth orbit. Then,ionisation energy will be given by,

i n H 2

1E E E hcR

n

Since E 0, therefore i nE E .

For example. when the hydrogen atom is inthe ground state. then the energy of theelectron is E

1 = –13.6 eV. And therefore

ionisation energy is Ei = – E

1 = 13.6 eV. The

ionisation energy of the first excited state is10.2 eV.

c) Ionisation Potential

The potential through which an electron

need to be accelerated so that it acquires

energy equal to the ionisation energy is

called ionisation potential.

For example. the ionisation energy ofthe hydrogen atom in the ground state is13.6 eV. And its ionisation potential is13.6 V.

7. Hydrogen like atoms

The ions such as He+, Li++, Be+++ possessonly one electron orbiting around the nucleus.They are called hydrogen like atoms. Bohr'sAtomic Theory can be applied to them keepingin view that the charge in their nucleus is Ze,where Z is the atomic number. Below. we givesimplified expressions for the various parametersof hydrogen like atoms.

The energy of the orbital electron in thehydrogen like atom is given by :

24 2

n 2 20

1 2 me ZE

4 h n

which may be written as :

2

n H 2

ZE hc R

n

That is, 2

n 2

ZE

n .

Orbital radius is given by :

2 2

n 0 2

h nr (4 )

4 me Z

That is, 2

n

nr

Z .

And orbital velocity is given by :

2

n

0

1 2 e Z

4 h n

That is, n

Z

n .

Also frequency of the light emitted 2Z and

wavelength 2

1

Z .

i) Spectrum of the radiations emitted from

the hydrogen atom.

The radiation spectrum of the hydrogen isgrouped into series as follows. Each seriesis named after its discoverer. According tothe Bohr's theory. the wavelength of theradiations emitted from hydrogen atom isgiven by :

H 2 2i o

1 1 1R

n n

The different groups or the series ofspectral lines depend upon the value of n

i

as described below :

a) Lyman series. For the Lyman series ni = 1

and no = 2, 3, 4 .....

The wavelength of the radiation isgiven by :

H 2 2o

1 1 1R

1 n

They lie in the ultraviolet region.

b) Balmer series. The Balmer series of theradiations correspond to n

i = 2 and n

o = 3,

4, 5 ....





The wavelength of the radiation isgiven by :

H 2 2o

1 1 1R

2 n

They lie in the visible region.

c) Paschen series. For Paschen series, ni = 3

and no = 4, 5, 6 ....

The wavelength of the radiations isgiven by :

H 2 2o

1 1 1R

3 n

They lie in the infra red region.

d) Brackett series. Here ni = 4 and n

o = 5, 6,

7 .....


H 2 2o

1 1 1R

4 n

They lie in the infrared region.

e) Pfund series. This series of radiationscorrespond to n

i = 5 and n

o = 6, 7, 8, 9.....


H 2 2o

1 1 1R

5 n

They lie in far infrared region. Figure7.1 shows the nature of transitions for thedifferent spectral series

Fig. 7.1

ii) Longest and shortest wavelength in thedifferent radiation series of hydrogen atom.

Series Longest Shortest

Lyman 121.6 nm 91.2 nm

Balmer 656.3 nm 364.8 nm

Paschen 1876.1 nm 820.8 nm

Brackett 4053.3 nm 1459.2 nm

Pfund 7461.8 nm 2280.0 nm

iii) According to the Rutherford atomic model,the path of the electron around the nucleusshould be a spiral with progressively decrea-sing radius.

iv) The number of electron in the energy statecorresponding to the nth principal quantumnumber is : 2 n2

v) Fraunhoffer lines refer to absorption linesin the solar spectrum.

vi) The potential energy Ep and kinetic energy

Ek of the orbiting electron in the hydrogen

atom are related to each other as follows :

2p

k

E keE

2 2r

where k is constant = 0

1

4, e = charge on

the electron, r = radius of the orbit.

Here Ek is +VE and E

p is –VE.

Total energy of the electron is,

2 2 2

k p

ke ke keE E E

2r r 2r

That is E is also –VE.

Thus, p

k

EE E

2

vii) The energy of the orbital electron dependson the principal quantum number n.

viii) Helium produces band spectrum.

ix) If a meson (mass = 207 me) orbits around

the nucleus, then radius of the orbit will be :

1r

207 times the radius for the electron

around the nucleus.

x) In the above case the ionisation potential ofthe meson will be 207 times that forelectron.





xi) The Nuclear model of atom was proposedby Earnest Rutherford.

xii) According to the Bohr's theory of hydrogenatom an electron can orbit around thenucleus indefinitely without radiating energyprovided the orbit is circular.

xiii) The energy of the electron in the nth orbit ofhydrogen like atom of atom is :

2

n 2

ZE 13.6 eV

n

xiv) That most of the -particles pass throughthe thin gold sheet, shows that most of thespace occupied by the atom is empty.

xv) Bohr's theory assumes that angular momen-tum of the orbital electron is quantised.

xvi) Speed of the electron in the orbit of hydrogen

atom in the ground state is c

.137

xvii) Angular momentum of the electron in the

nth orbit of hydrogen atom is : h

L n2

xviii) Ionisation potential for hydrogen is 13.6 eV.

xix) Bohr theory of hydrogen atom assumesquantisation of angular momentum alone.

xx) Balmer series of hydrogen atom were thefirst to be discovered.

xxi) H line of every series is the longest and

series limit is the shortest.

xxii) Ionisation energy 2

2

Z13.6 .

n

xxiii) First excitation potential refers to the electronin n = 2 state.

xxiv)

2 2

2 2

2 2

2 2

2 2

4 2 1 1Lyman

3R 3R R R36 6 4 2

Balmer5R 5R R R144 12 9 3

Paschen7R 7R R R

400 20 16 4Brackett

9R 9R R R

900 30 25 5Pfund

11R 11R R R

Series Longest λ Series limit

xxv) The difference in angular momentum associ-ated with the electron in the two successiveorbits of hydrogen atom is :

h nh hL (n 1)

2 2 2

xxvi)As the quantum number increases, the diff-erence of energy between the consecutiveenergy levels decreases.

8. Quantum number

i) Each state of the atom is quantised as regardsthe size, shape and orientation of the electronorbit.

ii) Principal quantum number n is also calledtotal quantum number

n 1, 2, 3, ......

It determines the general size, the velocityas well as energy of the orbital electrons

K n 1

L n 2

M n 3

N n 4

iii) Azimuthal quantum numbers ()

a) It is also known as orbital quantum number.

= 0, 1, 2, 3, ...... (n – 1)

b) It determines the orbital angular momentumof the electron and also the shape of theorbit.

c) gives the number of subshells associatedwith the orbit.

d) e

h hL ( 1)

2 2

e) 0 s

1 p

2 d

iv) Spin quantum number (s) is connectedwith the spin angular momentum of theelectron. It can have only two values,

1s

2 corresponds to clockwise spin

1s

2 corresponds to anticlock wise spin.





The spin angular momentum of the electronis,

s

h shL s(s 1)

2 2

v) Magnetic quantum number (m1)

It represents the components of theorbital angular momentum in the presenceof external magnetic field.

1m , ( 1), ( 2)....... 1,0

So the total number of m1 is 2 + 1.

vi) The time period of orbital electron in theBohr's orbit is :

2 r 2 0.53ÅT

c

137

61.52 10 s

And the frequency of revolution is,

151f 6.5757 10 cps.

T

vii) For given set of n, and m there can be

only two electrons corresponding to,

1 1s and s

2 2

viii) For given set of n, , s and m there can be

only one electron.

ix) For given value of n and , there can be2(2 + 1) electrons. Because correspondingto given , the m

can have (2 + 1) values

and corresponding to each value of m, there

can be two values of s. Note that each valueof refers to a subshell.

s 0 2

p 1 6

d 2 10

f 3 14

No. of electronsSubshell

2(2 + 1)

x) Since each shell has n subshells for which varies from 0 to – 1, hence total numberof electrons for given value of n is :

n 12

0

2(2 1) 2n

2

Electrons inTotal

Shell n Subshells subshells2n

2(2 + 1)K 1 0 1s 2 2L 2 0,1 2s,2p 2,6 8M 3 0,1,2 3s,3p,3d 2,6,10 18

xi) Franck Hertz experiment confirms quanti-sation of energy states.

xii) Area of nth orbit in the hydrogen atom isproportional to n4.

xiii) Radius of nth orbit in hydrogen atom is :

2nr 0.53 n Å

xiv) The wavelength of the light emitted byhydrogen atom is :

12375Å

E

where E is the energy difference of theelectron in the two orbits.

xv) When the electron jumps from one orbit tothe other, the charge, the rest mass and thespin do not change as these are the intrinsicproperties of the electron. In this case onlythe energy and angular momentum of theelectron change.

xvi) All electrons in each subshell have almostidentical energies.

xvii) A subshell having full quota of electrons issaid to be closed or filled.

xviii) The magnetic moment of the closed shell iszero.

xix) The total energy of an orbital electron is lessthan zero (–VE).

xx) Speed of the electron in the nth orbit ofhydrogen atom is,

1 c

n 137

And that in case of hydrogen like atom is :

Z c

n 137

xxi) If elements with n > 4 were not allowed toexist, then total number of elements would

be : 2 2 2 22 [1 2 3 4 ] 60





xxii) Spin angular momentum of electron

1 h h

2 2 4

xxiii) The radius of hydrogen atom in the lowestexcited state is 4 times that in the groundstate.

xxiv)The speed of electron in the orbit of radiusr

n around the hydrogen like nucleus is :

12 2

n

0 n

1 Ze

4 mr

xxv) In the hydrogen atom the linear momentum

of the electron is proportional to n

.

That is Z

m pn

, because Z

.n

xxvi)Rutherford atom could collapse in about10–6 seconds.

xxvii) Wave nature of electrons was experi-mentally confirmed by Davison and Germerin 1927.

xxviii) Permitted value of n ranges upto .However, only values upto 7 has so far beenobserved/established.

xxix)The letter s, p , d, f for = 0, 1, 2, 3, .....correspond to old spectral terms :

s – sharp, p – principal,

d – diffuse, f – fundamental.

xxx) Orbit is assumed to be a circular path aroundthe nucleus.

xxxi)Orbital is three dimensional region wherethere is the maximum probability of findingthe electron.

Nuclear Physics

9. Atomic Nucleus

The existence of atomic nucleus was suggestedby Rutherford while postulating his atomic model.The nucleus is the central part of the atom. Itsdiameter is of the order of 10–14 m. It is about10,000 times smaller than the atomic size. Mostof the mass and whole of the positive charge ofthe atom is contained in the nucleus. The nucleiconsist of protons and neutrons. Protons carry+VE charge and the neutrons are neutral particles.The common name for protons and neutrons inthe nucleus is nucleon.

10. Atomic number and mass number

The number of protons in the nucleus gives itsatomic number (Z).

The number of nucleons (protons and neutrons)in the nucleus gives its mass number (A).

A nucleus with atomic number Z and massnumber A is denoted as

ZXA, where X is the

chemical symbol for the element of the atom.

1. Proton

The proton is a fundamental particle, whichis essential constituent of all atomic nuclei.The nucleus of hydrogen contains only oneproton. Therefore, we may say that theproton is the nucleus of hydrogen atom.

Properties :

i) The proton carries a +VE charge equal to

1.6 10–19 C

ii) The mass of proton is about

1.6726 10–27 kg

iii) Its spin angular momentum is

1 hJs

2 2

iv) Its magnetic moment is

1.41 10–26 JT–1

v) The proton is a stable particle.

2. Neutron

The neutron is also a fundamental particle,which is essential constituent of all nucleiexcept that of hydrogen atom.





Properties :

i) The neutron carries no charge.

ii) The mass of neutron is about

1.6750 10–27 kg

iii) Its spin angular momentum is

1 hJs

2 2

iv) Its magnetic moment is

9.57 10–27 JT–1

v) The neutron is unstable particle. Outside thenucleus it decays into a proton and electron.

vi) Its half life is 12 minutes.

vii) Due to its neutral character it has very highpenetrating power.

viii) Slow neutrons cause nuclear fission.

11. Properties of the nucleus

i) Mass. A nucleus ZXA contains Z protons

and (A – Z) neutrons. The mass of thenucleus is given by :

M = Zmp + (A – Z) m

n – M

where M is the mass lost in putting thenucleons together in the nucleus. It is calledmass defect.

ii) Charge. The charge on the nucleus is : +Ze,where e is the charge on each proton.

iii) Radius. The volume of the nucleus is pro-portional to the mass number (A). Therefore,radius (R) of the nucleus is proportional toA1/3.

That is : 1/ 3 1/30R A Or R R A

where, R0 1.1 10–15 m

iv) Density. The density of the nucleus is ofthe order of 1017 kg m–3.

Atomic mass unit.

The atomic mass unit is defined as 1

12

th of

the mass of a 6C12 atom. It is abbreviated as amu

and is often denoted by the symbol 'u',

The mass of one atom of 6C12 atom is

1.992678 10–26 kg. Therefore, the value of amuis given by :

261.992678 10 kg1 amu

12

271.660565 10 kg

Upto three significant figures it may bewritten as 1.66 10–27 kg.

12. Energy equivalent of amu

Using Einstein's mass energy relation (E= mc2)the energy equivalent to a mass of 1 amu is givenby :

8 227

19

(2.9979 10 )1 amu 1.660565 10 eV

1.6021892 10

6931.486 10 eV

That is 1 amu 931 MeV..

13. Isotopes, Isobars, Isotones

i) Isotopes. The atoms of an element havingsame atomic number (Z) but different massnumber (A) are called isotopes. They arethe nuclei of the same element havingdifferent number of neutrons but samenumber of protons. Their chemical propertiesare similar but they differ in physicalproperties such as mass. Examples ofisotopes are :

a)1H1,

1H2,

1H3

b)8O16,

8O17,

8O18

c)17

Cl35, 17

Cl37

d)92

U235, 92

U238

ii) Isobars. The atoms having same massnumber but different atomic number arecalled isobars. They are atoms of differentelements. Examples of isobars are :

a)1H3,

2He3

b)3Li7 and

4Be7

c)18

Ar40, 20

Ca40

d)32

Ge76, 34

Se76

iii) Isotones. Atoms having same number ofneutrons are called isotones. Examples ofisotones are :

a)1H3,

2He4

b)7N17,

8O18,

9F19





14. Mass defect

The difference in the sum of the masses of theneutrons and protons in the nucleus and the actualmass of the nucleus is called mass defect.

Consider a nucleus ZXA. It has Z protons

and (A – Z) neutrons. Suppose its mass is M.Let the mass of the neutron be m

n and that of

proton be mp. Then mass defect is given by :

p nM [Zm (A Z)m ] M

15. Binding Energy

The energy that keeps the neutrons and protonsbound to the nucleus is called binding energy.

It is the energy equivalent to mass defect.If M be the mass defect of a nucleus, then itsbinding energy is given by :

2Mc , where c = speed of light

The binding energy may also be defined asthe energy that need to be supplied to the nucleusto split it into individual neutrons and protons.

16. Nuclear stability

The stability of the nucleus depends uponthe value of B.E. per nucleon. Greater its valuesmore should be the stability of the nucleus. Thestudy of B.E/A versus A curve reveals thefollowing facts about the stability of the nuclei.

i) Nuclei both with small values of A as wellas with large value of A tend to possess lessstability as compared to those with moderatevalues of A.

ii) Nuclei with even values of both Z and Ashould be more stable than their immediateneighbours. This is indicated by the peakscorresponding to

2He4,

6C12,

8O16. Such

recurrence of peaks is observed for nucleihaving A upto 20. Heavier nuclei such as

82Pb208 are also stable because for them both

Z and A are even.

iii) The lightest and most stable nucleus is 2He4

for which N = Z.

iv) The graph between Z and N for differentnuclei shows that as Z and A increases theZ-N graph bends upwards.

v) The unstable isotopes of different elementsoccupy positions either above or below theband of stability.

17. Tendency to fusion and fission

From the above discussion we find that thereshould be a tendency among the lighter nuclei tofuse together to form more stable nuclei. This isthe cause of fusion in which hydrogen nuclei jointogether to form the helium nucleus. Also theheavier nuclei should disintegrate to producelighter nuclei. This is the cause of fission ofuranium. Also, radioactive decay of the unstableisotopes occurs due to this tendency of the nucleito achieve higher stability. There are about 300stable isotopes and more than 1100 unstableisotopes of different elements.

18. Cause of stability and decay of nuclei

The nucleons in the nucleus are boundtogether due to nuclear forces which donotdepend upon the charge of the particle.

The Coulomb's repulsion of the protons tendsto disrupt the assembly of the nucleons. Thistendency is overcome by the presence of neutrons.The nuclei deficient in the optimum number ofneutrons and protons decay to move towards thegreater stability.

19. Nuclear force

The nucleons have the gravitational forcebetween them. Also, the protons in the nucleushave Coulomb's repulsion between them. It isfound that for the same separation, the Coulomb'srepulsion (F

e) between two protons is about 1036

times the gravitational attraction Fg between them.

That is : 36e

g

F10

F

Therefore, the protons cannot be kept boundto the nucleus by the gravitational force alone. Itis found that another force called the nuclear

force Fn, which is about 100 times greater than

the Coulomb's repulsions keeps the nucleonstogether in the nucleus. Their relative values are :

Fg : F

e : F

n : : 1 : 1036 : 1038

20. Properties of Nuclear forces

i) Nuclear forces are short range forces.They become negligible beyond a distanceof 10–14 m.





ii) Nuclear forces are charge independent.

iii) Nuclear forces are spin independent.

iv) Nuclear forces are repulsive for separationless than 0.5 10–15 m.

v) Nuclear forces are attractive for separationmore than 0.5 10–15 m.

a) Nuclear forces are saturated. A nucleonexerts nuclear force only on its nearestneighbours and not on all the nucleons inthe nucleus.

b) Nuclear forces are the strongest forces

in nature. As explained earlier Fn is about

100 times Fe and 1038 times F

g.

c) Nuclear forces are noncentral in nature.

