Modern Physics

E28-1

kg29103.3 m/sec. Its

frequency will be

(1) Hz3103 (2) Hz3106

(3) Hz12105.7 (4) Hz13105.1

Ans. (4)

Sol.h

pc

c

hp

34

829

106.6

103103.3

Hz13105.1

Q.2 The rest mass of the photon is

(1)0

(2) (3) Between 0 and

(4) Equal to that of an electron

Ans. (1)

Q.3 If the momentum of a photon is p, then its frequency is

Where m is the rest mass of the photon

(1)c

ph(2)

h

pc

(3)c

mh(4)

h

mc

Ans. (2)

Sol.h

pc

c

h

c

Ep

Q.4 Which of the following statement is not correct

(1) Photographic plates are sensitive to infrared rays

(2) Photographic plates are sensitive to ultraviolet rays

(3) Infra-red rays are invisible but can cast shadows

like visible light

(4) Infrared photons have more energy than photons

of visible light

Ans. (4)

Sol. ;1

E also visibleinfrared so visibleinfrared EE

Q.5 There are 1n photons of frequency 1 in a beam of

light. In an equally energetic beam, there are 2n

photons of frequency 2 . Then the correct relation is

(1) 12

1 n

n(2)

2

1

2

1

n

n

(3)1

2

2

1

n

n(4) 2

2

21

2

1

n

n

Ans. (3)

Sol.1

2

2

11

n

n

nnhE .

Q.6 Einstein’s photoelectric equation states

that hEk . In this equation kE refers to

(1) Kinetic energy of all the emitted electrons

(2) Mean kinetic energy of the emitted electrons

(3) Maximum kinetic energy of the emitted electrons

(4) Minimum kinetic energy of the emitted electrons

Ans. (3)

Sol. According to Einstein’s photoelectric equation

Q.7 The threshold wavelength for photoelectric emission

from a material is 5200 Å. Photo-electrons will be

emitted when this material is illuminated with

monochromatic radiation from a

(1) 50 watt infrared lamp

(2) 1 watt infrared lamp

(3) 50 watt ultraviolet lamp

(4) Both (3) and (4)

Ans. (4)

Sol. In this case, for photoelectric emission the wavelength

of incident radiations must be less then Å5200 .

Wavelength of ultraviolet radiations is less then this

value (5200 Å) but wavelength of infrared radiations is

higher than this value.

Q.8 Threshold frequency for a metal is 1510 Hz. Light of

Å4000 falls on its surface. Which of the following

statements is correct

(1) No photoelectric emission takes place

(2) Photo-electrons come out with zero speed

(3) Photo-electrons come out with 103 m/sec speed

(4) Photo-electrons come out with 105 m/sec speed

Ans. (1)

Sol. Frequency of light of wavelength )4000( Å is

15

10

8

1075.0104000

103

cwhich is less than

the given threshold frequency. Hence no photoelectric

emisssion takes place.

Q.9 When light falls on a metal surface, the maximum kinetic

energy of the emitted photo-electrons depends upon

(1) The time for which light falls on the metal

(2) Frequency of the incident light

(3) Intensity of the incident light

(4) Velocity of the incident light

Ans. (2)

Modern Physics

Photoelectric effect

Q.1 The momentum of a photon is

EXERCISE-I

Modern Physics

E28-2

Sol. );( 0max WhK frequency of incident light.

Q.10 The work function of a metal is 4.2 eV, its threshold

wavelength will be

(1) 4000 Å (2) 3500 Å

(3) 2955 Å (4) 2500 Å

Ans. (4)

Sol. Intensity (No. of photons) (No. of photoelectrons)

Q.11 The work function of metal is 1 eV. Light of wavelength

3000 Å is incident on this metal surface. The velocity

of emitted photo-electrons will be

(1) 10 m/sec (2) 3101 m/sec

(3) 4101 m/sec (4) 6101 m/sec

Ans. (4)

Sol. eVEKWE 125.43000

12375;max0

eVeVeVWEK 125.31125.40max

Jmv 192max 106.1125.3

2

1

31

19

max101.9

106.1125.32

v sm /101 6

Q.12 The work function of a metal is 19106.1 J. When

the metal surface is illuminated by the light of

wavelength 6400 Å, then the maximum kinetic energy

of emitted photo-electrons will be

(Planck’s constant Jsh 34104.6 )

(1) J191014 (2) J19108.2

(3) J19104.1 (4) eV19104.1

Ans. (3)

Sol.19

10

834

0max 106.1106400

103104.6

W

hcK

J19104.1

Q.13 The work function for metals A, B and C are respectively

1.92 eV, 2.0 eV and 5 eV. According to Einstein’s

equation, the metals which will emit photo electrons

for a radiation of wavelength 4100 Å is/are

(1) None of these (2) A only

(3) A and B only (4) All the three metals

Ans. (3)

Sol. Energy of incident radiations (in eV)

eV01.34100

12375

Work function of metal A and B are less then eV01.3 ,

so A and B will emit photo electrons.

with light of wavelength 332 nm. The retarding potential

required to stop the escape of photo-electrons is

(1) 4.81 eV (2) 3.74 eV

(3) 2.66 eV (4) 1.07 eV

Ans. (3)

Sol. Energy of incident light eVeVE 72.33320

12375)(

)3320332( Ånm

According to the relation 00 eVWE

e

eVeV

e

WEV

07.172.3)( 00

.65.2 Volt

Q.15 The number of photo-electrons emitted per second

from a metal surface increases when

(1) The energy of incident photons increases

(2) The frequency of incident light increases

(3) The wavelength of the incident light increases

(4) The intensity of the incident light increases

Ans.. (4)

Sol. Intensity (No. of photons) (No. of photoelectrons)

Q.16 A photo cell is receiving light from a source placed at

a distance of 1 m. If the same source is to be placed at

a distance of 2 m, then the ejected electron

(1) Moves with one-fourth energy as that of the initial

energy

(2) Moves with one-fourth of momentum as that of

the initial momentum

(3) Will be half in number

(4) Will be one-fourth in number

Ans. (4)

Sol. Number of ejected electrons 2)Distance(

1)(Intensity

Therefore an increment of distance two times will

reduce the number of ejected electrons to th4

1of the

previous one.

Q.17 In a photoelectric experiment for 4000 Å incident

radiation, the potential difference to stop the ejection

is 2 V. If the incident light is changed to 3000 Å, then

the potential required to stop the ejection of electrons

will be

(1) 2 V (2) Less than 2 V

(3) Zero (4) Greater than 2 V

Ans. (4)

Sol. According to Einstein’s photoelectric equation

max0 KWE

00

11

e

hcV

Hence if decreases 0V increases.

Experimental study of photoelectric effect

Q.14 A metal surface of work function 1.07 eV is irradiated

Modern Physics

E28-3

Q.18 Stopping potential for photoelectrons

(1) Does not depend on the frequency of the incident

light

(2) Does not depend upon the nature of the cathode

material

(3) Depends on both the frequency of the incident

light and nature of the cathode material

(4) Depends upon the intensity of the incident light

Ans. (3)

Q.19 Which one of the following is true in photoelectric

emission

(1) Photoelectric current is directly proportional to the

amplitude of light of a given frequency

(2) Photoelectric current is directly proportional to the

intensity of light of a given frequency at moderate

intensities

(3) Above the threshold frequency, the maximum K.E.

of photoelectrons is inversely proportional to the

frequency of incident light

(4) The threshold frequency depends upon the

wavelength of incident light

Ans. (2)

Q.20 If in a photoelectric experiment, the wavelength of

incident radiation is reduced from 6000 Å to 4000 Å

then

(1) Stopping potential will decrease

(2) Stopping potential will increase

(3) Kinetic energy of emitted electrons will decrease

(4) The value of work function will decrease

Ans. (2)

Sol. Stopping potential

00

11

e

hcV . As decreases

so 0V increases.

Q.21 As the intensity of incident light increases

(1) Photoelectric current increases

(2) Photoelectric current decreases

(3) Kinetic energy of emitted photoelectrons increases

(4) Kinetic energy of emitted photoelectrons decreases

Ans. (1)

Sol. Intensity increases means more photons of same energy

will emit more electrons of same energy, hence only

photoelectric current increases.

Q.22 The maximum kinetic energy of photoelectrons emitted

from a surface when photons of energy 6 eV fall on it is

4 eV. The stopping potential in volts is

(1) 2 (2) 4

(3) 6 (4) 10

Ans. (2)

Sol. eVVK s ||max VVs 4||

(1) When it is stationary

(2) When it is in motion with the velocity of light only

(3) When it is in motion with any velocity

(4) None of the above

Ans. (3)

Sol. According to de-Broglie hypothesis.

Q.24 A photon, an electron and a uranium nucleus all have

the same wavelength. The one with the most energy

(1) Is the photon

(2) Is the electron

(3) Is the uranium nucleus

(4) Depends upon the wavelength and the properties

of the particle.

Ans. (1)

Sol. :2mE

h

mv

h

2

2

2 m

hE

is same for all, som

E1

. Hence energy will be

maximum for particle with lesser mass.

Q.25 When the kinetic energy of an electron is increased,

the wavelength of the associated wave will

(1) Increase

(2) Decrease

(3) Wavelength does not depend on the kinetic energy

(4) None of the above

Ans. (2)

Sol.EmE

h

p

h 1;

2 (h and m = constant)

Q.26 If the de-Broglie wavelengths for a proton and for a

particle are equal, then the ratio of their velocities

will be

(1) 4 : 1 (2) 2 : 1 (3) 1 : 2 (4) 1 : 4

Ans. (1)

Sol. 1

4;

1

2

2

1

2211

m

m

v

v

vm

h

vm

h

Q.27 The de-Broglie wavelength associated with an

electron having kinetic energy E is given by the

expression

(1)mE

h

2(2)

mE

h2(3) mhE2 (4)

h

mE22

Ans. (1)

Sol.mE

h

mv

hmEmvEmv

2;2

2

1 2

Q.28 Dual nature of radiation is shown by

(1) Diffraction and reflection

(2) Refraction and diffraction

(3) Photoelectric effect alone

(4) Photoelectric effect and diffraction

De-Broglie Wavelength

Q.23 Wave is associated with matter

Modern Physics

E28-4

Ans. (4)

Sol. natureDualnatureWavenDiffractio

natureParticleeffectricPhotoelect

Q.29 The de-Broglie wavelength of an electron having

eV80 of energy is nearly (1eV = 1.6 10–19 J, Mass of

electron = 9 10–31kg , Plank’s constant = 6.6 10–34 J-

sec)

(1) 140 Å (2) 0.14 Å (3) 14 Å (4) 1.4 Å

Ans. (4)

Sol. 1931

34

106.1801092

106.6

2

mE

h

Å4.1

Q.30 The kinetic energy of electron and proton is J3210 .