That is they need not act along the linejoining the particles.

d) Nuclear forces are exchange forces. Thecause of nuclear forces is the exchange ofparticle called -meson between thenucleons.

21. Nuclear fission

The process of splitting the heavy nucleus bybombarding it with neutron is called fission. Themost commonly discussed fission is that of

92U235.

The process occurs as follows :

1 235 2360 92 92n U U

141 92 156 36 0Ba Kr 3 n Q

Thus, when 92

U235 is bombarded with aneutron, the neutron enters the uranium nucleusproducing a compound nucleus

92U236. Which

splits producing one atom each of Ba, Kr, and 3neutrons. About 200 MeV energy is also releasedthat is Q = 200 MeV.

22. Thermal neutrons

Neutrons moving with a speed of about 2.2 kms–1 and having energy of the order of 0.025 eVare called thermal neutrons. They are so calledbecause their velocity is of the same order as thevelocity of the gas atoms at room temperature.Thus, thermal neutrons are the slow movingneutrons.

a) How to obtain tbennal neutrons ?

To obtain thermal neutrons, the fast neutronsare passed through substances like heavywater, paraffin etc. which are rich inhydrogen. The neutrons collide withhydrogen atoms which are roughly of thesame mass as that of neutron. Therefore,they interchange their energies and weobtain neutrons moving with same speedsas that of hydrogen atoms in the substance.

The substance used for slowing downthe fast neutrons is called moderator.

b) Uses of nuclear reactors.

i) They are used for generation of electricpower.

ii) They can be used for the propulsion of ships,submarines etc.

iii) They can produce radioisotopes which maybe used in medicines, industry & agriculture.

iv) Nuclear reactors can also be used for produ-cing high intensity neutron beams, which canbe used to cure cancer or for research.

c) Critical size

Some of the secondary neutrons producedduring fission are lost. Therefore, to sustaina nuclear chain reaction the rate ofproduction of secondary neutrons should beequal or more than the rate of loss ofneutrons. The size of the fissionable fuel thatcan just sustain the chain reaction is calledcritical size. The mass of critical size ofthe fissionable substance is called criticalmass.

d) Atom bomb

It is a device in which energy is released

due to uncontrolled chain reaction

involving the fission of uranium-235.

In the atom bomb pieces of uranium,each of mass less than critical mass areplaced in the container along with a sourceof neutrons. Since, the mass of each pieceis less than the critical mass, the fission mayoccur in them but the chain reaction is notsustained. To explode the bomb, the differentpieces of uranium are brought together bysome means. Immediately a sustained chainreaction is set up and large amount of energyis released.





23. Nuclear fusion

The combination of lighter nuclei to formheavy nucleus with the release of energy is calledfusion. Simplest example is the fusion of hydrogento form helium

1 4 01 2 14 H He 2 e Q

Hydrogen Helium + Positron + Energy

Similarly, 2 2 41 1 2H H He Q

And 2 3 4 11 1 2 0H H He n Q

a) Cause of fusion

The binding energy per nucleon forhydrogen nuclei is small. Therefore, theyfuse together to form nuclei with greaterbinding energy per nucleon. Thus, the fusionis a process to achieve the stability of thenucleus.

b) Thermonuclear fusion

For the two nuclei to fuse together,each must overcome the electrostaticrepulsion of the positive charge of the othernucleus. Hence, they must approach eachother with high speed. For this reason, weneed high temperature. Fusion due to hightemperature is called thermonuclear fusion.However, even at very high temperature,the percentage of nuclear fusion together issmall. For example, in the sun even at a veryhigh temperature, not more than one per centof the hydrogen has fused together duringthe last thousand million year.

c) Hydrogen bomb

Uncontrolled fusion of hydrogen intohelium is called hydrogen bomb. Mixture ofdeutron and tritium is placed inside a strongcasing. To obtain a high temperature fortrigering the fusion, an atom bomb is alsoplaced inside it. For exploding the hydrogenbomb, first we explode the atom bomb. Itraises the temperature to about 107 kelvin.Fusion takes place as follows :

3 2 4 11 1 2 0H H He n 17.6 MeV

Thus, a large amount of energy is released.

24. Energy released in fission and fusion

Fusion of one uranium atom releases about200 MeV of energy. But the fusion of a deutronand a triton releases about 17.6 MeV of energy.However, the release of energy per nucleon infission is about 0.85 Me V but that in fusion is4.4 MeV. So, for the same mass of the fuel, theenergy released in fusion is much larger than infission. It is because of this reason that hydrogenbomb is more dangerous than the atom bomb.

25. Merits of fusion reactor over fission reactor.

i) The fusion reactors require very high temp-erature and they stop operating as soon assomething goes wrong with the reactor. Thisis not the case with the fission reactors.

ii) The fusion reactor produces no radioactivewaste, which is abundant in the fissionreactors.

26. Nuclear reactions

The transformation of a nucleus into anotherisotope by bombarding it with a fast movingparticle is called nuclear reaction. The general,expression for the nuclear reaction is as follows

P + X C Y +

Projectile Target Compound Productparticle nucleus nucleus nucleus

Pr + QProduct Energy

particle

Here, P is the fast moving particle calledprojectile that bombards the target nucleus X. Thebombardment may result in the absorption of theprojectile and produce a compound nucleus C.The compound nucleus being unstable decays intoa product nucleus Y and a product particle Prwith the release of energy Q.

Laws of nuclear reactions

The nuclear reactions take place accordingto the following laws.

i) Conservation of charge

ii) Conservation of nucleon number

iii) Conservation of energy

iv) Conservation of momentum.





27. Artificial transmutation

The nuclear reactions lead to artificialtransmutation of nuclei. Rutherford was the firstto carry out artificial transmutation of nitrogen tooxygen, in the year 1919 A.D.

He bombarded nitrogen with -particlesproducing a compound nucleus of fluorine, whichdecayed into an oxygen nucleus and a proton asfollows :

4 14 18 17 12 7 9 8 1He N F O H

It is called (, p) reaction. The nuclearreactions are generally named in terms of theprojectile and product particles. Below we give afew examples of different types of nuclearreactions.

(p, n) reaction

1 11 12 11 11 5 6 6 0H B C C n

(p, ) reaction

1 7 8 4 41 3 4 2 2H Li Be He He

(p, ) reaction

1 12 13 131 6 7 7H C N N

(n, p) reaction

1 14 15 14 10 7 7 6 1n N N C H

(, n) reaction

2 1 11 1 0 H H n

i) Recent experiments have shown that thedensity of nucleus is highest in the centreand it falls as we go outwards. The nucleusdoes not have a sharp boundary.

The effective value of the radius ofnucleus is the distance from the centre whendensity falls to half of its value at the centre.

ii) Fission was discovered by Otto Hahn andStrassmann.

Fission Reaction :

235 1 236 14192 0 92 56U n ( U ) Ba

92 136 0 Kr 3 n Q

The three neutrons released due to fissionare called secondary neutrons.

i) Q 200 MeV

ii) Each of the released secondary neutroncarries about 2 MeV of energy. So, they arevery fast neutrons.

iii) Q is released as kinetic energy of thefragments. A part of the energy may alsobe released as -rays, heat or light rays.

iv) Temperature becomes very high during thefission process. So, the pressure is also veryhigh.

v) Fission fragments are radioactive.

vi) Natural uranium contains three isotopes :

92U238,

92U236 and

92U235. Most of it is

92U238 and

92U236 is rare. Only 0.7% is

92U235.

vii)92

U235 can be fissioned with thermalneutrons. But

92U238 can be fissioned only

with fast neutrons.

28. Radioactivity

i) Radioactivity.

The decay of the atomic nuclei with

the emission of helium nuclei or electrons

and high energy photons is called

radioactivity.

The helium nuclei are called -particles, theelectrons are called -particles and the highenergy photons are called -particles.

ii) Natural radioactivity

The radioactivity exhibited by thenaturally occurring elements is called natural

radioactivity. The natural radioactivitytakes place spontaneously without anyexternal cause. It is exhibited by the nucleiwith Z > 82. And the ultimate product of thenatural radioactivity is lead with Z = 82.

iii) Artificial radioactivity

Certain nuclei, which are otherwisestable can be converted into unstableisotopes by bombarding them with fastmoving particles. The unstable isotopes soproduced undergo radioactive decay.

Thus, the phenomenon of radioactive

decay by artificial means is called

artificial radioactivity.

In general, the half life of the artificiallyproduced isotope may be short and the decaymay stop as soon as the bombardment withfast moving particles ceases.





iv) Inducedradioactivity

The phenomenon of artificial radio-activity that persists long after thebombardment with fast moving particlesceases, is called induced radioactivity.That is, the life time of the unstable isotopeis long enough so that the decay continueseven when the bombardment is over.

v) Properties of -rays

a) They consist of doubly ionised helium atoms.

b) They are deflected by the electric field.

c) They are deflected by the magnetic field.

d) They carry positive charge of

3.2 10–19 C.

e) Their velocity is about 10% the velocity oflight.

f) They affect the photographic plate.

g) They are absorbed by thin foils. For example,an aluminium foil 0.01 cm thick is sufficientto absorb them. In air at normal pressurethey may peneterate up to 3 to 4 cm,

h) They ionise the gas through which they pass.A single -particle can ionise even up to20,000 gas atoms.

i) They cause fluorescence in zinc sulphide,barium platinocyanide etc.

j) They get scattered by the thin foils.

vi) Properties of -rays

a) They consist of electrons.

b) They are deflected by the electric field.

c) They are deflected by the magnetic field.

d) They carry negative charge of

1.6 10–19 C

e) Their velocity is upto 90% the velocity oflight.

j) They affect the photographic plate.

g) Their peneterating power is about 1000times more than the -particles.

h) They can cause ionisation of the gases. But

their ionisation power is about 1

100th of the

-particles.

i) They cause fluorescence in zinc sulphide andother materials.

j) They are scattered by the metallic sheetmore than the -particles.

vii) Properties of -rays

a) They are photons of very short wavelengthof the order of 10–11 m to 10–13 m.

b) They are not deflected by the electric field.

c) They are not deflected by the magnetic field.

d) They carry no charge.

e) They move with the speed of light.

f) They affect the photographic plate.

g) Their peneterating power is about 100 timesmore than that of -rays.

h) Their ionising power is about 1

100th of that

of -rays.

i) They can cause fluorescence.

j) They are diffracted by the crystals and cancause photo electric emission from metalsof high atomic weight.

viii) Laws of radioactivity decay

The radioactive decay of the nuclei takesplace according to the following laws.

a) Radioactive decay is a spontaneous process.It is independent of the physical factors suchas temperature and pressure. It occurs inaccordance with the laws of chance.

b) At a time either or -particle is emitted.That is both the and -particles are notemitted simultaneously.

c) A nucleus cannot emit more than one a or-particles at a time.

d) The -particle is emitted when the nucleusis left in the excited state after the emissionof or -particle.

e) The nucleon number is conserved during theradioactive decay.

f) The emission of -particle decreases themass number by 4 and the atomic numberby 2 as follows :

decayA 4 A 4Z 2 Z 2X He Y

g) The emission of -particle does not changethe mass number but increases the atomicnumber by 1 as follows :

decayA 0 AZ 1 Z 1X e Y





h) The emission of -particle neither changesthe mass number nor the atomic number asfollows :

* decayA AZ ZX X

The * indicates excited state of ZXA

nucleus.

i) The rate of disintegration of the radioactiveatoms is directly proportional to the number(N) of radioactive atoms present at thatinstant.

That is : dN

Ndt

Or dN

Ndt

where is a constant of proportionalityand is called decay constant.

j) If N be the number of undecayed atoms attime t and N

0 be the number of atoms at

t = 0, then : t0N N e

ix) Units of radioactivity

The rate of decay of the radioactivesubstance is called activity or radioactivity

of the substance.

It is measured in the following three units :

a) Curie (Ci). The activity of a radioactivesample is said to be one curie if it undergoes3.7 1010 disintegrations per second.

Note. The unit curie is defined on the basisof the activity of one gram sample ofradium. It undergoes 3.7 1010 disintegra-tions per second.

b) Rutherford (Rd). The activity of a radio-active substance is said to be one rutherford

if it undergoes 106 disintegrations persecond.

c) The unit of radioactivity in SI is calledbecquerel (Bq). The activity of a radio-active substance is said to be one becquerel

if it undergoes one disintegration per second.

Relation between different units :

1 Ci = 3.7 104 Rd = 3.7 1010 Bq.

x) Half life

The time interval during which half ofthe atoms of the given radioactive sampledecay is called half life. It is denoted by T.

If N0 = number of radioactive atoms at t = 0,

then at time t = T we have 0NN

2 .

Using the relation t0N N e , we find

T00

NN e .

2

This gives : 0.693

T

Thus, half life of a radioactive substance isa characteristic property and is inverselyproportional to the decay constant.

It cannot be changed by any chemicalor physical means.

xi) Decay constant

We know that t0N N e . If

1,

t then :

11 0 0

0 0

N NN N e N e

e 2.718

0 00.368 N 36.8% of N

Thus, decay constant may be defined as

the inverse of the time during which the

number of the atoms in the radioactive

sample is reduced to 36.8% of their

original value.

xii) Average life time Average life of aradioactive sample is defined as the sum ofthe life times of all atoms divided by thenumber of atoms in the sample. It may bedenoted by . Thus,

0

Sum of life times of all atoms 1

No. of atoms in the sample (N )

Thus average life time of the radioactivesample is equal to the inverse of the decayconstant.

xiii) Activity

The number of disintegrations per

second of the radioactive sample is called

activity.

It may be denoted by Ac. Mathematically

we can write : tc 0

dNA N A e

dt ,

where N is the number of atoms of thesample.





xiv) Atoms remaining after n half lives are

given by :

n

0

1N N

2

29. Maser

It stands for micorwave amplification bystimulated emission of radiations.

30. Laser

It stands for light amplification by stimultedemission of radiations. Lasers are called lightmasers or optical masers.

i) Types of Lasers

1. Solid state laser (Ruby laser)

2. Gas lasers (He and Ne laser)

3. Semi-conductor lasers or laser diode(LD)

4. Liquid lasers.

ii) The working of laser is based on stimulatedemission of radiation.

iii) T. Mainman made laser first.

iv) Einstein gave the phenomenon of stimulatedemission in the year 1917.

v) Optical pump or flash lamp is the best pumpsource in case of solid state laser.

vi) In He-Ne laser, the ratio of He to Ne is 7 : 1.

vii) Population inversion means the phenomenonof making the atoms in higher energy statemore than that in lower energy state byinduced absorption.

viii) The maximum time is spent by atoms inmetastable state i.e., 10–3 s.

ix) CO2 laser is used in the treatment of cancer.

x) Laser beam has only one frequency. Thatis, it is highly monochromatic.

xi) The sharpness of the laser beam is measured

in terms of the ratio

.

Where is the spread of frequenciespresent in laser beam. This ratio is 1 : 105.

xii) Laser beam is coherent over a long distanceof hundreds of kilometres.

xiii) Laser beam is highly directional and can befocussed very sharply.

The intensity of the beam at the spot isof the order of 1017 times the intensity ofthe incident laser beam.

xiv) Laser beam is used to bore a hole of verysmall diameter in metal plates, boring tunnelover a long distance, for communicationpurposes, for raising the temperature in anarrow region over million degree, inastronomy, manufacturing and readingcompact discs, cutting cloths, welding ofauto parts, bloodless surgery, removing braintumours, for· fusing detached retina.

xv) The working and principle of maser is sameas that of laser except the wavelength ofemitted radiation. If the wavelength ofemitted radiation is higher than the wave-length of infrared region, then it is calledmaser and if the wavelength is lower thanthe infrared region, then it is called laser.

31. Electron Microscope

Electron microscope is based on the waveproperties of electrons. This microscope has veryhigh resolving power.

Electron microscope is used to study atomicand crystal structure, the structural details oftextile, nylon, fibres, polymers, paper, paints,plastics etc.

i) In the phenomena where light interacts withitself, such as dispersion, interference,diffraction and polarisation, the wave natureof light dominates.

ii) In the phenomena where the light interactswith matter, such as Photoelectric effect,Compton effect, Raman effect, the particlenature of light dominates.

iii) In the phenomena where the light interactswith neither itself nor with matter, both thewave as well as particle nature is exhibited.This is the case with reflection of light.

iv) The de Broglie wavelength of a particle ofmass m and moving with velocity is givenby :

h

m





v) The de Broglie wave length varies inverselyas the velocity of the particle. That is, fasterthe motion of the particle shorter is the valueof .

vi) The de Broglie wave length is inde-

pendent of the nature of the material

particles.

vii) The de Broglie waves are not electro-

magnetic waves. Because the velocity ofmatter waves is different than that of light.

viii) If m0 be the rest mass of the particle. Then,

2 2 1/ 2

0

h[1 / c ]

m

ix) The de Broglie hypothesis of matter waveswas enunciated in 1924.

x) The de Broglie wavelength of a particle ofmass m and kinetic energy K is given by :

h

2 mK

xi) If a particle of mass m carrying charge q0 is

accelerated through potential V, then its deBroglie wavelength is given by :

0

h

2 mq V

xii) The de-Broglie wavelength of a gas moleculeof mass m at temperature T (in kelvin) isgiven by :

h

3 mkT

Here, k is Boltzmann constant.

xiii) If an electron is accelerated through a potentialV volts, then its de Broglie wavelength isgiven by :

1/ 2150

ÅV

xiv) In general the de-Broglie wavelength of acharged particle of mass m, charge qaccelerated through a potential differenceV is given by :

h

2mqV

xv) De, Broglie wavelength associated withorbital electron.

In the nth orbit, we have

nh h 2 rL m r

2 m n

Number of waves in nth orbit is :

2 rN n

Thus the number of de-Broglie waves in nth

orbit is n.

32. Davison Germer experiment

This experiment verified the wave natureof electrons using Ni crystal.

Let b = distance between the lattice points andd = distance between the scattering planes. Alsolet = glancing angle for the incident beam ofelectrons and be the angle between the incidentand diffracted beams. Then for a glancing

incidence, we have 2d sin n . And for normal

incidence, we have bsin n .

Fig. 32.1

33. Heisenberg's Principle of Uncertainty

a) The principle of uncertainty states thataccurate simultaneous measurement ofcertain canonically conjugate pair ofquantities is not possible. And the productof uncertainty in the measurement of twocanonically conjugate quantities is equal to

or more than h

2 or h.

b) Canonically conjugate quantities are asfollows :

i) Displacement (r) and momentum (p).

ii) Angular displacement () and angularmomentum (L).

iii) Energy (E) and time (t).

c) According to the Heisenberg's uncertaintyprinciple, we can write :





i)h

r p2

ii)h

L2

iii)h

E t2

Here r, p, ..... etc. are uncertaintiesin the measurement of the correspondingquantities.

d) Canonically conjugate quantities are thosewhose product has the dimensions of action,that is energy time (Unit : Js).

e) The principle of uncertainty does not applyto all the conjugate pairs of quantities. Forexample, it does not apply to theX-component of displacement and Y or Zcomponent of momentum. That is :

yx p 0

zx p 0

f) According to the principle of uncertainty, iferror in the measurement of position be zerothen that in the measurement of momentumwill be infinite and vice versa. That is :

if r = 0, then p = Similarly if t = 0, then E =

g) Uncertainty principle successfully explainsthe following :

i) Non existence of electrons in thenucleus

ii) Finite size of spectral lines.

h) The energy of the -particle emitted fromwithin the nucleus is of the order of 100 MeV,whereas, for the electron to reside withinthe nucleus it should be of the order of4 MeV. This is explained on the basis of theuncertainty principle.

i) Uncertainty in the measurement of momen-tum of proton within the nucleus is :

hp

2 d

where, d = diameter of the nucleus. Hered = x is the uncertainty in the measurementof position of proton. Same is true for theneutron.







ATOMIC PHYSICS

1. Pauli's exclusion principle states that no twoatomic electrons can :

a) be in the same orbital

b) be in the same shell

c) have same values of all the quantum numbers

d) have same angular momentum

2. Pauli's exclusion principle is also called :

a) equivalence principle

b) correspondence principle

c) uncertainty principle

d) none of the above

3. The total energy of the electron orbiting aroundthe nucleus in the ground state of the atom is :

a) less than zero b) zero

c) more than zero

d) sometimes less and sometime more than zero

4. The angular momentum of the orbital electron isintegral multiple of :

a) h b) 2 h

c)h

2d) none of the above

5. Bohr's atomic model gained acceptance aboveall other models because it :

a) is based on quantum hypothesis

b) explained the constitution of atom

c) assumed continuous radiation of energy byorbiting electrons

d) explained hydrogen spectrum

6. Rutherford's experiments on scattering of-particles proved that :

a) atom is mostly empty

b) positive charge is uniformly distributed in theatom

c) number of positive charges is equal to thenumber of negative charges

d) atoms contain electrons

7. For the electron to revolve around the atomicnucleus without radiating energy, the electronicorbit should be :

a) circular b) elliptical

MULTIPLE CHOICE QUESTIONS

c) such as the angular momentum of the electronis integral multiple of the Planck's constant

d) such as to contain integral number of the deBroglie wavelengths of the electron

8. Rutherford's atomic model accounts for:

a) concentration of positive charge at the centrein the atom

b) stability of electron orbits

c) stability of the nucleus

d) line spectrum of hydrogen

9. Given that R is Rydberg's constant. When anelectron in an atom of hydrogen jumps from anouter orbit n = 3 to an inner orbit n = 2, thewavelength of emitted radiations will be equal to :

a) 2

R

6 b)

26

R

c) 5R

36 d)

36

5R

10. Who proposed that the orbits of the electron inthe atom are elliptical ?

a) Thomson b) Bohr

c) Rutherford d) Sommerfield

11. There are discrete energy levels in atoms. It wasfirst experimentally demonstrated by :

a) Rutherford's experiment

b) Franck Hertz experiment

c) Marsden's experiment

d) Sommerfield experiment

12. Which of the following sources give discreteemission spectrum ?

a) Incandescent electric bulb

b) Sun

c) Mercury vapour lamp

d) Candle

13. In which of the following states does the incan-descent substance give continuous spectrum ?

a) Vapours in atomic state

b) Vapours in molecular state

c) Solid or fluid in bulk state

d) Solid or fluid in plasma state

14. Band spectrum is produced by :

a) H b) He

c) H2

d) Na





15. Who explained the origin of the Fraunhofferlines ?

a) Fraunhoffer b) Kirchhoff

c) Fresnel d) Snell

16. The nuclear model of atom was proposed by :

a) J. J. Thomson b) E. Rutherford

c) Niel Bohr d) Sommerfeld

17. To explain his theory Bohr used :

a) conservation of linear momentum

b) conservation of angular momentum

c) conservation of quantum frequency

d) conservation of energy

18. In which region of electromagnetic spectrum doesthe Lyman series of hydrogen atom lie :

a) Ultraviolet b) Infra red

c) Visible d) X-ray

19. According to classical theory the proposedcircular path of an electron in Rutherford modelof atom will be :

a) Circular b) Straight line

c) Parabolic d) Spiral

20. Electrons in the atom are held in the atom dueto :

a) Coulomb forces

b) Nuclear forces

c) Gravitational forces

d) Van der Waal's forces

21. According to Classical theory, the Rutherfordmodel of atom is :

a) stable b) unstable

c) semi-stable d) meta-stable

22. The angular momentum of electron in nth orbit isgiven by :

a) nh b) h

2 n

c) h

n2

d) 2 h

n2

23. The difference in angular momentum associatedwith the electron in the two successive orbits ofhydrogen atom is :

a) h

b)

h

2

c) h

2d)

h(n 1)

2

24. What will be the angular momentum in fourth orbitif L is the angular momentum of the electron inthe second orbit of hydrogen atom ?

a) 2

L3

b) L

2

c) 2 L d) 3

L2

25. When electron in hydrogen atom jumps to theinner most orbit, the radiation emitted belongs towhich one of the following series ?

a) Paschen b) Balmer

c) Lyman d) Brackett

26. When a hydrogen atom is raised from the groundstate to an excited state :

a) P.E. increases and K.E. decreases

b) P.E. decreases and K.E. increases

c) Both kinetic energy (K.E.) and potentialenergy (P.E.) increases

d) Both K.E. and P.E. decreases

27. How does the energy difference between theconsecutive energy level vary as the quantumnumber 'n' increases ?

a) Increases b) Decreases

c) Remains unchanged

d) First increases and then decreases

28. The frequency of the first line of the Lyman seriesin the hydrogen atom is . What will be thefrequency of the corresponding line for the singlyionised helium atom ?

a) b) 2

c) 4 d) 8

29. Suppose the mass of electron decreases by 25%.How will it affect the Rydberg constant ?

a) Remains unchanged

b) Becomes one fourth

c) Reduced to 75% of its original value

d) It is doubled

30. The charge on the electron and protons is reducedto half. Let the present value of the Rydbergconstant be R. What will be the new value of theRydberg constant ?





a) R

2b)

R

4

c) R

8d)

R

16

31. Which one of the following is the property ofRydberg constant ?

a) It is universal constant

b) It is same for all the hydrogen like atoms

c) It depends on the atomic number of the atom

d) It depends on the mass number of the atom

32. The transition of the electron takes place fromn = 2 orbit to n = 1 orbit. Which of the followinggives the shortest wavelength ?

a) Hydrogen atom

b) Deutrium atom

c) Singly ionised helium

d) Doubly ionised helium

33. The ionisation energy of hydrogen atom is 13.6 eV.The ionisation energy ofhelium atom would be :

a) 1.6 eV b) 27.2 eV

c) 6.8 eV d) 54.4 eV

34. The total energy of an electron in an excitedstateis E. What is its kinetic energy with propersign ?

a) – 2 E b) 2 E

c) – E d) E

35. The hydrogen atom in a sample are in the excitedstate corresponding to n = 3. How many spectrallines can be emitted ?

a) 1 b) 2

c) 3 d) 4

36. The line spectrum is obtained when the incande-scent vapours at low pressure of the excitedsubstance are in :

a) atomic state

b) molecular state

c) plasma state

d) ionised state

37. The band spectrum is obtained whenever theincandescent vapour of the excited substance arein their :

a) atomic state b) molecular state

c) plasma state d) ionised state

38. The ionization potential of a hydrogen atom is13.6 V. What will be the energy of the electronin the second orbit ?

a) 10.2 eV b) 3.40 eV

c) 1.51 eV d) 0.85 eV

39. The total energy of an electron in the excited statecorresponding to n = 3 is E. What is its potentialenergy with proper sign ?

a) – 2 E b) 2 E

c) – E d) E

40. The potential energy of the orbital electron in theground state of hydrogen atom is E. What is itskinetic energy ?

a) E

4b)

E

2

c) 2 E d) 4 E

41. The orbital radius of the electron in the hydrogenatom changes from r to 4 r. The energy of theorbital electron will change from E to :

a) 4 E b) 2 E

c) E

2d)

E

4

42. The minimum energy in electron volt required tostrip off ten times ionized sodium atom (i.e.Z = 11) of its last electron is :

a) 13.6 MeV

b) 13.6 11 eV

c) 13.6 112 eV

d) 13.6 113 eV

43. The orbital electron of the hydrogen atom jumpsfrom the ground state to a higher energy stateand its orbital velocity is reduced to one third ofits initial value. If the radius of the orbit in theground state is r, then what is the radius of thenew orbit ?

a) 2 r b) 3 r

c) 4 r d) 9 r

44. The radius of Bohr's first orbit is r. What is theradius of the first orbit in the singly ionised heliumatom ?

a) 4 r b) 2 r

c) r

2d)

r

4





45. The wavelength of the first line of Balmer seriesof hydrogen atom is . What will be the wave-length of the same line in doubly ionised lithium ?

a) 2

b)

9

c) 8

d)

27

46. The ionisation potential of hydrogen atom is13.6 V. How much energy need to be supplied toionise the hydrogen atom in the first excitedstate ?

a) 13.6 eV b) 27.2 eV

c) 3.4 eV d) 6.8 eV

NUCLEAR PHYSICS

47. 'A' stands for atomic mass number and 'Z' foratomic number. The number of electrons in anatom is :

a) A – Z b) A + Z

c) Z d) A

48. A = atomic mass number, Z = atomic number.The number of neutrons in the nucleus is :

a) Z + A b) Z – A

c) A – Z d) none of the above

49. Which of the following is NOT an elementaryparticle ?

a) -particle b) -particle

c) -particle d) Muon

50. From the following equations pick out the possiblenuclear fusion reaction :

a)6C13 +

1H1

6C14 + 4.3 MeV

b)6C12 +

1H1

7N13 + 2 MeV

c)7C14 +

1H1

8O16 + 7.3 MeV

d)92

U235 + 0n

1 54

Xe140 + 38

Sr94

+ 2(0n

1) + + 200 MeV

51. Cosmic rays originate :

a) on the sun

b) in the solar system but not on the sun

c) outside the solar system

d) in the centre of the universe

52. Which of the following is used as a moderator inthe reactor at Trombay ?

a) Heavy water b) Graphite

c) Ordinary water d) Beryllium oxide

53. In the nuclear reactors the cadmium rods are usedto :

a) generate the neutrons

b) slow down the neutrons

c) accelerate the neutrons

d) absorb the neutrons

54. The repulsive force between the positivelycharged protons does not throw them apart,because :

a) Coulomb's force does not act at small distances

b) nuclear forces are stronger

c) neutrons sit in between the protons

d) of some reason other than the mentioned above

55. Which of the following particles cannot be usedfor the disintegration of a nucleus ?

a) Neutron b) Proton

c) Electron d) Deutron

56. In the nuclear reactors the moderators are usedto :

a) slow down the neutrons

b) generate neutrons

c) accelerate the neutrons

d) absorb the neutrons

57. Which of the following is not conserved in nuclearreactions ?

a) Charge b) Mass

c) Momentum d) Nucleons

58. What is the number of neutrons in 17

C37 ?

a) 17 b) 20

c) 37 d) 54

59. Given M = mass of the nucleus, A = atomic mass.What is packing fraction ?

a) M A

A

b)

A M

A

c) A M

M

d)

M A

M

60. Which of the following helps in knowing aboutthe stability of nucleus ?

a) Binding energy

b) Binding energy per nucleon

c) Both binding energy and binding energy pernucleon

d) Neither binding energy nor binding energy pernucleon





61. If M be the mass of the nucleus and m be thesum of the individual masses of the nucleonsforming the nucleus, then :

a) M is slightly more than m

b) M is slightly less thanm

c) M = m

d) M may be less or more than m depending uponthe nature of the nucleus

62. The binding energy per neucleon is almostconstant for many nuclei. To what characteristicof the nuclear forces does it point ?

a) Saturative nature

b) Short range

c) Attractive nature

d) Exchange force

63. Which of the following is NOT the inverse squarelaw force ?

a) Electric force

b) Gravitational force

c) Nuclear force

d) Magnetic force between two poles

64. In the Bainbridge mass spectrograph which ofthe following is used for the separation ofisotopes ?

a) Electric field only

b) Magnetic field only

c) Both electric and magnetic fields

d) either electric nor magnetic fields

65. Which of the following is NOT the use ofBainbridge mass spectrograph ?

a) To separate isotopes of an element

b) To identify the isotopes of different elements

c) To measure atomic masses

d) To determine the relative percentage of theisotopes

66. Which of the following is NOT the property ofthe atomic nucleus ?

a) Sharp boundary

b) Definite charge

c) Definite number of particles

d) Characteristic atomic number

67. The volume of the nucleons is proportional to :

a) atomic number

b) number of neutrons

c) number of protons

d) mass number

68. Who discovered nuclear fission ?

a) Rutherford

b) Bohr

c) Hahn and Strassmann

d) Becquerel

69. A fusion bomb involves :

a) breaking of a heavy nucleus into lighter ones

b) synthesis of lighter nuclei into heavier ones

c) explosion of TNT

d) burning of huge amount of coal

70. In a nuclear reactor :

a) Moderator is used to control the number ofneutrons

b) Moderator is used to slow down the neutrons

c) Control rods are used to slow down theneutrons

d) Coolant is used to slow down the neutrons

71. What is critical mass of uranium ?

a) 1 kg equivalent

b) 75 kg

c) The rest mass equivalent to 1020 Joules

d) Minimum mass needed for chain reaction

72. Which of the following is best nuclear fuel forthe nuclear reactor ?

a) Thorium - 236 b) Plutonium - 239

c) Uranium - 236 d) Neptunium - 239

73. At what temperature the fusion occurs ?

a) 3 102 K b) 3 103 K

c) 3 105 K d) 3 106 K

74. What amount of energy is released in the fissionof

92U235 ?

a) 20 eV b) 200 eV

c) 200 keV d) 200 MeV

75. What is the main source of energy on the sun ?

a) The burning of hydrogen in the oxygen

b) Fission of uranium present in the sun

c) The energy liberated in the fusion of protonsduring the synthesis of heavier nuclei

d) Gravitational contraction





76. Why does the fusion occur at high temperature ?

a) Atoms are ionised at high temperature

b) Molecules break up at high temperature

c) Nuclei break up at high temperature

d) Kinetic energy is high enough to overcomerepulsion between nuclei

77. The volume of atom in comparison to the volumeof nucleus is of the order of :

a) 105 b) 1015

c) 1025 d) 1030

78. The fusion of hydrogen into helium is more likelyto take place :

a) At high temperature and high pressure

b) At high temperature and low pressure

c) At low temperature and low pressure

d) At low temperature and high pressure

79. What is nuclear holocaust ?

a) Formation of a nuclear bomb

b) Making holes in a metallic case by nuclearradiations

c) Nuclear atmosphere

d) The aftermath of an atomic explosion

80. The phenomenon of pair production is :

a) The production of an electron and a positronfrom -rays

b) Ejection of an electron from a metal surfacewhen exposed to ultraviolet light

c) Ejection of an electron from a nucleus

d) Ionisation of a neutral atom

81. Positron is a particle with :

a) same mass as that of proton and with positivecharge

b) same mass as that of a proton but with anegative charge

c) same mass as that of an electron but with nocharge

d) same mass as that of an electron but withpositive charge

82. The nucleus of 92

U238 has all the followingexcept :

a) 92 protons b) 238 nucleons

c) 146 neutrons d) 92 electrons

83. The mean density of the nuclei is proportionalto :

a) mass number

b) atomic number

c) the number of nucleons


84. Which of the following is most unstable ?

a) Electron b) Proton

c) Neutron d) -particle

85. Which of the following cannot be used to separateisotopes ?

a) Thermal diffusion

b) Centrifuge

c) Chemical reactions

d) Electric and Magnetic fields

86. Of the three basic forces gravitational, electrostaticand nuclear which two are able to provide anattractive force between two neutrons ?

a) Electrostatic and gravitational

b) Electrostatic and nuclear

c) Gravitational and nuclear

d) Some other forces like van der Waals

87. Artificial disintegration with -particles of whichof the following led to the discovery of neutron ?

a) Be b) N

c) Na d) Ba

88. What led to the discovery of proton ?

a) Artificial disintegration of 4Be9 with -particles

b) Artificial disintegration of 7N14 with -particles

c) Radioactive decay of certain elements

d) Scattering of -particles by the heavier nuclei

89. Who achieved the first nuclear transmutation orartificial disintegration of atomic nucleus ?

a) Rutherford

b) Chadwick

c) Heisenberg

d) de Broglie

90. Who is credited with the discovery of proton ?

a) Chadwick b) Rutherford

c) Millikan d) Thomson

91. The nucleus of an atom consists of :

a) electrons and protons

b) electrons, protons and neutrons

c) electrons and neutrons

d) neutrons and protons





92. The helium atom does not contain :

a) two protons b) two electrons

c) two neutrons d) six nucleons

93. In stable nuclei, the number of neutrons (N) isrelated to the number of protons Z in neutral atomin general as :

a) N < Z b) N = Z

c) N > Z d) N Z

94. Neutron was discovered by :

a) Rutherford

b) Chadwick

c) Hahn and Strassmann

d) Millikan

95. What is the binding energy of the hydrogennucleus ?

a) Zero

b) 13.6 eV

c) More than 13.6 eV

d) Infinite

96. What is the cause of the fractional atomic weightof elements ?

a) Isotopes b) Isobars

c) Nucleons d) Electrons

97. Which of the following statements is true fornuclear forces :

a) They obey the inverse square law of distance

b) They obey the inverse third power law ofdistance

c) They are short range forces

d) They are equal in strength to the electro-magnetic forces

98. The nuclei 6C13 and

7N14 can be described as :

a) isotones b) isobars

c) isotopes of carbon

d) isotopes of nitrogen

99. When boron 5B10 is bombarded by neutron, alpha-

particles are emitted. The resulting nucleus hasthe mass) number :

a) 11 b) 7

c) 6 d) 15

100. The first fusion bomb was tested in :

a) 1945 b) 1954

c) 1965 d) 1984

101. When a 4Be9 is bombarded with -particle, one

of the products of nuclear transmutations is 6C12.