Then the relation between their de-Broglie wavelengths

is

(1) ep (2) ep

(3) ep (4) ep 2

Ans. (1)

Sol. By usingmE

h

2 E = 10–32 J = Constant for both

particles. Hencem

1 Since ep mm so .ep

Q.31 The de-Broglie wavelength of a particle accelerated

with 150 volt potential is 1010 m. If it is accelerated by

600 volts p.d., its wavelength will be

(1) 0.25 Å (2) 0.5 Å

(3) 1.5 Å (4) 2 Å

Ans. (2)

Sol. By usingV

1

1

2

2

1

V

V

2

150

60010

2

10

2= 0.5 Å.

Q.32 The de-Broglie wavelength of a neutron at 27oC is .

What will be its wavelength at 927oC

(1) / 2 (2) / 3

(3) / 4 (4) / 9

Ans. (1)

Sol.T

neutron

1

1

2

2

1

T

T

2300

1200

)27273(

)927273(

2

.

22

principal quantum number n > 4, then the total possible

number of elements will be

(1)60 (2)32 (3)4 (4)64

Ans.. (1)

Sol. For n=1, maximum number of states 22 2 n and for

n = 2, 3, 4, maximum number of states would be 8, 18, 32

respectively, Hence number of possible elements

= 2 + 8 + 18 + 32 = 60.

Q.34 In the Bohr’s hydrogen atom model, the radius of the

stationary orbit is directly proportional to (n = principle

quantum number)

(1) 1n (2) n (3) 2n (4) 2n

Ans. (4)

Sol. Bohr radius2

2

220 ; nrZme

hnr

Q.35 In the n th orbit, the energy of an electron

eVn

En 2

6.13 for hydrogen atom. The energy

required to take the electron from first orbit to second

orbit will be

(1) eV2.10 (2) eV1.12

(3) eV6.13 (4) eV4.3

Ans.. (1)

Sol.

1 2E 3.4 (13.6) 10.2eV

Q.36 The Lyman series of hydrogen spectrum lies in the

region

(1) Infrared (2) Visible

(3) Ultraviolet (4) Of X rays

Ans.. (3)

Sol. Lyman series lies in the UV region

Q.37 The size of an atom is of the order of

(1) m810 (2) m1010

(3) m1210 (4) m1410

Ans. (2)

Sol. The size of the atom is of the order of 1Å = 10–10m.

Q.38 Which one of the series of hydrogen spectrum is in

the visible region

(1) Lyman series (2) Balmer series

(3) Paschen series (4) Bracket series

Bohr’s model

Q.33 If in nature there may not be an element for which the

Modern Physics

E28-5

Ans. (2)

Sol. Balmer series lies in the visible region.

Q.39 The energy levels of the hydrogen spectrum is shown

in figure. TherearesometransitionsA, B, C, D and E.

Transition A, B and C respectively represent

(1) First member of Lyman series, third spectral line of

Balmer series and the second spectral line of Paschen

series

(2) Ionization potential of hydrogen, second spectral

line of Balmer series and third spectral line of Paschen

series

(3) Series limit of Lyman series, third spectral line of

Balmer series and second spectral line of Paschen

series

(4) Series limit of Lyman series, second spectral line of

Balmer series and third spectral line of Paschen series

Ans. (3)

Sol. Transition A (n = to 1) : Series limit of Lyman series

Transition B (n = 5 to n = 2) : Third spectral line of

Balmer series

Transition C (n = 5 to n = 3) : Second spectral line of

Paschen series

Q.40 The following diagram indicates the energy levels of a

certain atom when the system moves from 2E level to

E, a photon of wavelength is emitted. The

wavelength of photon produced during its transition

from3

4 Elevel to E is

(1) 3/ (2) 4/3 (3) 3/4 (4) 3

Ans. (4)

Sol.

hcE

hcEE 2

3'3

'

'3'3

4

hcEhcE

E

Q.41 Figure shows the energy levels P, Q, R, S and G of an

atom where G is the ground state. A red line in the

emission spectrum of the atom can be obtained by an

energy level change from Q to S. A blue line can be

obtained by following energy level change

(1) P to Q (2) Q to R

(3) R to S (4) R to G

Ans. (4)

Sol. If E is the energy radiated in transition

then QPRQSRSQGR EEEEE

For getting blue line energy radiated should be

maximum

1E . Hence (4) is the correct option.

Q.42 The figure indicates the energy level diagram of an

atom and the origin of six spectral lines in emission

(e.g. line no. 5 arises from the transition from level B to

A). The following spectral lines will also occur in the

absorption spectrum

1 2 3 4 5 6 X

A

B

C

(1) 1, 4, 6 (2) 4, 5, 6

(3) 1, 2, 3 (4) 1, 2, 3, 4, 5, 6

Ans. (3)

Sol. The absorption lines are obtained when the electron

jumps from ground state (n = 1) to the higher energy

states. Thus only 1, 2 and 3 lines will be obtained.