The other is :

a) –1

e0 b) 1H1

c) 1H2 d)

0n1

102. In the following reaction,

9 4 a 14 2 6 0Be He X n

what is the value of a ?

a) 16 b) 12

c) 10 d) 14

103. In the nuclear process,

11 116 5C B e X

X stands for :

a) neutron b) neutrino

c) antineutrino d) photon

104. What is the rest mass energy of electron ?

a) 1 eV b) 0.51 eV

c) 0.051 MeV d) 5.1 MeV

105. What is average binding energy of a nucleus ?

a) 8 eV b) 8 keV

c) 8 MeV d) 8 BeV

RADIOACTIVITY

106. If I1, I

2, I

3 be the ionising powers of , and

particles, then which of the following relations iscorrect ?

a) I1 > I

2 > I

3

b) I1 < I

2 < I

3

c) I1 > I

2 but I

2 < I

3

d) I1 < I

2 but I

2 > I

3

107. Which of the following is NOT conserved innuclear decay ?

a) Number of the fundamental particles

b) Mass number

c) Atomic number

d) Nucleon number

108.92

U239 decays emitting a -particle producingneptunium nucleus, which further decaysemitting a -particle and the daughter productis plutonium (Pu). The grand daughter productcan be expressed as :

a) 90

Pu239 b) 90

Pu241

c) 94

Pu239 d) 94

Pu241





109. How many radioactive disintegration per secondis called rutherford ?

a) 102 b) 104

c) 106 d) 108

110. Radioactivity is the phenomenon associated with :

a) decay of nucleus

b) production of radio waves

c) transmission of radio waves

d) reception of radio waves

111. What are -rays ?

a) Singly ionised gas atoms

b) Helium nuclei

c) Electromagnetic waves

d) Fast moving electrons


a) Singly ionised gas atoms

b) Helium nuclei

c) Fast moving electrons

d) Electromagnetic waves

113. -rays pass through a strong uniform electric field,in which direction are they deflected ?

a) In the direction of electric field

b) In the direction opposite to that of electric field

c) In the direction Perpendicular to electric fieldand direction of propagation of rays

d) Do not get deflected

114. During a -decay :

a) an atomic electron is ejected

b) an electron which is already present withinthe nucleus is ejected

c) a neutron in the nucleus decays emitting anelectron

d) a part of binding energy of nuclei is convertedinto an electron


a) Electromagnetic radiations

b) The electrons orbiting around the nucleus

c) Charged particles emitted by nucleus

d) Neutral particles

116. Which of the following are deflected by theelectric field ?

a) X-rays b) neutrons

c) -particles d) gamma rays

117. Which of the following isotopes is used for thetreatment of cancer ?

a) K40 b) Co60

c) Sr90 d) I131

118. Consider the following nuclear reaction,

92U234

90Th230 + X + energy..

The nuclide X represents :

a) 1H3 b)

1H1

c) 2He3 d)

2He4

119. A nuclide A (with mass number m and atomicnumber n) disintegrates emitting an alpha and onebeta particle. The resulting nuclide B has massnumber and atomic number respectively equal to :

a) m – 4 and n – 2 b) m – 2 and n

c) m + 4 and n + 1 d) m – 4 and n – 1

120. A radioactive isotope ZXA decays in series by

emitting 3-particles & 2-particles. The resultantisotope will be :

a) Z – 3

YA – 13 b) Z – 4

YA – 12

c) Z – 5

YA – 11 d) Z – 6

YA – 11

121. Atomic mass number of an element is 232 andits atomic number is 90. The end products of thisradioactive element is an isotope of lead (Atomicmass 208 and atomic number 82). The numberof and -particle emitted is :

a) = 3, = 3

b) = 6, = 4

c) = 6, = 0

d) = 4, = 6

122. T is the half life period and Ta is the average life

of a radioactive substance. Which of the followingstatement is correct ?

a) T > Ta

b) T is about 69% of Ta

c) T is inversely proportional to Ta

d) T and Ta both are directly proportional to

radioactive decay constant

123. A positron is emitted by a radioactive nucleus ofatomic number 90. What is the atomic number ofthe product nucleus ?

a) 90 b) 91

c) 89 d) 88

124. The specific charge of -rays is found to be lessthan that of cathode rays. Why ?





a) Charge has decreased by virtue of its largevelocities

b) Charge has increased by virtue of largevelocities

c) Mass has increased by virtue of largevelocities

d) Mass has decreased by virtue of largevelocities

125. How does the decay constant of a radioactivesample vary ?

a) Decrease as the age of atoms increases

b) Increases as the age of atoms increases

c) It is independent of the age

d) Depends on the nature of activity

126. In a cloud chamber , and -radiations aresent. The nature of tracks produced by theseparticles respectively will be :

a) thin and long, thick and short, thin and verylong

b) thick and short, thin and long, fuzzy

c) thick and long, thin and short, fuzzy

d) thick and short, thin and long, thick and long

127. The relation between half life T1/2

of a radio-activesample and its mean life is :

a) 1/ 2T 0.693 b) 1/ 20.693 T

c) 1/ 2T d) 1/ 22.718 T

128. What is the half life of lead ?

a) zero b) Infinite

c) 1590 days d) 1590 years

129. What determines the half life of a radioactivesample ?

a) Temperature

b) Pressure

c) Nature of substance

d) All of above

130. The difference between 92

U235 and 92

U238 atomsis that :

a) U238 contains 3 more protons

b) U238 contains 3 more protons and 3 moreelectrons

c) U238 contains 3 more neutrons and 3 moreelectrons

d) U238 contains 3 more neutrons

131. Of the following which one can penetrate through20 cm thick steel plate ?

a) -rays b) -rays

c) -rays d) positive rays

132. What determines the half life of the radioactiveelements ?

a) Atomic number b) Mass number

c) Temperature d) None of the above

133. Which of the following radioactive decay emits-particle ?

a) 214 21482 93Pb Bi ......

b) 238 23492 90U Th ......

c) 234 23490 91Th Pa ......

d) 234 23491 92Pa U ......

134. As a result of radioactive decay a 92

U238 nucleusis changed to a

91P234 nucleus. Which particles

are emitted in the decay ?

a) One proton and two neutrons

b) One -particle and one -particle

c) Two -particles and one neutron

d) Two -particles and one proton

135. In which radioactive disintegration, neutrondissociates into proton and electron ?

a) He++ emission

b) -emission

c) -emission

d) Positron emission

136. The equation ZXA

Z + 1YA +

–1e0 + represents :

a) -decay b) -decay

c) fusion d) fission

137. A radioactive element has a half life of 2.5 hours.In 10 hours 1 gram of radioactive material isreduced to :

a) 1

4 gram b)

1

8 gram

c) 1

16 gram d)

1

32 gram

138. The half life of a radioactive element is 5 min.The fraction of the sample of this isotope thatwill remain after 30 min is :





a) 1

6b)

1

36

c) 1

32d)

1

64

139. The half life period of radioactive nuclide is3 hours. In 9 hours, its activity will be reduced bya factor of :

a) 1

9b)

1

27

c) 1

6d)

1

64

140. Particles emitted from some radioactive materialare observed to be deflected in a magnetic field :

i) the particles may be electrons

ii) the particles may be protons

iii) the particles may be neutrons

iv) the particles may be hydrogen atoms.

State if :

a) only (i) is correct

b) (i) and (ii) are correct

c) (i) and (iii) are correct

d) (i) and (iv) are correct

141. Matter waves are similar in nature to :

a) X-rays b) -rays

c) cathode rays d) none of the above

142. The wavelength of the matter waves is indepen-dent of :

a) mass b) velocity

c) momentum d) charge

143. Which of the following will have shortest wave-length while moving with same speed ?

a) Proton b) Deutron

c) Neutron d) Electron

144. The hypothesis regarding dual nature of thematerial particles was proposed by :

a) Heisenberg b) Davison

c) de Broglie d) Germer

145. Wave particle duality of matter suggests that it isnot possible to measure the time interval withcertainty simultaneously with :

a) location b) momentum

c) energy d) mass

146. The resolving power of the electron microscopeis proportional to :

a) the de Broglie wavelength

b) numerical aperture

c) the accelerating potential

d) momentum of the electron

147. Matter waves :

a) are electromagnetic waves

b) are transverse waves

c) are longitudinal waves

d) exhibit diffraction

148. In order to raise the resolving power of theelectron microscope we should :

a) accelerate the electron through low potential

b) accelerate the electron through high potential

c) retard the electron

d) increase the de Broglie wavelength of theelectron

149. What is the de Broglie wavelength of 1 kg massmoving with a velocity of 10 ms–1 ?

a) 6.626 10–33 m

b) 6.626 10–34 m

c) 6.626 10–35 m


150. A photon and a neutron are moving with the same

kinetic energy. What is the ratio of p

n

?

a) 1 b) 1.6 10–19

c) 9

1

1.6 10d) none of the above

151. In the Davison Germer experiment if the incidentbeam consists of electrons, then the diffractedbeam consists of :

a) protons b) neutrons

c) -particles d) electrons

152. What will be the ratio of the de Broglie wave-length associated with a deutron and protonaccelerat through the same potential difference ?

a) 1

2b)

1

2

c) 2 d) 2





153. The de Broglie wavelength of an atom of mass mof a diatomic gas at temperature T will be :

a) h

3 mkTb)

h

3 mkT

c) h

5 mkTd)

h

5 mkT

154. What will be the de Broglie wavelength of aparticle of rest mass m

0, if it moves with the speed

of light ?

a) 0

h

m c b) 0

2h

m c

c) d) zero

155. For the Davison Germer experiment if the angleof diffraction be 520, then what is the glancingangle ?

a) 260 b) 640

c) 520 d) 1040

156. Through what potential difference should anelectron be accelerated to associate a de Brogliewave of length 1 Å with it ?

a) 50 V b) 100 V

c) 150 V d) 200 V

157. The de Broglie wavelength of an electron is0.5 nm. What is the retarding potential requiredto stop it ?

a) 2 V b) 3 V

c) 4 V d) 6 V

158. A deutron is accelerated through 100 V. What isits de Broglie wavelength ?

a) 2.02 Å

b) 0.202 Å

c) 0.0202 Å d) 0.002 Å

159. Which out of the following will have longestwavelength associated with it ?


c) Deutron d) Photon

160. What is the de Broglie wavelength associatedwith nth orbital electron ? Given that the radius ofthe orbit is r :

a) 2 m b) m

c) r

n

d)

2 r

n

161. The de Broglie wavelength of electron and protonare same. Which quantity will be same for both ?

a) Kinetic energy

b) Momentum

c) Accelerating potential

d) Velocity

162. What is the de Broglie wavelength of a neutronhaving energy 6.4 10–19 J ?

a) 0.286

Å2

b) 0.286

Å2

c) 0.286 2 Å d) 0.286 2 Å

Recent Questions from MH-C.E.T. Exams.

163. The radii of Bohr's orbit are directly proportionalto :

a) principal quantum number

b) square of the principle quantum number

c) cube of the principal quantum number

d) fourth power of the principal quantum number

164. In the hydrogen atom spectrum the series whichlies in far ultra violet region is :

a) Lyman series b) Balmer series

c) Paschen series d) Brackett series

165. A radioactive substance has a half life of 4 hours.Three-fourths of the substance would decay in :

a) 3 hours b) 4 hours

c) 8 hours d) 12 hours

166. The K.E. possessed by an electron revolving roundthe nucleus in an orbit of radius r is proportionalto :

a) r b) r–1

c) r–2 d) r–3

167. The electron in the hydrogen atom jumps fromthe second orbit to the fourth orbit after absorbingphoton. In this process its :

a) energy doubles

b) velocity doubles

c) angular momentum doubles

d) linear momentum doubles

168. If (the Rydberg const.) R = 1.096 107 m–1, theseries limit of Paschen series is :

a) 8211 A.U. b) 6563 A.U.

c) 3648 A.U. d) none of the above





169. A radio-active element has a half-life of 2.5 hours.In 10 hours 1 g of material is reduced to :

a) 3.13 10–2 g b) 6.25 10–2 g

c) 12.5 10–2 g d) 25.0 10–2 g

170. In a -decay :

a)n

p ratio increases

b)n

p ratio decreases

c)n

p ratio does not change

d) n remains constant

171. Energy levels of a hypothetical one-electron atom

are given by, n 2

15.6E eV

n . If an electron, with

initial kinetic energy 6.0 eV, interacts with thisatom in the ground state, then :

a) The colliding electron leaves the encounter withthe initial kinetic energy leaving the atom inits ground state

b) The colliding electron leaves the encounter withan energy of 3.78 eV while the atom is excitedto state n = 3

c) The colliding electron is capatured by the atomin some of its excited state

d) The atom is ionized and the atomic electroncarries away 6.0 eV as kinetic energy whilethe colliding electron comes to rest

172. In the H2-atom spectrum, the series which lies in

far ultra-violet region is :

a) Lyman series b) Paschen series

c) Balmer series d) Brackett series

173. In hydrogen atom, moment of inertia of theelectron in the nth orbit is :

a)

2 2 4

2 4 40

m e

h n

b)

2 440

2 4

hn

e

c) 2

202

hn

e

d)

nh

2

174. A radioactive substance has a decay constant of0.25 s–1. After 4 s,

a) There is no appreciable change in activity

b) The number of original radioactive nucleipresent decreases by a factor of e

c) The number of original radioactive nucleipresent decreases by a factor of 1 – e

d) The activity increases by a factor of e

175. The ratio of speed of an electron in ground statein Bohr's first orbit of hydrogen atom to velocityof light in air is :

a) 2

0

e

2 hcb)

202e

hc

c) 2

0

e

2 hcd)

02

2 hc

e

176. An atom of mass number A and atomic numberZ emits successively -particle, -particle,-particle. Then the mass number and atomicnumber of the end product are :

a) A – 4, Z – 1 b) A – 4, Z + 2

c) A, Z + 1 d) A – 1, Z – 4

177. Energy of the electron in nth orbit of hydrogen

atom is given by, n 2

13.6E eV

n . The amount of

energy needed to transfer electron from first orbitto third orbit is :

a) 13.6 eV b) 3.4 eV

c) 12.09 eV d) 1.51 eV

178. Balmer series is obtained in :

a) visible region

b) visible and infra red

c) ultra violet d) None of these

179. Shortest wavelength of Lymen series is 912 Å.That of Paschen series is :

a) 8408 Å b) 8415 Å

c) 8430 Å d) 8460 Å

180. rays are :

a) high velocity electromagnetic radiation of highenergy

b) positively charged

c) have no effect in the magnetic field

d) none of these

181. What is the ratio of wavelength of radiationsemitted when an electron in hydrogen atom jumpfrom fourth orbit to second orbit and from thirdorbit to second orbit ?





a) 27 : 25 b) 27 : 20

c) 20 : 25 d) 25 : 27

182. Light of wavelength 4000 Å is incident on a metalsurface. The maximum kinetic energy of emittedphotoelectron is 2 eV. What is the work functionof the metal surface ?

a) 4 eV b) 1 eV

c) 2 eV d) 6 eV

183. The Balmer series of hydrogen spectra lies in :

a) Visible region spectra

b) Ultra violet spectra

c) Infra red region spectra

d) -rays spectra

184. Given that R is Rydberg constant for hydrogen,the H

line in the hydrogen spectrum has

wavelength of :

a) 1

R6

b) 6 R

c) 5

R36

d) 36

5R

185. The angular momentum of an electron in nth orbitis given by :

a) nh b) h

2 n

c) nh

2d)

2n h

2

186. What percentage of radioactive substance is leftafter 5 half lives ?

a) About 97 % b) less than 90 %

c) 20 % d) About 3 %

187. Which of the following transition in hydrogenatom, gives emission line of highest frequency ?

a) n = 2 to n = 1 b) n = 1 to n = 2

c) n = 10 to n = 2 d) n = 5 to n = 4

188. The energy in ground state of hydrogen atom is–13.6 eV, its energy in third orbit is :

a) 12.05 eV b) – 1.51 eV

c) 2.51 eV d) – 13.6 eV

189. For radioactive substance 'A' half life period is1 hr and for substance 'B' half life period is 2 hr,after 6 hrs what is the ratio of remaining amountof A to B :

a) 1 : 8 b) 8 : 1

c) 1 : 64 d) 1 : 32

190. If 2

P

KE

R ; then E

K = ?

a) 2K

2Rb)