Q.43 In the lowest energy level of hydrogen atom, the

electron has the angular momentum

(1) h/ (2) /h

(3) 2/h (4) h/2

Ans. (3)

Modern Physics

E28-6

Sol.2

nhmvr , for n =1 it is

2

h

Q.44 The absorption transitions between the first and the

fourth energy states of hydrogen atom are 3. The

emission transitions between these states will be

(1)3 (2)4 (3)5 (4)6

Ans. (4)

Sol. By using2

)1(

nnN E 6

2

)14(4

EN

Q.45 In Bohr’s model of hydrogen atom, let PE represents

potential energy and TE the total energy. In going to a

higher level

(1) PE decreases, TE increases

(2) PE increases, TE increases

(3) PE decreases, TE decreases

(4) PE increases, TE decreases

Ans. (2)

Sol. As n increases P.E. increases and K.E. decreases

Q.46 The third line of Balmer series of an ion equivalent to

hydrogen atom has wavelength of 108.5 nm. The

ground state energy of an electron of this ion will be

(1) 3.4 eV (2) 13.6 eV

(3) 54.4 eV (4) 122.4 eV

Ans. (3)

Sol. For third line of Balmer series 21 n , 52 n

22

21

2 111

nnRZ

givesRnn

nnZ

)( 21

22

22

212

On putting values Z = 2

From eVn

ZE 4.54

)1(

)2(6.136.132

2

2

2

Q.47 When hydrogen atom is in its first excited level, its

radius is .... its ground state radius

(1) Half (2) Same

(3) Twice (4) Four times

Ans. (2)

Sol. 2nr . For ground state n=1 and for first excited state

wavelength produced is

(1) 0.5 Å (2) 0.75 Å

(3) 0.25 Å (4) 1 Å

Ans. (3)

Sol. ÅÅ 25.0247.01050

123753min

.

Q.49 The voltage applied across an X-rays tube is nearly

(1) 10 V (2) 100 V

(3) 10000 V (4) 106 V

Ans. (3)

Sol. The voltage applied across the X-ray tube is of the

range of 10 kV – 80 kV.

Q.50 The shortest wavelength of X-rays emitted from an X-

ray tube depends on the

(1) Current in the tube

(2) Voltage applied to the tube

(3) Nature of gas in the tube

(4) Atomic number of target material

Ans. (2)

Sol. .mineV

hc where h, c and e are constants. Hence

V

1min

Q.51 The wavelength of X-rays is of the order of

(1) Centimetre

(2) Micron (10-6 m)

(3) Angstrom (10-10 m)

(4) Metre

Ans. (3)

Sol. Range of X-rays is 0.1Å to 100 Å.

Q.52 X – rays and rays of the same energies may be

distinguished by

(1) Their velocity

(2) Their ionising power

(3) Their intensity

(4) Method of production

Ans. (4)

Sol. The production of X-rays is an atomic property whereas

the production of -rays is a nuclear property

Q.53 The X-ray beam coming from an X-ray tube will be

(1) Monochromatic

(2) Having all wavelengths smaller than a certain

maximum wavelength

(3) Having all wavelengths larger than a certain

minimum wavelength

(4) Having all wavelengths lying between a minimum

and a maximum wavelength

Ans. (3)

n=2.

Classification of X’ray, continuous X’ray

Q.48 An X-ray tube is operated at 50 kV. The minimum

Modern Physics

E28-7

(1) The electrons are accelerated to a fixed energy

(2) The source of electrons emits a monoenergetic

beam

(3) The bombarding electrons knock out electrons from

the inner shell of the target atoms and one of the outer

electrons falls into this vacancy

(4) The valence electrons in the target atoms are

removed as a result of the collision

Ans. (3)

Q.55 Molybdenum is used as a target element for production

of X-rays because it is

(1) A heavy element and can easily absorb high

velocity electrons

(2) A heavy element with a high melting point

(3) An element having high thermal conductivity

(4) Heavy and can easily deflect electrons

Ans. (2)

Sol. In X-ray tube, target must be heavy element with high

melting point.

Q.56 Mosley’s law relates the frequencies of line X-rays

with the following characteristics of the target element

(1) Its density

(2) Its atomic weight

(3) Its atomic number

(4) Interplaner spacing of the atomic planes

Ans. (3)

Sol. 22 )()( bZabZ

Z = atomic number of element (a, b are constant).

Q.57 The wavelength of the K line of characteristic X-

ray spectra varies with atomic number approximately

(1) Z (2) Z

(3) 2

1

Z (4)

Z

1

Ans. (4)

Sol. Nucleus of heavy atom captures electron of k-orbit.

This is a radioactive process, so vacancy of this

electron is filled by an outer electron and x-rays are

produces.

Q.58 Mosley measured the frequency (f) of the characteristic

X-rays from many metals of different atomic number

(Z) and represented his results by a relation known as

Mosley’s law. This law is (a, b are constants)

(1) 2)( bZaf (2) 2)( bfaZ

(3) )(2 bZaf (4) 2/1)( bZaf

Ans. (1)

Sol. Mosley’s law is 2)( bZaf

Q.59 For harder X-rays

(1) The wavelength is higher

(2) The intensity is higher

(3) The frequency is higher

(4) The photon energy is lower

Ans. (3)

Q.60 The wavelength of K line for an element of atomic

number 43 is . Then the wavelength of K line for an

element of atomic number 29 is

(1) 29

43(2)

28

42

(3) 4

9(4)

9

4

Ans. (3)

Sol. 2)1(

1

Z

2

2

1

1

2

1

1

Z

Z

22

2

28

42

129

143

4

92 .

Characteristic X’ray

Q.54 The characteristic X-ray radiation is emitted, when

Modern Physics

E28-8

Q.1 Let nrand n

bbe respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time.

(1) nr= n

b(2) n

r< n

b(3) n

r> n

b(4) data insufficient

Ans. (3)

Sol.12400( eV)

E=

λ( inÅ)

IAt λNo. of Photon=

hc

Eλ

hc

PtλNo. ofPhoton= =

hc

if E is constant no. of photon is l

Q.2 The stopping potential for the photo electrons emitted from a metal surface of work function 1.7eV is 10.4 V. Identify the

energy levels corresponding to the transitions in hydrogen atom which will result in emission of wavelength equal to

that of incident radiation for the above photoelectric effect

(1) n = 3 to 1 (2) n = 3 to 2 (3) n = 2 to 1 (4) n = 4 to 1

Ans. (1)

Sol.hf =1.7+10.4=12.1eV=energy

in H-atom

12.09 ev

x = 3

n = 1

Q.3 A photon of light enters a block of glass after travelling through vacuum. The energy of the photon on entering the glass

block

(1) increases because its associated wavelength decreases

(2) Decreases because the speed of the radiation decreases

(3) Stays the same because the speed of the radiation and the associated wavelength do not change

(4*) Stays the same because the frequency of the radiation does not change

Ans. (4)

Sol. Frequency of light does not change with medium.

Q.4 If the frequency of light in a photoelectric experiment is doubled then maximum kinetic energy of photoelectron

(1) be doubled (2) be halved

(3*) become more than double (4) become less than double

Ans. (3)

Sol. Einstein's formula

kmax 1

= eV1+ f

if frequency is doubled,

kmax 2

= ev2

+ f > 2 Kmax 1

Q.5 Two separate monochromatic light beams A and B of the same intensity (energy per unit area per unit time) are falling

normally on a unit area of a metallic surface. Their wavelength are A

and B

respectively. Assuming that all the incident

light is used in ejecting the photoelectrons, the ratio of the number of photoelectrons from beam A to that from B is

(1*)

A

B

(2)

B

A

(3)

A

B

2

(4)

B

A

2

EXERCISE-II

Modern Physics

E28-9

Ans. (1)

Sol. The number of photo electron depends on the number of photons

Number of photon =/hc

I=

hc

·Iµ l

Ratio of no. of photo electrons =B

A

Q.6 When a photon of light collides with a metal surface, number of electrons, (if any) coming out is

(1) only one (2) only two (3) infinite (4) depends upon factors

Ans. (1)

Sol. A Photon can interact with only a single electron.

Q.7 The energy of a photon of frequency n is E = hn and the momentum of a photon of wavelength l is p = h/l. From this

statement one may conclude that the wave velocity of light is equal to :

(1) 3 × 108 ms–1 (2*)p

E(3) E p (4)

2

p

E

Ans. (2)

Sol. C = l · n =p

h·

h

E=

p

E

Q.8 Let p and E denote the linear momentum and the energy of a photon. For another photon of smaller wavelength (in same

medium)

(1*) both p and E increase (2) p increases and E decreases

(3) p decreases and E increases (4) both p and E decreases

Ans. (1)

Sol. Applying p =

hand E =

hc

If l decreases E and p increases.

Q.9 Radiation of two photon energies twice and five times the work function of metal are incident sucessively on the metal

surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be

(1) 1 : 2 (2) 2 : 1 (3) 1 : 4 (4) 4 : 1

Ans. (1)

Sol.

1 22 1 1 12

1 25 42 2 22

: 1 : 21 2

K K mv

K K mv

v v

Q.10 By increasing the intensity of incident light keeping frequency (v > v0) fixed on the surface of metal

(1) kinetic energy of the photoelectrons increases

(2) number of emitted electrons increases

(3) kinetic energy and number of electrons increases

(4) no effect

Ans. (2)

Sol. no. of Photons I

I ­, no. of photon e- ejection ­

Modern Physics

E28-10

Q.11 If h is Planck’s constant is SI system, the momentum of a photon of wavelength 0.01 Å is:

(1) 10–2 h (2) h (3) 102 h (4) 1012h

Ans. (4)

Sol.12h

=10 hλ

statements.

(i) The saturation photocurrent remains almost the same.

(ii) The maximum kinetic energy of the photoelectrons is doubled.

(1) Both (i) and (ii) are true(2*) (i) is true but (ii) is false

(3) (i) is false but (ii) is true (4) both (i) and (ii) are false

Ans. (2)

Sol. Since frequency of light solurce is double, the energy carried by each photon will be doubled.

Hence intensity will be doubled even if number of photons remains constant. Hence saturation current is constant. Since

frequency is doubled, maximum KE increases but it is not doubled.

Q.13 The work function for aluminium surface is 4.2 eV and that for sodium surface is 2.0 ev. The two metals were illuminated

with appropriate radiations so as to cause photo emission. Then :

(1) Both aluminium and sodium will have the same threshold frequency

(2*) The threshold frequency of aluminium will be more than that of sodium

(3) The threshold frequency of aluminium will be less than that of sodium

(4) The threshold wavelength of aluminium will be more than that of sodium

Ans. (2)

Sol. The threshold frequency for Al must be greater as it has higher work function.

Q.14 The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV.

The stopping potential is :

(1) 2V (2*) 4V (3) 6V (4) 10V

Ans. (2)

Sol. Stopping potential = maximum kinetic energy of e = 4V.

Q.15 If the frequency of light in a photoelectric experiment is doubled, the stopping potential will

(1) be doubled (2) halved

(3) become more than doubled (4) become less than double

Ans. (3)

Sol. hf = +evs

Q.16 10–3 W of 5000 Å light is directed on a photoelectric cell. If the saturationcurrent in the cell is 0.16 mA, the

percentage of incident photons which produce photoelectrons, is

(1) 0.4% (2) 0.04% (3) 20% (4) 10%

Ans. (2)

Experimental study of photoelectric effect

Q.12 In a photoelectric experiment, the frequency and intensity of a light source are both doubled. Then consider the following

Modern Physics

E28-11

Sol.-3

10No.ofPhotons=

12400 -13×1.6×10

5000

16=0.25×10

-60.16×10- +12

No.of e reaching= =10-19

1.6×10

1210

%= ×100=0.04%16

0.25×10

Q.17 Which one of the following graphs in figure shows the variation of photoelectric current (I) with voltage (V) between

the electrodes in a photoelectric cell ?