K

2R

c) 2K

Rd)

22K

R

191. Radius of nth Bohr orbit of H-atom is directlyproportional to :

a) n b) n2

c) 1

nd) 2

1

n

192. Velocity of the electron in Ist Bohr orbit is2.16 106 and radius of Ist Bohr orbit is 0.5 Å.Then i = ?

a) 0.5 mA b) 1 mA

c) 1.5 mA d) 2 mA

193. If the velocity of an electron in its first orbit ofhydrogen atom is 2.1 106 m/s, then its velocityin the third orbit is :

a) 7 106 m/s b) 7 105 m/s

c) 7 104 m/s d) 2 104 m/s

194. Which of the following quantities has same unitsand dimensions as that of Planck's constant ?

a) Moment of inertia

b) Angular momentum

c) Linear momentum

d) Rate of the change of linear momentum

195. The product of linear momentum and angularmomentum of an electron of the hydrogen atomis proportional to nx, where x is :

a) 0 b) 1

c) – 2 d) 2

196. The orbital frequency of an electron in thehydrogen atom is proportional to :

a) n3 b) n–3

c) n d) n0

197. Balmer series of hydrogen atom lies in :

a) microwave region b) visible region

c) ultraviolet region d) infrared region





198. The acceleration of electron in Bohr's Ist orbit isgiven by :

a) 2 3

h

4 m rb) 2

h

4 m r

c) 2

2 3

h

4 m rd)

2h

4 mr

199. An electron moves in Bohr's orbit. The magneticfield at the centre is proportional to :

a) n–5 b) n–3

c) n–4 d) n–2

200. In Bohr's orbit, angular momentum of an electronis proportional to :

a) r b) 2r

c) r d) r–1/2

201. In Bohr's orbit, kinetic energy of an electron inthe nth orbit of an atom in terms of angularmomentum is :

a) 1

Lb) 2

1

L

c) L2 d) 3

1

L

202. If an electron in hydrogen atom jumps from anorbit of level n = 3 to an orbit of level n = 2,emitted radiation has a frequency :

[R = Rydberg's constant, c = velocity of light]

a) 3Rc

27b)

Rc

25

c) 8Rc

9d)

5Rc

36

203. The de-Broglie wavelength of an electron in 4th

orbit is : [r = radius of 1st orbit]

a) 2 r b) 4 r

c) r

2

d) 16 r

204. For Balmer series, wavelength of first line is '1'

and for Brackett series, wavelength of first line

is '2' then 1

2

is :

a) 0.081 b) 0.162

c) 0.198 d) 0.238

205. For the hydrogen atom, the energy of radiationemitted in the transition from 4th excited state to2nd excited state, according to Bohr's theory is :

a) 0.567 eV b) 0.667 eV

c) 0.967 eV d) 1.267 eV

206. The de-Broglie wavelength '' of a particle :

a) is proportional to mass

b) is proportional to impulse

c) is inversely proportional to impulse

d) does not depend on impulse







REVISION OUESTIONS

from Competitive Exams

1. A certain radioactive substance has a half-life of5 years. Thus for a nucleus in a sample of theelement, the probability of decay in ten years is :

a) 50 % b) 75 %

c) 100 % d) 60 %

2. A beam of least moving alpha particles weredirected towards a thin film of gold. The parts A,B and C of the transmitted and reflected beamscorresponding to the incident parts A, B and C ofthe beam, are shown in the adjoining diagram.The number of alpha particles in :

a) B' will be minimum and in C' maximum

b) A' will be maximum and in B' minimum

c) A' will be minimum and in B' maximum

d) C' will be minimum and in B' maximum

3. When a radioactive isotope 88

Ra228 decays inseries by the emission of 3 alpha particles and abeta particle, the isotope finally formed is :

a) 22884 X b) 222

86 X

c) 22683 X d) 215

83 X

4. Energy levels A, B, C of a certain atom correspondto increasing values of energy i.e., E

A < E

B < E

C.

If 1,

2,

3 are the wavelengths of radiation

corresponding to the transitions C to B, B to Aand C to A respectively, which of the followingrelations is correct ?

a) 3 1 2 b) 1 23

1 2

c) 1 2 3 0 d) 2 2 23 1 2

5. The nucleus 6C12 absorbs an energetic neutron

and emits a beta particle (). The resulting nucleusis :

a) 7N14 b)

5B13

c) 7N13 d)

6C13

6. The energy of a hydrogen atom in its ground stateis –13.6 eV. The energy of the level correspon-ding to the quantum number n = 5 is :

a) – 0.54 eV b) – 5.40 eV

c) – 0.85 eV d) – 2.72 eV

7. A gamma ray photon creates an electron positronpair. If the rest mass energy of an electron is0.5 MeV and the total kinetic energy of theelectron positron pair is 0.78 MeV, then the energyof the gamma ray photon must be :

a) 0.78 MeV b) 1.78 MeV

c) 1.28 MeV d) 0.28 MeV

8. In the reaction represented by,

A A 4 A 4 A 4Z Z 2 Z 2 Z 1X Y Y K

the decays in the sequence are :

a) , , b) , ,

c) , , d) , ,

9. When a hydrogen atom is raised from the groundstate to excited state :

a) Both kinetic energy (K.E.) & potential energy(P.E.) increases

b) Both K.E. and P.E. decreases

c) P.E. increases, K.E. decreases

d) P.E. decreases. K.E. increases

10. The half life of a radio-isotope is 5 years. Thefraction of atoms decayed in this substance after15 years will be :

a) 1 b) 3 / 4

c) 7

8d)

5

8

11. The energy of an electron in nth orbit of thehydrogen atom is given by,

n 2

13.6E eV

n

The energy required to raise an electron fromthe first orbit to the second orbit will be :

a) 10.2 eV b) 12.1 eV

c) 13.6 eV d) 3.4 eV

12. In terms of the Bohr radius a0, the radius of the

second Bohr orbit of a hydrogen atom is givenby :

a) 4 a0

b) 8 a0

c) 02 a d) 2 a

0





13. The average binding energy of a nucleon insidean atomic nucleus is about :

a) 8 MeV b) 8 eV

c) 8 joules d) 8 ergs

14. The ionisation energy of Hydrogen atom is13.6 eV. Following Bohr's theory the energycorresponding to a transition between the 3rd andthe 4th orbit is :

a) 3.40 eV b) 1.51 eV

c) 0.85 eV d) 0.66 eV

15. A radioactive sample with a half life of 1 monthhas the label : "Activity = 2 micro curies on1.8.1991." What was its activity two monthslater ?

a) 1.0 micro curie b) 0.5 micro curie

c) 4 micro curies d) 8 micro curies

16. The energy equivalent of one atomic mass unitis :

a) 1.6 10–19 joules

b) 6.02 10+23 joules

c) 931 MeV d) 9.31 MeV

17. The mass density of a nucleus varies with massnumber A as :

a) A2 b) A

c) constant d) 1 / A

18. Curie is a unit of :

a) Energy of gamma-rays

b) Half-life

c) Radioactivity

d) Intensity of gamma-rays

19. The nucleus 115 48 Cd, after two successive –

decays will give :

a) 115 46 Pa b) 114

49 In

c) 113 50 Sn d) 115

50 Sn

20. Which one of the following is the weakest kindof bonding in solids ?

a) Ionic b) Metallic

c) van der Waals d) Covalent

21. The ground state energy of H-atom is 13.6 eV.The energy needed to ionise H-atom from itssecond excited state :

a) 1.51 eV b) 3.4 eV

c) 13.6 eV d) 12.1 eV

22. Hydrogen atoms are excited from ground stateof the principal quantum number 4. Then thenumber of spectral lines observed will be :

a) 3 b) 6

c) 5 d) 2

23. Which source is associated with a line emissionspectrum ?

a) Electric fire b) Neon street sign

c) Red traffic light d) Sun

24. The binding energy per nucleon is maximum inthe case of :

a) 42 He b) 56

26 Fe

c) 141 56 Ba d) 235

92 U

25. The electronic configuration for the noble gas is :

a) 1s2 2s2 2p6

b) 1s2 2s2 2p5

c) 1s2 2s2 2p6 3s2 3p6 4s2

d) 1s2 2s2

26. What is the radius of iodine atom (At. No. 53,Mass number 126) ?

a) 2.5 10–11 m b) 2.5 10–9 m

c) 7 10–9 m d) 7 10–6 m

27. Energy released in the fission of a single 235 92 U

nucleus is 200 MeV. The fission rate of a 235 92 U

fuelled reactor operating at a power level of 5Wis :

a) 1.56 10–10 s–1 b) 1.56 10–11 s–1

c) 1.56 10–16 s–1 d) 1.56 10–17 s–1

28. In a given reaction,

A A A 4 A 4Z Z 1 Z 1 Z 1X Y K K

Radioactive radiations are emitted in the sequenceof :

a) , , b) , , c) , , d) , ,

29. A radioactive element has half-life period 1600years. After 6400 years what amount willremain ?

a) 1

2b)

1

16

c) 1

8d)

1

4





30. A star initially has 1040 deutrons. It producesenergy via the processes,

2 2 31 1 1H H H p and

2 3 41 1 2H H H n

If the average power radiated by the star is 1016 W,the deutron supply of the star is exhausted in atime of the order of :

a) 106 second b) 108 second

c) 1012 second d) 1016 second

The masses of the nuclei are as follows :

M(H2) = 2.014 amu ; M(p) = 1.007 amu ;

M(n) = 1.008 amu ; M(He4) = 4.001 amu.

31. A positron has the same mass as :

a) proton b) -particle

c) neutron d) electron

32. Hydrogen atom emits blue light when it changesfrom n = 4 energy level to the n = 2 level. Whichcolour of light would the atom emit when itchanges from the n = 5 level to the n = 1 level ?

a) Red b) Yellow

c) Green d) Violet

33. Isotopes are atoms having :

a) same number of protons but different numberof neutrons

b) same number of neutrons but different numberof protons

c) same number of protons and neutrons


34. Doubly ionised helium atoms and hydrogen ionsare accelerated from rest through the same potentialdrop. The ratio of the final velocities of the heliumand the hydrogen ions is :

a) 1

2b) 2

c) 1

2d) 2

35. Gases begin to conduct electricity at low pressurebecause :

a) at low pressure gases turn to plasma

b) colliding, electrons can acquire higher kineticenergy due to increased mean free path leadingto ionisation of atoms

c) atoms break up into electrons and protons

d) the electrons in atoms can move freely at lowpressures

36. The radius of hydrogen atom in its ground stateis 5.3 10–11 m. After collision with an electron itis found to have a radius of 21.2 10–11 m. Whatis the principle quantum number n, of the finalstate of the atom :

a) n = 4 b) n = 2

c) n = 16 d) n = 3

37. In Rutherford scattering experiment, what willbe correct angle for a scattering for an impactparameter b = 0 ?

a) 900 b) 2700

c) 00 d) 1800

38. The mass number of He is 4 and that for sulphuris 32. The radius of sulphur nucleus is larger thanthat of helium, by times :

a) 8 b) 4

c) 2 d) 8

39. If the binding energy per nucleon in Li7 and He4

nuclei are respectively 5.60 MeV and 7.06 MeV,then the energy of the reaction,

7 42Li p 2 He is :

a) 19.6 MeV b) 2.4 MeV

c) 8.4 MeV d) 17.3 MeV

40. An element A decays into element C by a twostep process :

42A B He

B C 2e

Then :

a) A and C are isotopes

b) A and C are isobars

c) A and B are isotopes

d) A and B are isobars

41. When the electron jumps from a level n = 4 ton = 1, momentum of the recoiled Hydrogen atomwill be :

a) 6.8 10–27 kg m/s

b) 12.75 10–19 kg m/s

c) 13.6 10–19 kg m/s

d) zero





42. By increasing the intensity of incident light on thesurface of a metal :

a) kinetic energy of the photo electrons increases

b) number of emitted electrons increases

c) kinetic energy and number of the electronsincreases

d) no effect

43. The essential distinction between X-rays and-rays is that :

a) -rays have smaller wavelength than X-rays

b) -rays emanate from nucleus while X-raysemanate from outer part of the atom

c) -rays have greater ionizing power thanX-rays

d) -rays are more penetrating than X-rays

44. Which one of the following nuclear reactions is asource of energy in the sun ?

a) 9 4 12 14 2 6 0Be He C n

b) 3 3 4 1 12 2 2 1 1He He He H H

c) 144 92 235 1 56 56 92 0Be Kr U n

d) 56 112 167 126 48 74 0Fe Ca W n

45. An atom of mass number 15 and atomic number07 captures an -particle and then emits a proton.The mass number and atomic number of theresulting product will respectively be :

a) 14 and 2 b) 15 and 3

c) 16 and 4 d) 18 and 8

46. A radioactive substance has half life of fourmonths. Three fourth of the substance will decayin :

a) 3 months b) 4 months

c) 12 months d) 8 months

47. Which of the following undergo fission reactioneasily by slow moving neutrons ?

a) U-235, P-239

b) P-239, Th-234

c) U-238, Rn-232 d) Th-234, U-238

48. A radioactive substance has a half-life of 60minutes. During 3 hours the fraction of atom thathave decayed would be :

a) 12.5 % b) 87.5 %

c) 8.5 % d) 25.1 %

49. A radioactive reaction is 92

U238 82

Pb206. Howmany and particles are emitted ?

a) 10 , 6

b) 4 protons, 8 neutrons

c) 6 electrons, 8 protons

d) 6 , 8

50. The element used for radioactive Carbon datingfor more than 5600 years is :

a) C-14 b) U-234

c) U-238 d) Po-94

51. In the Bohr's model of the hydrogen atom, thelowest orbit corresponds to :

a) Infinite energy

b) The maximum energy

c) The minimum energy

d) Zero energy

52. According to Bohr's theory, the moment ofmomentum of an electron revolving in second orbitof Hydrogen atom will be :

a) 2 h b) h

c) h

d)

2h

53. According to Bohr's principle the relation betweenmain quantum number (n) and radius (r) of orbitis :

a) 1

rn

b) r n

c) 2r n d) 2

1r

n

54. Ionisation potential of Hydrogen atom is 13.6 eV.Hydrogen atoms in the ground state are excitedby monochromatic radiation of photon energy12.1 eV. The spectral lines emitted by Hydrogenatoms according to Bohr's theory will be :

a) one b) two

c) three d) four

55. If the half life of a radioactive substance is T,then its decay constant is given by :

a) T 1 b) 1

T2

c) eT log 2 d) elog 2T





56. At any instant the ratio of the amount of radio-active substance is 2 : 1. If their half lives berespectively 12 and 16 hours, then after two days,what will be the ratio of the substances ?

a) 1 : 1 b) 2 : 1

c) 1 : 2 d) 1 : 4

57. What percentage of radioactive substance is leftafter 5 half lives ?

a) 31 % b) 3.125 %

c) 0.3 % d) 1 %

58. 1 1 2 01 1 1 1H H H X e Energy

The emitted particle is :

a) Neutron b) Proton

c) -particle d) Neutrino

59. 23592U and 238

92U differ as :

a) 23592U has 2 protons less

b) 23892U has 3 protons more

c) 23892U has 3 neutrons more

d) None of these

60. If an electron jumps from 1st orbital to 3rd orbital,then it will :

a) absorb energy

b) release energy

c) have no gain of energy

d) show none of these

61. Fusion reactions take place at high temperaturebecause :

a) atoms are ionized at high temperature

b) molecules break up at high temperature

c) nuclei break up at high temperature

d) kinetic energy is high enough to overcomerepulsion between nuclei

62. The energy of the ground electronic state ofhydrogen atom is –13.6 eV. The energy of thefirst excited state will be :

a) – 3.4 eV b) – 6.8 eV

c) – 27.2 eV d) – 54.4 eV

63. When hydrogen atom is in its first excited level,its radius is ....... its ground state radius :

a) half b) same

c) twice d) four times

64. Which of the following is used as a moderator innuclear reactors ?

a) Uranium b) Heavy water

c) Cadmium d) Plutonium

65. A free neutron decays into a proton, an electronand :

a) a neutrino b) an anti neutrino

c) an alpha particle d) a beta particle

66. In a fission reaction,

236 117 117 92 U X Y n Q,

the binding energy per nucleon of X and Y is8.5 MeV whereas of 236U is 7.6 MeV. The totalenergy liberated will be about :

a) 200 keV b) 2 MeV

c) 200 MeV d) 2000 MeV

67. The activity of a radioactive sample is measuredas 9750 counts per minute at t = 0 and as 975counts per minute at t = 5 minutes. The decayconstant is approximately :

a) 0.230 per minute

b) 0.461 per minute

c) 0.691 per minute

d) 0.922 per minute

68. The most penetrating radiation out of the followingis :

a) X-rays b) Beta-rays

c) Alpha-particles d) Gamma-rays

69. A radioactive substance disintegrates 1

64 of initial

value in 60 seconds. The half life of this substanceis :

a) 5 s b) 10 s

c) 30 s d) 20 s

70. Half life of a radioactive substance is 140 days.Initially it is 16 g. Calculate the time for thissubstance when it reduces into 1 g :

a) 140 days b) 280 days

c) 420 days d) 560 days

71. Hydrogen atom excites energy level from funda-mental state to n = 3. Number of spectrum lines,according to Bohr, is :

a) 4 b) 3

c) 1 d) 2





72. Which one is not emitted from radioactivesubstance ?

a) electron b) proton

c) gamma rays d) helium nucleus

73. Number of spectral lines in hydrogen atom is :

a) 3 b) 6

c) 15 d) infinite

74. Atomic number of a nucleus is Z and atomic massis M. The number of neutron is :

a) M – Z b) M

c) Z d) M + Z

75. In a given nuclear reaction K is,

2He4 +

ZXA

Z + 2YA + 3 + K :

a) Electron b) Positron

c) Proton d) Neutron

76. -rays emitted from a radioactive material are :

a) electromagnetic radiations

b) electron orbiting around the nucleus

c) charged particles emitted by the nucleus

d) neutral particles

77. If half-life of a radioactive atom is 2.3 days thenits decay constant would be :

a) 0.1 b) 0.2

c) 0.3 d) 2.3

78. Rutherford's -scattering particle concludes that :

a) there is a heavy mass at centre

b) electrons are revolving around the nucleus

c) both (a) and (b)

d) none of these

79. The wavelength of Lyman series is :

a) 4

cm3 10967

b) 3

cm4 10967

c) 4 10967

cm3

d)

310967cm

4

80. In a nuclear reaction, which of the following isconserved ?

a) Atomic number

b) Mass number

c) Atomic number, Mass number and Energy

d) None

81. A radio isotope has a half life of 75 years. Thefraction of the atoms of this material that woulddecay in 150 years will be :

a) 66.6 % b) 85.5 %

c) 62.5 % d) 75 %

82. A radioactive element 90

X238 decay into 83

Y222.The number of particles emitted are :

a) 4 b) 6

c) 2 d) 1

83. The binding energy per nucleon of Deutron (1H2)

and Helium atom (2He4) is 1.1 MeV and 7 MeV

respectively. If two deutron atoms react to forma single helium atom, then the energy releasedis :

a) 13.9 MeV b) 26.9 MeV

c) 23.6 MeV d) 19.2 MeV

84. In nuclear reaction there is conservation of :

a) mass only b) energy only

c) momentum only

d) mass, energy and momentum

85. In Bohr's model, the atomic radius of the firstorbit is r

0, then the radius of the third orbit is :

a) 0r

9b) r

0

c) 9 r0

d) 3 r0

86. The wavelength of the energy emitted whenelectron come from fourth orbit to second orbitin hydrogen is 20,397 cm–1. The wavelength ofenergy for the same transition in He+ is :

a) 5,099 cm–1 b) 20,497 cm–1

c) 40,994 cm–1 d) 81,988 cm–1

87. The absorption transitions between the first andthe fourth energy states of Hydrogen atom are3. The emission transitions between these stateswill be :

a) 3 b) 4

c) 5 d) 6

88. In Nuclear Fission 0.1 % mass is converted intoenergy. The energy released by the fission of lkgmass will be :

a) 9 1016 J b) 9 1019 J

c) 9 1013 J d) 9 1017 J

89. The specific charge of an electron is :

a) 0.6 10–19 coulomb

b) 4.8 10–10 stat coulomb

c) 1.76 1011 coulomb/kg

d) 1.76 10–11 coulomb/kg





90. The half-life (T) and the disintegration constant() of a radioactive substance are related as :

a) T = 1 b) T = 0.693

c) T

0.693

d) 0.693T

91. The half-life period of a radioactive substance is5 min. The amount of substance decayed in20 min will be :

a) 93.75 % b) 75 %

c) 25 % d) 6.25 %

92. The Rydberg constant R for hydrogen is :

a)2 2

20

1 2 meR

4 ch

b)2 4

20

1 2 meR

4 ch

c)

22 4

2 20

1 2 meR

4 c h

d)

22 4

20

1 2 meR

4 ch

93. In 88

Ra226 nucleus there are :

a) 138 protons and 88 neutrons

b) 138 neutrons and 88 protons

c) 226 protons and 88 electrons

d) 226 neutrons and 138 electrons

94. In X-ray tube the accelerating potential appliedat the anode is V

a volts. The minimum wavelength

of the emitted X-rays will be :

a) aeV

hb)

a

h

eV

c) aeV

chd)

a

hc

eV

95. In the Bohr model of a hydrogen atom, thecentripetal force is furnished by the coulombattraction between the proton and the electron.If a

0 is the radius of the ground state orbit, m is

the mass and e is the charge on the electron and

0 is the vacuum permittivity, the speed of the

electron is :

a) 0 b) 0 0

e

a m

c) 0 0

e

4 a md)

0 04 a m

e

96. Half-lives of two radioactive substances A andB are respectively 20 minutes and 40 minutes.Initially the sample of A and B have equal numberof nuclei. After 80 minutes the ratio of remainingnumber of A and B nuclei is :

a) 1 : 16 b) 4 : 1

c) 1 : 4 d) 1 : 1

97. Atomic weight of Boron is 10.81 and it has two

isotopes 10 5 B & 11

5 B . Then the ratio of 10 11 5 5B : B

in nature would be :

a) 19 : 81 b) 10 : 11

c) 15 : 16 d) 81 : 19

98. A nucleus nXm emits one and -particles. The

resulting nucleus is :

a) m 4n X b) m 4

n 2 Y

c) m 4n 4 Z d) m 4

n 1 Z

99. Complete the equation for the following fissionprocess :

235 1 9092 0 38U n Sr .....

a) 143 154 0X 3 n b) 145

54 Xe

c) 14254 Xe d) 142 1

54 0Xe n

100. What is the stopping potential, when the metalwith work function 0.6 eV is illuminated with thelight of 2 eV ?

a) 2.6 V b) 3.6 V

c) 0.8 V d) 1.4 V

101. Radius of first Bohr orbit is 'r'. What is the radiusof 2nd Bohr orbit ?

a) 4 r b) 2 r

c) 8 r d) 2 2 r

102. Minimum excitation potential of Bohr's first orbitin Hydrogen atom is :

a) 13.6 V b) 3.4 V

c) 10.2 V d) 3.6 V





103. An artificial radioactive decay series begins with

unstable 241 94 Pu . The stable nuclide obtained after

eight -decays and five -decays is :

a) 209 83 Bi b) 209

82 Pb

c) 205 82 TI d) 201

82 Hg

104. Which of the following radiation series is foundin the visible region ?

a) Lyman b) Paschen

c) Pfund d) Balmer

105. When a -particle is emitted from a nucleus, theeffect on its neutron-proton ratio is :

a) increased b) decreased

c) remains same d) first 'A' then 'B'

106. When a slow neutron goes sufficiently close to aU235 nucleus then the process that takes placeis :

a) fission of U235

b) fusion of neutron

c) fusion of U235

d) first 'A' then 'B'

107. An electron starts from rest in an electric fieldand acquires a speed u in reaching a point A.The potential difference between the starting pointand the point A is V

A:

a) 2Au V b) Au V

c) Au V d) 2/ 3Au V

108. The binding energy per nucleon for deutron 21 H

and helium 42 He are 1.1 MeV and 7.0 MeV

respectively. The energy released when twodeutrons fuse to form a helium nucleus is :

a) 2.2 MeV b) 28 MeV

c) 23.6 MeV d) 30.2 MeV

109. If the radioctive decay constant of radium is1.07 10–4 per year, then its half-life period isapprox. equal to :

a) 8,900 years b) 7,000 years

c) 6,476 years d) 2,520 years

110. When a proton is accelerated through 1 V, thenits kinetic energy will be :

a) 1840 eV b) 13.6 eV

c) 1 eV d) 0.54 eV

111. Alpha-particles are :

a) protons

b) positron

c) neutrally charged

d) ionized helium atoms

112. Which of the following is deflected by electricfield ?

a) -particles b) -rays

c) X-rays d) Neutrons

113. Nucleus of an atom whose atomic mass is 24consists of :

a) 11 electrons, 11 protons and 13 neutrons

b) 11 electrons, 13 protons and 11 neutrons

c) 11 protons and 13 neutrons

d) 11 protons and 13 electrons

114. Radius of 42 He nucleus is 3 fermi. The radius of

206 82 Pb nucleus will be :

a) 5 fermi b) 6 fermi

c) 7 fermi d) 8 fermi

115. Average binding energy per nucleon for a heavynucleus is :

a) 8 10–3 eV b) 0.5 eV

c) 7.6 MeV d) 13.5 eV

116. Energy required to ionise a hydrogen atom fromits ground state is :

a) – 13.6 eV b) 13.6 eV

c) – 10.2 eV d) 10.2 eV

117. 1 million electron volt is :

a) 1.6 10–19 J b) 1.6 10–16 J

c) 1.6 10–13 J d) 1.6 10–11 J

118. The 1st excitation energy of hydrogen atoms is :

a) 9.23 10–9 b) 9.23 10–15

c) 9.23 10–24 d) none

119. An -particle and a proton are accelerated atsame potential difference from rest. Find the ratioof their final velocity :

a) 2 :1 b) 1 : 1

c) 1: 2 d) 1 : 2

120. The density of nucleus is of order of :

a) 103 kg/m3 b) 1012 kg/m3

c) 1017 kg/m3 d) 1024 kg/m3





121. Beams of electrons and protons are made to movein a uniform electric field with same K.E. at 900

to field lines, then :

a) electron trajectory is less curved

b) proton trajectory is less curved

c) both trajectories are equally curved

d) both trajectories are undeflected

122. Shortest wavelength of Lymen series is 911 Å,then that of Paschen series is :

a) 4600 Å b) 5500 Å

c) 7300 Å d) 8200 Å

123. In a breeder reactor, useful fuel obtained fromU238 is :

a) Pu239 b) U235

c) Th235 d) Ac233

124. The rate of disintegration is 1017 atoms/second &half-life is 1445 years. Then number of atoms is :

a) 1.44 1017 b) 1.4 1017

c) 6.57 1027 d) none of these

125. The frequencies of X-rays, -rays and ultravioletrays are respectively a, b and c. Then :

a) a > b, b > c b) a < b, b > c

c) a < b, b < c d) a > b, b < c

126. Who indirectly determined the mass of theelectron by measuring the charge of the electron ?

a) Rutherford b) Millikan

c) Einstein d) Thomson

127. When an electron jumps from the fourth orbit tothe second orbit, one gets the :

a) second line of Paschen series

b) second line of Lyman series

c) second line of Balmer series

d) first line of Pfund series

128. Which of the following transitions in a hydrogenatom emits the photon of highest frequency ?

a) n = 2 to n = 6 b) n = 2 to n = I

c) n = 6 to n = 2 d) n = 1 to n = 2

129. The decay constant () and the half-life (T) of aradioactive isotope are related as :

a) elog 2

T b)

e

1

(log 2)T

c) e

T

log 2 d)

2

T

130. In the following nuclear reaction,

11 116 5C B X

what does X stand for ?

a) A proton b) A neutron

c) A neutrino d) An electron

131. It is possible to understand nuclear fission on thebasis of the :

a) liquid drop model of nucleus

b) proton-proton cycle

c) meson theory of the nuclear forces

d) independent particle model of the nucleus

132. Atomic hydrogen has a life period of :

a) one day

b) one minute

c) a fraction of a second

d) one hour

133. Electron microscope was invented by :

a) Zemicke

b) Lehmann

c) Knoll and Ruska

d) Janssen and Janssen

134. Electron microscope has a high resolution power.This is due to :

a) Electromagnetic lenses

b) Low wavelength of light source used

c) Very low wavelength of electron beam

d) High numerical aperture of glass lenses used

135. Maximum magnification possible by an electronmicroscope is :

a) 2000 b) 200

c) 200000 d) 20000

136. In electron microscope, higher magnification isdue to the use of :

a) Magnetic system

b) Achromatic lenses

c) High velocity electrons

d) Higher wavelengths of light

137. Electron microscope has more advantages thanlight microscope because it :

a) Uses vacuum

b) Requires no light

c) Gives depth focus

d) Has higher magnification





138. In electron microscope, high speed electrons areused having the wavelength of about :

a) 0.01 Å b) 0.05 Å

c) 0.15 Å d) 0.25 Å

139. The kinetic energy of an electron which is accele-rated through a potential of 100 volts is :

a) 1.602 10–17 joules

b) 418.6 calories

c) 1.16 104 K

d) 6.626 10–34 watt-second

140. If elements with principal quantum n > 4 was notfound in nature, possible number of elementswould have been :

a) 60 b) 32

c) 16 d) 4

141. When green light is incident on a certain metalsurface electrons are emitted, but no electronsare emitted by yellow light. If red light is incidenton the same metal surface, then :

a) more energetic electrons will be emitted

b) less energetic electrons will be emitted

c) emission of electrons will depend on theintensity of light

d) no electrons will be emitted

142. Particle nature & wave nature of electromagneticwaves and electrons can be shown by :

a) electrons have small mass, deflected by themetal sheet

b) X-ray is diffracted, reflected by thick metalsheet

c) light is refracted and diffracted

d) photoelectricity and electron microscopy

143. A ball of mass m travelling with a certain velocityhas a kinetic energy K. Then the de Brogliewavelength associated with the ball is :

a)h

2 Kmb)

h

2 Km

c)h

2 Km

d) It is only associated with atomic particles

144. Source of Sun's energy is :

a) burning of hydrogen

b) fission reactions involving hydrogen

c) fusion reactions involving hydrogen

d) some other source

145. Recently some particles have been discoveredtravelling with more than the velocity of light, theyare :

a) electrons b) neutrons

c) nucleons d) tachyons

146. The population inversion necessary for laser actionused in solid state lasers is :

a) electrical discharge

b) inelastic atom-atom collision

c) direct conversion

d) optical pumping

147. If particles are moving with same velocity, thenmaximum de-Broglie wavelength is for :

a) proton b) -particle

c) neutron d) -particle

148. The de Broglie wavelength of an electron in thefirst Bohr orbit is :

a) equal to half the circumference of the firstorbit

b) equal to one fourth the circumference of thefirst orbit

c) equal to the circumference of the first orbit

d) equal to twice the circumference of the firstorbit

149. A laser beam is used for carrying out surgerybecause it :

a) is highly monochromatic

b) is highly coherent

c) is highly directional

d) can be sharply focussed

150. A particle of mass M at rest decays into twomasses m

1 and m

2 with non zero velocities. The

ratio of de-Broglie wavelengths of the particles

1

2

is :

a) 1

2

m

mb) 1 : 1

c) 2

1

m

m d) 1

2

m

m





151. The de-Broglie wavelength of a particle moving

with a velocity 2.25 108 m/s is equal to thewavelength of a photon. The ratio of kineticenergy of the particle to the energy of the photonis :

[Velocity of light is 3 108 m/s]

a) 1

8b)

3

8

c) 5

8d)

7

8

152. For a given kinetic energy which of the followinghas the smallest de-Broglie wavelength ?


c) Neutron d) Deuteron

e) -particle

153. We wish to see inside an atom. Assuming theatom to have a diameter of 100 pm, this meansthat one must be able to resolve a width of say10 pm. If an electron microscope is used, theminimum electron energy required is about :

a) 1.5 keV b) 15 keV

c) 150 keV d) 1.5 MeV

154. The binding energy per nucleon for the parent

nucleus is E1 and that for the daughter nuclei is

E2. Then :

a) E2 = 2 E

1b) E

1 > E

2

c) E2 > E

1d) E

1 = 2 E

2

155. The speed of daughter nuclei is :

a) m

cM m

b) 2 m

cM

c) m

cM

d)

mc

M m

156. A radioactive nucleus (initial mass number A

and atomic number Z) emits 3 -particles and2 positrons. The ratio of number of neutrons tothat of protons in the final nucleus will be :

a) A Z 8

Z 4

b) A Z 4

Z 8

c) A Z 12

Z 4

d) A Z 4

Z 2

157. The wavelength of the first line of Lyman seriesfor hydrogen atom is equal to that to the secondline of Balmer series for a hydrogen like ion. Theatomic number Z of hydrogen like ion is :

a) 3 b) 4

c) 1 d) 2

158. The half life of a radioactive isotope X is 50 years.It decays to another element Y which is stable.The two elements X and Y were found to be inthe ratio of 1 : 15 in a sample of a given rock.The age of the rock was estimated to be :

a) 150 years b) 200 years

c) 250 years d) 100 years

159. The power obtained in a reactor using U235

distintegration is 1000 kW. The mass decay ofU235 per hour is :

a) 10 microgram b) 20 microgram

c) 40 microgram d) 1 microgram

160. A radioactive nucleus of mass M emits a photonof frequency and the nucleus recoils. The recoilenergy will be :

a) 2Mc h b) 2 2

2

h

2Mc

c) zero d) h

161. A nucleus mn X emits one -particle and two

-particles. The resulting nucleus is :

a) m 6n 4 Z b) m 6

n Z

c) m 4 n X d) m 4

n 2 Y

162. Fusion reaction takes place at high temperaturebecause :

a) nuclei break up at high temperature

b) atoms get ionised at high temperature

c) kinetic energy is high enough to overcome thecoulomb repulsion between nuclei

d) molecules break up at high temperature

163. Electrons used in an electron microscope areaccelerated by a voltage of 25 kV. If the voltageis increased to 100 kV then the de-Brogliewavelength associated with the electrons would :

a) increase by 2 times

b) decrease by 2 times

c) decrease by 4 times

d) increase by 4 times





164. The half life of a radioactive substance is 20minutes. The approximate time interval (t

2 – t

1)

between the time t2 when

2

3 of it has decayed

and time t1 when

1

3 of it had decayed is :

a) 28 min b) 7 min

c) 14 min d) 20 min

165. Energy required for the electron excitation in Li++

from the first to the third Bohr orbit is :

a) 122.4 eV b) 12.1 eV

d) 108.8 eV c) 36.3 eV

166. If the nuclear radius of 27Al is 3.6 fermi, theapproximate nuclear radius of 64Cu in fermi is :

a) 1.2 b) 4.8

c) 3.6 d) 2.4

167. A mixture consists of two radioactive materialsA

1 & A

2 with half lives of 20 s & 10 s respecti-

vely. Initially the mixture has 40 g of A1 and 160 g

of A2. The amount of the two in the mixture will

become equal after :

a) 80 s b) 20 s

c) 40 s d) 60 s

168. Electron in hydrogen atom first jumps from thirdexcited state to second excited state and thenfrom second excited to the firstexcited state. Theratio of the wavelength

1 :

2 emitted in the two

cases is :

a) 27

20b)

27

5

c) 20

7d)

7

5

169. An -particle moves in a circular path of radius0.83 cm in the presence of a magnetic field of0.25 Wb/m2. The de-Broglie wavelength asso-ciated with the particle will be :

a) 0.1 Å b) 10 Å

c) 0.01 Å d) 1 Å

170. Monochromatic radiation emitted when electronon hydrogen atom jumps from first excited to theground state irradiates a photosensitive material.The stopping potential is measured to be 3.57 V.The threshold frequency of the material is :

a) 5 1015 Hz b) 1.6 1015 Hz

c) 2.5 1015 Hz d) 4 1015 HZ

171. An electron of a stationary hydrogen atom passesfrom the fifth energy level to the ground level.The velocity that the atom is required as a resultof photon emission will be :

a) 25hR

24mb)

25m

24hR

c) 24m

25hRd)

24hR

25m

172. Hydrogen atom is excited from ground state toanother state with principal quantum number equalto 4. Then the number of spectral lines in theemission spectra will be :

a) 6 b) 2

c) 3 d) 5

173. This question has Statement 1 and Statement 2.Of the four choices given after the Statements,choose the one that best describes the twoStatement.