(1*) (B) (C) (D)

Ans. (1)

Sol. Experimental obervation.

Q.18 When a centimetre thick surface is illuminated with light of wavelength , the stopping potential is V. When the same

surface is illuminated by light of wavelength 2, the stopping potential is V/3. The threshold wavelength for the surface

is :

(1)3

4(2*) 4 (3) 6 (4)

3

8

Ans. (2)

Sol.

hC= + eV ....(i)

2

hC= +

3

eV....(ii)

3 · II – I

1–

2

3

hc= 2 =

4

hc

th

=4

Modern Physics

E28-12

Q.19 A point source causes photoelectric effect from a small metal plate. Which of the following curves may represent the

saturation photocurrent as a function of the distance between the source and the metal?

(1)

i

t

(2)

i

t

(3)

t

i

(4)

i

t

Ans. (4)

Sol. As distance ses.

I ses.

i

24

PI

r

Q.20 In a photoelectric experiment, electrons are ejected from metals X and Y by light of intensity I and frequency f. The

potential difference V required to stop the electrons is measured for various frequencies. If Y has a greater work function

than X ; which one of the following graphs best illustrates the expected results ?

(1)

o f

v

X

Y (2)

o f

v

X

Y(C)

o f

v

X

Y (4)

o f

v

XY

Ans. (1)

Sol. Greater work function means greater cut off frequency.

Slope Remains same

fy>f

x

Intercept of y > Intercept of x

and must be parallel to each

Q.21 A image of the sun of formed by a lens of focal-length of 30 cm on the metal surface of a photo-electric cell and a

photo-electric current is produced. The lens forming the image is then replaced by another of the same diameter but

of focal length 15 cm. The photo-electric current in this case is

(1) I/2 (2) I (3) 2I (D) 4I

Ans. (2)

Sol. Diameter is same so light falling will be same so photoelectric current will be same.

Q.22 When ultraviolet light is incident on a photocell, its stopping potential is V0

and the maximum kinetic energy of the

photoelectrons is Kmax. When X-rays are incident on the same cell, then :

(1*) V0

and Kmax

both increase (2) V0

and Kmax

both decrease

(3) V0

increases but Kmax

remains the same (4) Kmax

increases but V0

remains the same

Ans. (1)

Sol. The energy of x–ray is more that of U.V. light. Hence, the K.E. of emitted photoelectron is more and hence stopping

potential required is also more.

Modern Physics

E28-13

8 ms–1 is equal to that of a photon. The ratio

of the kinetic energy of the electron to that of the energy of photon is :

(1)2(2)4 (3)2

1(4*)

4

1

Ans. (4)

Sol. ld =mv

h

El = energy of photon =

hcand energy of e– =

m2

p2

=2

hv

The required ratio =4

1

hc2

hv

.

Q.24 The de Broglie wavelength of a neutron correspoding to root mean square speed at 927ºC is . What will be the de

Broglie wavelength of the neutron correspoding to root mean square speed at 27ºC?

(1)2

(2) (3*) 2 (4) 4

Ans. (3)

Sol. K.E. of neutron E =2

3kT

d =p

h=

mE2

h= kT

2

3m2

h

; 2 =27327

)273927(.

= 2.

Q.25 The wavelength of de Broglie waves associated with an electron (mass m, charge e) accelerated through a potential

difference of V is given by (h is Planck’s constant) :

(1) = h/mV (2) = h/2 meV (3) = h/ meV (4*) = h/ meV2

Ans. (4)

Sol. =P

h=

mK2

h=

meV2

h

Q.26 A proton and an electron are accelerated by same potential difference have de-Broglie wavelength p

and e.

(1)e=

p(2)

e<

p(3)

e>

p(4) none of these

Ans. (3)

Sol. They have same K.E.

hλ=

2m K.E.

mp> m

eand q

p=q

e

p<

eas

1

m

Q.27 An electron with initial kinetic energy of 100eV is acceleration through a potential difference of 50V. Now the de-

Broglie wavelength of electron becomes.

(1) 1 Å (2) 1 5. Å (3) 3 Å (4) 12.27 Å

Ans. (1)

De-Broglie Wavelength.

Q.23 The de Broglie wavelength of an electron moving with a velocity 1.5 × 10

Modern Physics

E28-14

Sol. KE =100+50 =150eV

v =150volt

150λ =

V

0

A1

(1) 4a0

(2) a0

(3) a0/4 (4) a

0/16

Ans. (2)

Sol. r = a0 Z

n2

= a0.

4

22

= a0

Q.29 Which energy state of doubly ionized lithium (Li++) has the same energy as that of the ground state of hydrogen ?

Given Z for lithium = 3 :

(1) n = 1 (2) n = 2 (3*) n = 3 (4) n = 4

Ans. (3)

Sol. En(Li2+) = E

1(H)

– 13.6 2

2

n

3= –13.6 ×

1

1

n = 3

Q.30 The angular momentum of an electron in the hydrogen atom is3

2

h

. Here h is Planck’s constant. The kinetic energy of

this electron is :

(1) 4.53 eV (2) 1.51 eV (3) 3.4 eV (4) 6.8 eV

Ans. (2)

Sol. L

nhJ = mvr =

2

n = 3

1K.E. = - T.E. = 13.6 ×

9

=1.51ev

Q.31 The innermost orbit of the hydrogen atom has a diameter of 1.06 Å. What is the diameter of the tenth orbit ?

(1) 5.3 Å (2) 10.6 Å (3) 53 Å (4*) 106 Å

Ans. (4)

Sol. r n2

r10 = 102 × 1.06 Å = 106 Å.

Bohr’s model

Q.28 If a0

is the Bohr radius, the radius of the n = 2 electronic orbit in triply ionized beryllium is -

Modern Physics

E28-15

Q.32 Consider the following electronic energy level diagram of H-atom : Photons associated with shortest and longest

wavelengths would be emitted from the atom by the transitions labelled.

B

CD

n=

n=4

n=3

n=2

n=1

A

(1) D and C respectively (2) C and A respectively

(3) C and D respectively (4) A and C respectively

Ans. (3)

Sol.2

2 21 2

1 1 hcE Rcz

n n

C Shortest

D longest

Q.33 If an orbital electron of the hydrogen atom jumps from the ground state to a higher energy state, its orbital speed

reduces to half its initial value. If the radius of the electron orbit in the ground state is r, then the radius of the new

orbit would be :

(1) 2r (2*) 4r (3) 8r (4) 16r

Ans. (2)

Sol. Since speed reduces to half, KE reduced to

4

1th n = 2

mvr =2

nh

mv0r = 1.

2

h..........I

m2

v0r` = 2 ·

2

h.........II

from I and II

r´ = 4r

Q.34 In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in a quantum

state n is :

(1*) – 1 (2) + 1 (3)n1

(4) 2

1

n

Ans. (1)

Sol. According to the Bohr model

P.E. = – 2 K.E. = 2 T. E.

K.E. = – T.E.

Modern Physics

E28-16

Where T.E. =222

0

4

hn8

me–

K. E.= – 2220

4

hn8

me–

.E.T

.E.K= –1

Q.35 Three photons coming from emission spectra of hydrogen sample are picked up. Their energies are 12.1eV, 10.2eV

and 1.9eV. These photons must come from

(1) a single atom (2) two atoms

(3) three atom (4*) either two atoms or three atoms

Ans. (4)

Sol. 12.1 = E(n = 3) – E (n = 1)

10.2 = E(n = 2) – E (n = 1)

1.9 = E(n = 3) – E (n = 2)

At least two atoms must be enveloped as there connot be two transition from same level from same atom.

Q.36 In a hypothetical atom, if transition from n = 4 to n = 3 produces visible light then the possible transition to obtain

infrared radiation is :

(1) n = 5 to n = 3 (2) n = 4 to n = 2 (3) n = 3 to n = 1 (4*) none of these

Q.37 The ionization energy of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by electromagnetic

radiation of energy 12.1 eV. How many spectral lines will be emitted by the hydrogen atoms?

(1) one (2) two (3*) three (4) four

Ans. (3)

Sol 12.1 eV radiation will excite a hydrogen atom in ground state to n = 3

state number of possible transition = nC2

= 3C2

= 3.

Q.38 If the electron in a hydrogen atom were in the energy level with n = 3, how much energy in joule would be required to

ionise the atom ? (Ionisation energy of H-atom is 2.18 × 10–18 J):

(1) 6.54 × 10–19 (2) 1.43 × 10–19 (3) 2.42 × 10–19 (4) 3.14 × 10–20

Ans. (3)

Sol.

18

2

2.18 10I.E.

n

182.18 10

9

= 2.42 × 10-19 J

Q.39 Difference between nth and (n + 1)th Bohr’s radius of ‘H’ atom is equal to it’s (n – 1)th Bohr’s radius. The value of n

is :

(1)1(2)2 (3)3 (4)4

Ans. (4)

Sol. 2 22

2

0.529 1 0.529 1

2 1 1 2

0, 4

n n n

n n n

n

Ans. (4)

Sol. All the transition energies in option(1),(2) and (3) are greater than corresponding to n = 4 to n = 3. Hence, option (4).

Modern Physics

E28-17

Q.40 The wavelength of the first line in balmer series in the hydrogen spectrum is . What is the wavelength of the second

line :

(1*)27

20(2)

16

3(3)

36

5(4)

4

3

Ans. (1)

Sol.1

1

= R

9

1–

4

1 l

1=

R5

94

similarly2

1

= R

24

1–

4

1 l

2=

R3

16=

3

16×

94

5

=

27

20

Q.41 The frequency of the first line in Lyman series in the hydrogen spectrum is n. What is the frequency of the corresponding

line in the spectrum of doubly ionized Lithium ?

(1) n (2) 3 n (3*) 9 n (4) 27 n

Ans. (3)

Sol. E = 13.6

2

2

n

Z

D EH = 2

2

)1(

)1(6.13– 2

2

)2(

)1(6.13= 10.2 eV = hn

DELi = 2

2

)1(

)3(6.13– 2

2

)2(

)3(6.13= 91.80 eV = h (9 n)

Q.42 In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various

energies is passed. In absorption spectrum, five dark lines are observed. The number of bright lines in the emission

spectrum will be (Assume that all transitions take place)

(1)5(2)10 (3)15 (4) none of these

Ans. (3)

Sol. n - 1 = 5

n = 6

No. of briught lines = n n 1

2

=

6 5

2

= 15

Q.43 When a hydrogen atom, initially at rest emits, a photon resulting in transition n = 5 n = 1, its recoil speed is about