Statement 1 : Davisson-Germer experimentestablished the wave nature of electrons.

Statement 2 : If electrons have wave nature,they can interfere and show diffraction.

a) Statement 1 is true, Statement 2 is true,Statement 2 is not correct explanation ofStatement 1

b) Statement 1 is false, Statement 2 is true

c) Statement 1 is true, Statement 2 is false

d) Statement 1 is true, Statement 2 is true,Statement 2 is the correct explanation ofStatement 1

174. A diatomic molecule is made of two masses m1

and m2 which are separated by a distance r. If

we calculate its rotational energy by applyingBohr's rule of angular momentum quantization itsenergy will be given by :

[n is an integer]

a)

2 21 2

21 2

(m m )n h

2m m r

b)

2 2 21 2

2 2 21 2

(m m ) n h

2m m r

c)

2 2

21 2

n h

2(m m )r d)

2 2

21 2

2n h

(m m )r





175. Assume that a neutron breaks into a proton andan electron. The energy released during thisprocess is :

(Mass of neutron = 1.6725 10–27 kg

Mass of proton = 1.6725 10–27 kg

Mass of electron = 9 10–31 kg)

a) 5.4 MeV b) 0.73 MeV

c) 7.10 MeV d) 6.30 MeV

176. The anode voltage of a photocell is kept fixed.The wavelength of the light falling on the cathodeis gradually changed. The plate current I of thephotocell varies as follows :

a) b)

c) d)

177. In a hydrogen like atom electron makes transitionfrom an energy level with quantum number n toan other with quantum number (n – 1). If n >> 1,the frequency of radiation emitted is proportionalto :

a) 3

1

nb)

1

n

c) 2

1

nd) 3/ 2

1

n

178. A freshly prepared sample of a radioisotope ofhalf-life 1386 s has activity 103 disintegrations persecond. Given that Ln 2 = 0.693, the fraction ofthe initial number of nuclei (expressed in nearestinteger percentage) that will decay in the first80 s after preparation of the sample is :

Paragraph for Questions 761 and 762

The mass of the nucleus AZ X is less than the sum

of the masses of (A – Z) number of neutrons andZ number of protons in the nucleus. The energyequivalent to the corresponding mass differenceis known as the binding energy of the nucleus.

A heavy nucleus of mass M can break into twolight nuclei of masses m

1 & m

2 only if (m

1 + m

2)

< M. Also two light nuclei of masses m3 and m

4

can undergo complete fusion and form a heavynucleus of mass M' only if (m

3 + m

4) > M'. The

masses of some neutral atoms are given in thetable below :

11H 1.007825 u 2

1 H 2.014102 u

31 H 3.016050 u 4

2 He 4.002603 u

63 Li 6.015123 u 7

3 Li 7.016004 u

7030 Zn 69.925325 u 82

33Se 81.916709 u

152 64 Gd 151.919803 u 206

82 Gb 205.974455 u

152 83 Bi 208.980388 u 210

84 Po 209.982876 u

[1 u = 932 MeV/c2]

179. The kinetic energy (in keV) of the alpha particle,

when the nucleus 210 84 Po at rest undergoes alpha

decay, is :

a) 5319

b) 5422

c) 5707

d) 5818

180. The correct statement is :

a) The nucleus 63 Li can emit an alpha particle

b) The nucleus 210 84 Po can emit a proton

c) Deutron & alpha particle can undergo completefusion

d) The nuclei 7030 Zn & 82

34Se can undergo complete

fusion

181. Match List-I of the nuclear process with List-IIcontaining parent nucleus and one of the endproducts of each process and then select thecorrect answer using the codes given below thelists :

List-I List-II

P. Alpha decay 1. 15 15 8 7O N ....

Q. + decay 2. 238 234 92 90U Th ....

R. Fission 3. 185 184 83 82Bi Pb ....

S. Proton emission 4. 239 140 94 57Pu La ....





Codes :

P Q R S

a) 4 2 1 3

b) 1 3 2 4

c) 2 1 4 3

d) 4 3 2 1

182. The radius of the orbit of an electron in a Hydrogenlike atom is 4.5 a

0, where a

0 is the Bohr radius.

Its orbital angular momentum is 3h

2. It is given

that h is Planck constant & R is Rydberg constant.The possible wavelength (s), when the atom de-excites, is (are) :

a) 9

32 Rb)

9

16 R

c) 9

5 Rd)

4

3 R

183. Ratio of longest wavelengths corresponding toLyman and Balmer series in hydrogen spectrumis :

a) 7

29b)

9

31

c) 5

27d)

3

23

184. A certain mass of hydrogen is changed to Heliumby the process of fusion. The mass defect in fusionreaction is 0.02866 , The energy liberated per uis :

[given ; 1 = 931 MeV]

a) 6.675 MeV b) 13.35 MeV

c) 2.67 MeV d) 26.7 MeV

185. The half life of a radioactive isotope 'X' is 20years. It decays to another element 'Y' which isstable. The two elements 'X' and 'Y' were foundto be in the ratio 1 : 7 in a sample of a given rock.The age of the rock is estimated to be :

a) 80 years b) 100 years

c) 40 years d) 60 years

186. The wavelength e of an electron and

p of a

photon of same energy are related as :

a) P

e

1

b) P e

c) 2P e d) P e

187. If the kinetic energy of the particle is increasedto 16 times its previous value, the percentagechange in the de-Broglie wavelength of theparticle is :

a) 50 b) 25

c) 75 d) 60

188. Hydrogen atom in ground state is excited by amonochromatic radiation of = 975 Å. Numberof spectral lines in the resulting spectrum emittedwill be :

a) 10 b) 3

c) 2 d) 6

189. The Binding energy per nucleon of 73 Li and 4

2 He

nuclei are 5.60 MeV and 7.06 MeV, respectively.In the nuclear reaction,

7 1 4 43 1 2 2Li H He He Q

the value of energy Q released is :

a) 17.3 MeV b) 19.6 MeV

c) – 2.4 MeV d) 8.4 MeV

190. A radio isotope 'X' with a half life 1.4 109 yearsdecays to 'Y' which is stable. A sample of therock from a cave was found to contain 'X' and'Y' in ratio 1 : 7. The age of the rock is :

a) 8.40 109 years

b) 1.96 109 years

c) 3.92 109 years

d) 4.20 109 years

191. The radiation corresponding to 3 2 transitionof hydrogen atom falls on a metal surface toproduce photoelectrons. These electrons aremade to enter a magnetic field of 3 10–4 T. Ifthe radius of the largest circular path followed bythese electrons is 10.0 mm, the work function ofthe metal is close to :

a) 1.8 eV b) 1.1 eV

c) 0.8 eV d) 1.6 eV

192. Hydrogen (1H1), Deuterium (

1H2), singly ionised

Helium (2He4)1 and doubly ionised lithium (

3Li6)11

all have one electron around the nucleus. Consideran electron transition from n = 2 to n = 1. If thewave lengths of emitted radiation are

1,

2,

3

and 4 respectively then approximately which one

of the following is correct ?





a) 4 1 = 2

2 = 2

3 =

4

b) 1 = 2

2 = 2

3 =

4

c) 1 =

2 = 4

3 = 9

4

d) 1 = 2

2 = 3

3 = 4

4

193. If Cu

is the wavelength of KX-ray line of copper

(atomic number 29) and Mo

is the wave-lengthof the K

X-ray line of molybdenum (atomic

number 42), then the ratio Cu

Mo

is close to :

a) 1.99 b) 2.14

c) 0.50 d) 0.48

194. If radius of the 2713 Al nucleus is taken to be R

Al,

then the radius of 125 53 Te nucleus is nearly :

a) Al

3R

5b)

1/ 3

Al

13R

53

c) 1/ 3

Al

53R

13

d) Al

5R

3

195. Consider 3rd orbit of He+ (Helium), using non-relativistic approach, the speed of electron in thisorbit will be [given K = 9 109 constant, Z = 2and h (Plack's Constant) = 6.6 10–34 J s]

a) 0.73 106 m/s b) 3.0 108 m/s

c) 2.92 106 m/s d) 1.46 106 m/s

196. As an electron makes a transition from an excitedstate to the ground state of a hydrogen like atom/ion :

a) kinetic energy decreases, potential energyincreases but total energy remains same

b) kinetic energy and total energy decrease butpotential energy increases

c) its kinetic energy increases but potential energyand total energy decrease

d) kinetic energy, potential energy and total energydecrease

197. In the spectrum of hydrogen, the ratio of thelongest wavelength in the Lyman series to thelongest wavelength in the Balmer series is :

a) 27

5b)

5

27

c) 4

9d)

9

4

Brain Teasers

1. The ratio of the energy of the orbital electron infirst orbit to that in the second orbit is :

a) 2 b) 4

c) 8 d) 16

2. The ratio of the angular momentum of the orbitalelectron in the first orbit to that in the secondorbit is :

a) 2 b) 1

c) 0.5 d) none of the above

3. The ratio of the radius of the first orbit to that ofthe second orbit of the orbital electron is :

a) 4 b) 2

c) 0.5 d) 0·25

4. The ratio of the velocity of the electron in thefirst orbit and the second orbit is :

a) 8 b) 4

c) 2 d) none of the above

5. If the size of atom is enlarged such that the nucleushas a size of small seed (1 mm diameter) thenthe electron orbits will have the size of :

a) a big seed (1 cm diameter)

b) a cricket ball (10 cm diameter)

c) a cricket playground (100 m diameter)

d) the earth

6. Which of the following transitions in hydrogengives an absorption line of higher frequency ?

a) n = 1 to n = 3 b) n = 3 to n = 1

c) n = 1 to n = 2 d) n = 2 to n = 1

7. Which of the following transitions in hydrogenatom gives the emission line of highest frequepcy?

a) n = 8 to n = 3

b) n = 7 to n = 3

c) n = 7 to n = 2

d) n = 5 to n = 1

8. According to Bohr's theory the radius of electronin an orbit described by principal quantum numbern and atomic number Z is proportional to :

a) 2 2Z n b) 2

2

Z

n

c)

2Z

n

d)

2n

Z





9. The distance of closest approach of an -particlefired towards a nucleus with momentum p is r.What will be the distance of closest approachwhen the momentum of the -particle is 2p ?

a) 2 r b) 4 r

c) r

2d)

r

4

10. The area of the electron orbit for the ground stateof hydrogen atom is A. What will be the area ofthe electron orbit corresponding to the first excitedstate ?

a) 4 A b) 8 A

c) 16 A d) 32 A

11. What will be the ratio of the time periods ofelectrons in the ground and first excited states ofthe hydrogen atom :

a) 1 / 2 b) 1 / 4

c) 1 / 8 d) 1 / 16

12. First excitation potential of an atom is E. Whatwill be the ionization potential ?

a) E b) 2E

3

c) 4E

4d)

E

3

13. What is the ionization energy of 10 times ionisedsodium atom ?

a) 13.6 eV b) 13.6 11 eV

c) 13.6 (11)2 eV d) 13.6

eV11

14. The orbital velocity of the electron in the groundstate of hydrogen atom is . What will be itsorbital velocity when excited to the energy state–1.51 eV ?

a) 9

b)

4

c) 3

d)

2

15. The kinetic and potential energies of the orbitalelectron in the hydrogen atom without taking theirsign into account are E

k and E

p. Which of the

following gives the value of total energy withproper sign ?

a) p kE E b) k pE E

c) p k(E E )

2

d)

k p(E E )

2

16. The ionisation energy of hydrogen atom is 13.6 eV.Hydrogen atoms in the ground state are excitedby monochromatic radiation of photon energy12.1 eV. The spectral lines emitted by hydrogenatom according to Bohr's theory will be :

a) one b) two

c) three d) four

17. If the ionisation energy for hydrogen atom is13.6 eV. The energy required to excite it fromthe ground state to the next higher state is nearly :

a) 3.4 eV b) 10.2 eV

c) 12.1 eV d) 1.5 eV

18. How many different wavelengths may be observedin the spectrum of the particular sample if theatoms are excited to states with principle quantumnumber 10 ?

a) 9 b) 44

c) 45 d) 10

19. The ionisation energy of 10 times ionised sodiumatom is :

a) 13.6 eV b) 13.6 11 eV

c) 13.6

11d) 13.6 (11)2 eV

20. For the first member of Balmer series of hydrogenspectrum, the wavelength is . What is thewavelength of the second member ?

a) 5

30 b)

3

16

c) 4

9 d)

20

27

21. For the orbital electron Up is the potential energy

and Uk is the kinetic energy. Which of the following

relation is correct ?

a) 2 Uk = – U

pb) U

k = – U

p

c) Uk = – 2 U

pd) none of the above

22. Which of the following transitions of the hydrogenatom gives the absorption line of largest frequency?

a) n1 = 1 and n

2 = 3 b) n

1 = 2 and n

2 = 3

c) n1 = 1 and n

2 = 4 d) n

1 = 2 and n

2 = 4





23. If the elements with principal quantum numbern > 5 were not allowed in nature, what would havebeen the total number of elements in nature ?

a) 110 b) 60

c) 50 d) 10

24. What is the dimensional formula of the Rydberg'sconstant ?

a) MLT–1 b) M0LT–1

c) M0L–1T0 d) ML–1T0

25. Which of the following transitions in the hydrogenatom gives the emission line of largest wave-length ?

a) n = 8 to n = 3

b) n = 7 to n = 3

c) n = 7 to n = 2

d) n = 5 to n = 1

26. What is the ratio of the Rydberg constant forhelium to hydrogen atom ?

a) 4 b) 2

c) 1

2d)

1

4

27. Ionisation energy for hydrogen atom in the groundstate is E. What is the ionisation energy of Li++

atom in the 2nd excited state ?

a) E b) 3 E

c) 6 E d) 9 E

28. As the electron in Bohr orbit of hydrogen jumpsfrom n = 2 orbit to n = 1 orbit, the potential energyU

p and the kinetic energy U

k change as follows :

a) Uk = 2 times, U

p = 2 times

b) Uk = 4 times, U

p = 4 times

c) Uk = 4 times, U

n = 2 times

b) Uk = 2 times, U

p = 4 times

29. A spectral line is produced by transition from n = 4to n = 1 orbits. In which of the following casesthe wavelength will be the shortest ?

a) Helium atom

b) Singly ionised helium

c) Deuterium atom

d) 10 times ionised sodium atom

30. In a hydrogen atom, an electron jumps from thestate n to n – 1 where n >> 1. The frequency ofthe emitted radiation is proportional to :

a) n0 b) n–1

c) n–2 d) n–3

31. In terms of the Rydberg's constant (R), what isthe minimum value of the wavelength in theLyman series ?

a) 1

R16

b) 1

R8

c) 1

R4

d) 1

R

32. If the electron in hydrogen atom jumps from thirdorbit to second orbit, the wavelength of theemitted radiation is given by :

a) 36

5R b)

5R

36

c) 5

R d)

R

6

33. A gamma ray photon creates an electron positronpair. If the rest mass energy of electron is0.5 MeV and the total kinetic energy of theelectron positron pair is 0.78 MeV, the energy ofgamma ray photon must be :

a) 0.78 MeV b) 1.78 MeV

c) 1.28 MeV d) 0.28 MeV

34. A neutron strikes 5B10 nucleus with the sub-

sequent emission of -particles. The Z and A forthe remaining nucleus are :

a) 3, 6 b) 4, 6

c) 7, 4 d) 6, 3

35. Suppose the speed of light were half of thepresent value, the amount of energy released inthe atomic bomb explosion will be decreased bya fraction :

a) 1

4b)

1

2

c) 3

4d)

3

8

36. Which of the following is applicable to 1H1,

1H2,

1H3 ?

a) all of them are stable isotopes

b) all of them are unstable isotopes

c)1H3 decays to

1H2

d)1H3 decays to

2He3





37. The ratio of the radius of the -particle to that ofthe sulphur nucleus is :

a) 1

8b)