(1) 10–4 m/s (2) 2 × 10–2 m/s (3) 4.2 m/s (4) 3.8 × 10–2 m/s

Ans. (3)

Sol.E

PC

n1

= 1, n2= 5

2 219

8

13.6 13.6

1 51.6 10

3 10

2713.0561.6 10

3

mv = 6.96 × 10-27

v = 4.2 m/s

Modern Physics

E28-18

Q.44 Consider the spectral line resulting from the transition n = 2 n = 1 in the atoms and ions given below. The shortest

wavelength is produced by :

(1) hydrogen atom (2) deuterium atom

(3) singly ionized helium (4) doubly ionized lithium

Ans. (4)

2

2

2 21 2

2

1 1 hcΔE=Rcz - =

n n λ

1z

λ

For z = 3 Li

λwill be minimum

Q.45 The electron in a hydrogen atom make a transition from an excited state to the ground state. Which of the following

statement is true?

(1) Its kinetic energy increases and its potential and total energies decrease

(2) Its kinetic energy decreases, potential energy increases and its total energy remains the same.

(3) Its kinetic and total energies decrease and its potential energy increases.

(4) Its kinetic potential and total energies decreases.

Ans. (1)

Sol. T.E.=P.E. + K.E.

Existed

Ground

E

So both P.E. & K.E.

Q.46 Radius of the second Bohr orbit of singly ionised helium atom is

(1) 0.53 Å (2) 1.06 Å (3) 0.265 Å (4) 0.132 Å

Ans. (2)

Sol.2

2

2

0

nr = 0.529 ×

Z

20.529×

r =1.06 A

Q.47 An electron in Bohr’s hydrogen atom has an energy of –3.4 eV. The angular momentum of the electron is

(1) h/ (2) h/2

(3) nh/2 (n is an integer) (4) 2h/

Ans. (1)

Sol. E = -3.4 ev (for n = 2)

n = 2

angular momentum =

2h h

2

Modern Physics

E28-19

(1*) the kinetic energy of the stricking electron

(2) the kinetic energy of the free electrons of the target

(3) the kinetic energy of the ions of the target

(4) an atomic transition in the target

Ans. (1)

Sol. The contineous x-ray comes out because the striking electron lose its kinetic energy

Q.50 If the voltage across the filament is increased, the cutoff wavelength

(1) will increase (2) will decrease (3*) will remain unchanged (D) will change

Ans. (3)

Sol. The cut off wavelength depends on the accelerating potential difference which is unchanged. Hence, the wavelength

will remain unchanged.

Q.51 Which of the following wavelength falls in a X-rays region?

(1) 10,000 Å (2) 1000 Å (3) 1 Å (4) 10–2 Å

Ans. (3)

Sol.0

0.1 to 10 A (x-ray range)

Q.52 The penetrating power of X-ray increases with the

(1) Increases of its velocity (2) Increase in its intensity

(3) Decrease in its velocity (4) Increases in its frequency.

Ans. (4)

Sol. When freqency is increased energy increases

i.e. penetrating power increases

1and m

2, having non zero velocities. The ratio of the

de Broglie wavelengths of the particles, 1/

2is :

(1)2

1

m

m(2)

1

2

m

m(3*) 1 : 1 (4)

1

2

m

m

Ans. (3)

Sol =p

h

Since the momenta of the two particles are equal, are same.

Q.54 Consider a metal used to produced some charateristic X-rays. Energy of X-rays are given by E and wavelength as

represented by . Then which of the following is true :

(1)E(K) > E(K

) > E(K

) (2) E(M

) > E(L

) > E(K

)

(3*)(K) >(K

) >(K

) (4*)(M

) >(L

) >(K

)

Ans. (3)

Ans. (1)

Sol. In ultra violet region lyman series is present

Classification of X’ray, continuous X’ray

Q.49 Consider a photon of continuous X-ray coming from a Coolidge tube. Energy of photon comes from

Characteristic X’ray

Q.53 A particle of mass M at rest decays into two particles of masses m

Q.48 If radiation of allow wavelengths from ultraviolet to infrared is passed through hydrogen agas at room temperature,

absorption lines will be observed in the :

(1) Lyman series (2) Balmer series (3) Both (1) and (2) (4) neither (1) nor (2)

Modern Physics

E28-20

Sol. K

: transition from 2 1

Similarly for K

: 3 1 , K: 4 1 ; L

0: 3 2 : M

: 4 3

Now we can compare energy and .

Q.55 The characteristic X-ray spectrum is emitted due to transition of

(1) valence electrons of the atom

(2*) inner electrons of the atom

(3) nucleus of the atom

(4) both, the inner electrons and the nucleus of the atom

Ans. (2)

Sol. The characteristic x-rays are obtained due to the transition of electron from inner orbits.

Q.56 In a characteristic X-ray spectra of some atom superimposed on continuous X-ray spectra

PQ

Rel

ativ

ein

tens

ity

(1) P represents K

line

(2) Q represents K

line

(3) Q and P represents K

and K

lines respectively

(4) Relative positions of K

and K

depend on the particular atom

Ans. (3)

Sol.

p q

P Q

K K

hc hcE

E

E E

E E

So Q K

P K

Q.57 In X-ray tube, when the accelerating voltage V is doubled, the different between the wavelength of K line and the

minimum cut off of continuous X-ray spectum :

(1) remains constant (2) becomes more than two times

(3) becomes half (4) becomes less than 2 times.

Ans. (2)

Sol. When ever the energy of photon is doubled then work function increases must more than by 2 times.