1

4

c) 1

2d) 1

38. After 2 hours 1

16th of the initial amount of a

certain radioactive isotope remains undecayed.The half life of the isotope is :

a) 15 min b) 30 min

c) 45 min d) 60 min

39. In the nuclear reaction, given by,

4 14 p 12 7 q 1He N X H

The nucleus X is :

a) nitrogen of mass 16

b) nitrogen of mass 17

c) oxygen of mass 16

d) oxygen of mass 17

40. A negative -meson at rest can decay as,

0

Then the energy of :

a) is variable b) is a fixed quantity

c) is zero d) is equal to mc2

41. Of the three isotopes of hydrogen 1H1,

1H2 and

1H3 :

a) all are stable

b) two are unstable

c)1H3 decays to

1H2

d)1H3 decays to

2H3

42. For an atomic reactor being critical the ratio (r)of the average number of neutrons produced andused in chain reaction :

a) is less than one

b) is equal to one

c) is greater than one

d) depends on the mass of fissionable material

43. A nuclear holocaust of fusion bomb will makeweather forever :

a) hot b) rainy

c) cold d) cannot be decided

44. The mass number of a nucleus is :

a) always less than its atomic number

b) always more than its atomic number

c) sometimes equal to its atomic number

d) sometimes more than and sometimes equal toits atomic number

45. How does the binding energy per nucleon varywith the increase in the number of nucleons ?

a) Increases continuously with mass number

b) Decreases continuously with mass number

c) Remains constant with mass number

d) First increases and then decreases withincrease of mass number

46. If a proton is completely converted into energy,the amount of energy produced will be :

a) 6.61 1034 eV b) 6.02 1023 eV

c) 9 1020 eV d) 931 106 eV

47.Volume of the atom

Volume of the nucleus

a) 105 b) 1010

c) 1015 d) 1020

48. If the nuclei of masses x and y are fused to forma nucleus of mass m and some energy is released,then :

a) x + y = m b) x + y < m

c) x + y > m d) x – y = m

49. Nuclear fission experiments how that theneutrons split the Uranium nuclei into twofragments of about same size. This process isaccompanied by the emission of several :

a) protons and positrons

b) -particles

c) neutrons

d) protons and -particles

50. The mass of an -particle is :

a) less than the sum of masses of two protonsand two neutrons

b) equal to mass of four protons

c) equal to mass of four neutrons

d) equal to sum of masses of two protons andtwo neutrons

51. In an atom, the number of protons is 6 and numberof neutrons is 7. The number of electrons is :

a) 6 b) 7

c) 1 d) 13





52. An element X decays first by positron emissionand then two -particles are emitted in successiveradioactive decay. If the product nucleus has amass number 229 and atomic number 89, the massnumber and atomic number of element X are :

a) 237, 93 b) 237, 94

c) 238, 93 d) 237, 92

53. When a radioactive isotope 88

Ra228 decays inseries by the emission of three -particles and a-particle the isotope finally formed is :

a) 84

X220 b) 86

X222

c) 83

X216 d) 83

X215

54. An uranium nucleus (atomic number 92 and massnumber 238) emits -particle and the resultantnucleus emits a -particle. What is the massnumber (A) and atomic number (Z) of the finalproduct ?

a) A = 238, Z = 91 b) A = 234, Z = 91

c) A = 234, Z = 90 d) A = 238, Z = 90

55. A certain radioactive substance has a half life of5 years. Thus for a nucleus in a sample of theelement, probability of decay in 10 years is :

a) 50 % b) 75 %

c) 60 % d) 100 %

56. A radioactive substance decays as follows :

X Y Z M F

If atomic and mass numbers of F are 69 and 172respectively, what are their values for X ?

a) Z = 72, A = 180

b) Z = 71, A = 178

c) Z = 71, A = 176

d) Z = 70, A = 176

57. A radioactive source has a half life of 3 hours. Afreshly prepared sample of the same emitsradiation 16 times the permissible safe value. Theminimum time after which it would be possible towork safely with the source is :



58. After one -decay & two consecutive -decays,the daughter nucleus is an isotope of the :

a) same element

b) element with atomic number less by two

c) element with atomic number more by two


59. The half life period of a sample is 100 seconds.If we take 40 gram of the radioactive sample,then after 400 seconds how much substance willbe left undecayed ?

a) 10 gram b) 5 gram

c) 2.5 gram d) 1.25 gram

60. In the reaction given below what is the sequenceof decay ?

A A A 4 A 4Z Z 1 Z 1 Z 1X Y K K

a) , , b) , ,

c) , , d) , ,

61. If 10% of a radioactive substance decays in 5days then the amount of the substance left after25 days will be nearly :

a) 40 % b) 50 %

c) 60 % d) 70 %

62. The nuclear reaction 48

Cd107 47

Ag107 canoccur with the :

a) electron capture b) positron capture

c) proton emission d) -particle emission

63. In Rutherford's -scattering experiment, the ratioof the number of -particles scattered through600 and 1200 is :

a) 1 b) 4

c) 9 d) 16

64. In a hydrogen like atom the energy required toexcite the electron from 2nd to 3rd orbit is 47.2 eV.What is the atomic number of the atom ?

a) 2 b) 3

c) 4 d) 5

65. The energy difference between the first two levelsof hydrogen atom is 10.2 eV. For another elementof atomic number 10 and mass number 20, thiswill be :

a) 1020 eV b) 2040 eV

c) 0.51 eV d) 0.102 eV

66. An alpha particle of 10 MeV collides head onwith a nucleus (Z = 30) and is deflected back.Then the minimum distance of approach betweenthe centres of the two is :

a) 8.6 10–15 cm

b) 8.6 10–15 metre

c) 4.3 10–15 metre

d) 4.3 10–15 cm





67. An electron jumps from the 4th orbit to 2nd orbitof hydrogen atom. Given the Rydberg's constantR = 105 cm–1, the frequency in hertz of the emittedradiation will be :

a) 53

1016

b) 153

1016

c) 159

1016

d) 153

104

68. If the wavelength of the rust line of the Lymanseries for the hydrogen atom is 1210 Å, then thewavelength of the rust line of the Balmer seriesof the hydrogen spectrum is :

a) 1210 Å b) 2420 Å

c) 3660 Å d) none of the above

69. An -particles of energy 5 MeV is scatteredthrough 1800 by a fixed uranium nucleus. Thedistance of closest approach is of the order of :

a) 1 A b) 10–10 cm

c) 10–12 cm d) 10–15 cm

70. The ionisation potential of hydrogen atom is 13.6volt. The energy requird to remove an electron inthe n = 4 state of the hydrogen atom is :

a) 27.2 eV b) 13.6 eV

c) 1.5 eV d) 0.85 eV

71. The ratio of the areas within the electron orbitsfor the rust excited state to the ground state forthe hydrogen atom is :

a) 2 : 1 b) 4 : 1

c) 8 : 1 d) 16 : 1

72. An electron jumps from 5th to 4th orbit of hydrogenatom. Taking the Rydberg constant as 107 m–1,what will be the frequency of the radiationemitted ?

a) 6.75 1014 Hz b) 6.75 1013 Hz

c) 6.75 1012 Hz d) none of the above

73. The number of -particles scattered from a targetat 150 is 4 106. What is the number of particlesscatterd at angle 300 under similar conditions ?

a) 1

4 106 b) 2 106

c) 8 106 d) 16 106

74. The wavelength of the rust line of the Lymanseries of hydrogen is 121.6 nm. What is thewavelength of the second member of the Balmerseries ?

a) 30.4 nm b) 60.8 nm

c) 243.2 nm d) 486.4 nm

75. In each fission of 92

U235 releases 200 MeV, howmany fissions must occur per second to producea power of 1 kW ?

a) 3.125 1013 b) 1.25 1018

c) 1.25 1013 d) 3.2 108

76. If the speed of light were 50% of the presentvalue, by what percentage the energy releasedwill be decreased ?

a) 100 % b) 75 %

c) 50 % d) 25 %

77. In nuclear fission 0.1% mass is converted intoenergy. How much electrical energy can begenerated by the fission of 1 kg of fuel ?

a) 1 kWh b) 107 kWh

c) 2.5 kWh d) 2.5 107 kWh

78. The binding energy per nucleon for deutron is1.1 MeV and that for helium is 7.0 MeV. If twodeutrons fuse together to produce an -particle,how much energy will be released ?

a) 28 MeV b) 23.6 MeV

c) 4 MeV d) 2.2 MeV

79. A -ray photon produces an electron positron paireach moving with the kinetic energy 0.01 MeV.The mass of electron is 0.51 MeV. What is theenergy of the -ray photon ?

a) 1.02 MeV b) 1.04 MeV

c) 1.01 MeV d) 2.04 MeV

80. Consider the nuclear reaction,

X200 A110 + B90 + Energy

If the binding energy per nucleon for X, A and Bis 7.4 MeV, 8.2 MeV and 8.2 MeV respectively,what is the energy released ?

a) 200 MeV b) 160 MeV

c) 110 MeV d) 90 MeV

81. 200 MeV energy is released in the fission of asingle nucleus of

92U235. What should be the rate

of fission of the nuclei to generate 1 kW power ?

a) 3.12 1011 s–1 b) 3.12 1012 s–1

c) 3.12 1013 s–1 d) 3.12 104 s–1

82. The binding energies per nucleon for deutrons(

1H2) and helium (

2He4) are 1.1 MeV & 7.0 MeV

respectively. The energy released when twodeutrons fuse to form a helium nucleus (

2He4)

is :





a) 28 MeV b) 32.4 MeV

c) 23.6 MeV d) 11.8 MeV

83. The mass defect for the nucleus of helium is0.0303 amu. What is the binding energy pernucleon for helium in MeV ?

a) 1 b) 4

c) 7 d) 27

84. A radioactive element X with half life of 2 hoursdecays giving a stable element Y ? After howmany hours the ratio of X to Y will be 1 : 7 ?



85. The decay constant of a radioactive substance is1 per month. The percentage of radioactivesubstance left undecayed after two months willbe :

a) 25 % b) 50 %

c) 66 % d) 87 %

86. Intensity of gamma rays falls to one-eighth of itsvalue after passing through 27 mm of lead. Whatshould be the thickness of the lead sheet to reducethe intensity to half ?

a) 24 mm b) 18 mm

c) 12 mm d) 9 mm

87. The activity of a radioactive sample decreasesto one-third of the original value in 9 years. Whatwill be its activity after further 9 years ?

a) 0A

3b)

0A

6

c) 0A

9d)

0A

18

88. A radio isotope has a half life of 5 years. Thefraction of atoms of this material, that woulddecay in 15 years would be :

a) 1 b) 3 / 4

c) 7

8d)

5

8

89. Bi has half life of 5 days. What time is taken by

7

8

th part of the sample to decay ?

a) 3.4 days b) 10 days

c) 15 days d) 20 days

90. A sample contains 16 g of a radioactive material,the half life of which is 2 days. After 32 dayswhat amount of radioactive material is left in thesample ?

a) < 1 mg b) 1

g4

c) 1

g2

d) 1 g

91. In the following fig. the energy levels of hydrogenatom have been shown along with some transitionsmarked A, B, C, D and E. The transitions A, Band C respectively represent :

a) The first member of Lyman series, thirdmember of Balmer series and second memberof Paschen series

b) The ionisation potential of hydrogen, secondmember of Balmer series and third memberof Paschen series

c) The series limit of Lyman series, secondmember of Balmer series and second memberof Paschen series

d) The series limit of Lyman series, third memberof Balmer series and second member ofPaschen series

92. Energy levels A, B, C of a certain atomcorrespond to increasing values of energy i.e.,E

A < E

B < E

C. If

1,

2,

3 are the wavelengths of

radiation corresponding to the transitions C to B,B to A and C to A respectively, which of thefollowing statements is correct ?





a) 3 1 2 b) 1 23

1 2

c) 1 2 3 0 d) 2 2 23 1 2

93. The potential energy U between two moleculesas a function of the distance X between themhas been shown in the adjoining figure. The twomolecules are :

a) attracted when X lies between A and B andare repelled when X lies between B and C

b) attracted when X lies between B and C andare repelled when lies between A and B

c) attracted when they reach B

d) repelled when they reach B



Answer Key

MH Text Book Based MCQ's

01. (c)

02. (a)

03. (a)

04. (c)

05. (d)

06. (a)

07. (d)

08. (a)

09. (d)

10. (d)

11. (b)

12. (c)

13. (c)

14. (c)

15. (b)

16. (b)

17. (b)

18. (a)

19. (d)

20. (a)

21. (b)

22. (c)

23. (b)

24. (c)

25. (c)

26. (a)

27. (b)

28. (c)

29. (c)

30. (d)

31. (b)

32. (d)

33. (d)

34. (c)

35. (c)

36. (a)

37. (b)

38. (b)

39. (b)

40. (b)

41. (d)

42. (c)

43. (d)

44. (b)

45. (b)

46. (c)

47. (c)

48. (c)

49. (a)

50. (b)

51. (c)

52. (a)

53. (d)

54. (b)

55. (c)

56. (a)

57. (b)

58. (b)

59. (a)

60. (b)

61. (b)

62. (c)

63. (c)

64. (c)

65. (b)

66. (a)

67. (d)

68. (c)

69. (b)

70. (b)

71. (d)

72. (b)

73. (d)

74. (d)

75. (c)

76. (d)

77. (b)

78. (a)

79. (d)

80. (a)

81. (d)

82. (d)

83. (d)

84. (c)

85. (c)

86. (c)

87. (a)

88. (b)

89. (a)

90. (b)

91. (d)

92. (d)

93. (d)

94. (b)

95. (a)

96. (a)

97. (c)

98. (a)

99. (b)

100. (b)

101. (d)

102. (b)

103. (c)

104. (b)

105. (c)

106. (a)

107. (a)

108. (c)

109. (c)

110. (a)

111. (b)

112. (d)

113. (d)

114. (c)

115. (c)

116. (c)

117. (b)

118. (d)

119. (d)

120. (b)

121. (b)

122. (b)

123. (c)

124. (c)

125. (c)

126. (b)

127. (a)

128. (b)

129. (c)

130. (d)

131. (a)

132. (d)

133. (b)

134. (b)

135. (b)

136. (a)

137. (c)

138. (d)

139. (d)

140. (a)

141. (d)

142. (d)

143. (b)

144. (c)

145. (c)

146. (b,d)

147. (d)

148. (b)

149. (c)

150. (a)

151. (d)

152. (b)

153. (d)

154. (d)

155. (b)

156. (c)

157. (d)

158. (c)

159. (d)

160. (d)

161. (b)

162. (b)

163. (b)

164. (a)

165. (c)

166. (b)

167. (c)

168. (a)

169. (b)

170. (b)

171. (b)

172. (a)

173. (b)

174. (b)

175. (a)

176. (a)

177. (c)

178. (a)

179. (a)

180. (a)

181. (b)

182. (b)

183. (a)

184. (d)

185. (c)

186. (d)

187. (a)

188. (c)

189. (a)

190. (a)

191. (b)

192. (b)

193. (b)

194. (b)

195. (a)

196. (b)

197. (b)

198. (c)

199. (a)

200. (a)

201. (b)

202. (d)

203. (c)

204. (b)

205. (c)

206. (c)


DINESH [MHT - CET] PHYSICS




DINESH [MHT - CET] PHYSICS

Answer Key

REVISION QUESTIONS from Competitive Exams.

01. (b)02. (b)03. (c)04. (b)05. (c)06. (a)07. (b)08. (d)09. (c)10. (c)11. (a)12. (a)13. (a)14. (d)15. (b)16. (c)17. (c)18. (c)19. (d)20. (c)21. (a)22. (b)23. (b)24. (d)25. (a)26. (a)27. (b)28. (c)

29. (b)30. (c)31. (d)32. (c)33. (a)34. (c)35. (b)36. (b)37. (d)38. (c)39. (d)40. (a)41. (b)42. (b)43. (b)44. (b)45. (d)46. (d)47. (a)48. (b)49. (d)50. (a)51. (c)52. (c)53. (c)54. (c)55. (c)56. (a)

57. (b)58. (c)59. (c)60. (a)61. (a)62. (d)63. (d)64. (b)65. (b)66. (c)67. (b)68. (d)69. (b)70. (d)71. (b)72. (b)73. (d)74. (a)75. (d)76. (c)77. (c)78. (a)79. (a)80. (c)81. (d)82. (d)83. (c)84. (d)

85. (c)86. (a)87. (d)88. (c)89. (c)90. (b)91. (a)92. (d)93. (b)94. (d)95. (c)96. (c)97. (a)98. (d)99. (a)100. (d)101. (a)102. (c)103. (a)104. (d)105. (b)106. (a)107. (c)108. (c)109. (c)110. (b)111. (d)112. (a)

113. (a)114. (c)115. (c)116. (b)117. (c)118. (d)119. (a)120. (c)121. (b)122. (a)123. (b)124. (c)125. (b)126. (b)127. (c)128. (b)129. (a)130. (c)131. (a)132. (c)133. (c)134. (c)135. (c)136. (a)137. (d)138. (b)139. (a)140. (a)

141. (d)142. (d)143. (a)144. (d)145. (d)146. (d)147. (d)148. (c)149. (c)150. (c)151. (b)152. (b)153. (b)154. (c)155. (b)156. (b)157. (d)158. (b)159. (c)160. (b)161. (c)162. (c)163. (b)164. (d)165. (d)166. (b)167. (c)168. (c)

169. (c)170. (b)171. (d)172. (a)173. (d)174. (a)175. (b)176. (a)177. (a)178. (d)179. (a)180. (c)181. (c)

182. (a,c)183. (c)184. (a)185. (d)186. (c)187. (c)188. (d)189. (a)190. (c)191. (b)192. (c)193. (b)194. (d)195. (d)196. (c)197. (b)

BRAIN TEASERS

01. (b)02. (c)03. (d)04. (c)05. (c)06. (a)07. (d)08. (d)09. (d)10. (c)11. (c)12. (c)13. (c)14. (c)

15. (b)16. (c)17. (b)18. (c)19. (d)20. (d)21. (a)22. (c)23. (a)24. (c)25. (b)26. (a)27. (a)28. (a)

29. (d)30. (d)31. (d)32. (a)33. (b)34. (a)35. (c)36. (d)37. (c)38. (b)39. (d)40. (a)41. (d)42. (b)

43. (c)44. (d)45. (d)46. (d)47. (c)48. (c)49. (c)50. (a)51. (a)52. (b)53. (c)54. (b)55. (b)56. (a)

57. (b)58. (a)59. (c)60. (b)61. (c)62. (a)63. (c)64. (d)65. (a)66. (b)67. (c)68. (d)69. (c)70. (d)

71. (d)72. (b)73. (a)74. (d)75. (a)76. (b)77. (d)78. (b)79. (b)80. (b)81. (c)82. (c)83. (c)84. (a)

85. (d)86. (d)87. (c)88. (c)89. (c)90. (a)91. (d)92. (b)93. (b)






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