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Atomic Structure (Session - 5) – JEE Page | 1

Topic covered: Atomic Structure (Session - 5) - JEE

Worksheet

1. The ratio of radii of first Bohr orbits of n i is: a. 6 : 2 : 3 b. 6 : 3 : 2 c. 2 : 6 : 3 d. 3 : 2 : 6

2. In a hydrogen atom, an electronic transition takes place from an initial state (1) to a

final state (2). The difference in the orbit radius r r is 24 times the first Bohr radius. Identify the transition. a. b. c. d.

3. The radius of which of the following orbits is th s m s th t of th first Bohr’s orbit of

hydrogen atom? a. n b. i n c. i n d. B n

4. If the energy of the electron in hydrogen atom in a certain excited state is – 3.4 eV, then

what will be its angular momentum?

a.

b.

c.

d.

5. Difference between nth and n Bohr’s r ius of tom is qu l to its n Bohr’s r ius. Th v lu of n is: a. 1 b. 2 c. 3 d. 4



6. Assuming that having a velocity greater than velocity of light is not possible, find out the value of the highest atomic number of hydrogen like ion which can exist. Given that the velocity of electron in the first orbit of Bohr hydrogen atom is . m s a. 138 b. 238 c. 157 d. 257

7. Find the ratio of the time period for 2nd Bohr orbit of and 4th Bohr orbit of i

a. 32 : 9 b. 9 : 32 c. 9 : 16 d. None of these

8. How many times does the electron go around the first orbit of hydrogen atom in one

second?

a. . b. . c. .

d. . 9. Calculate the ratio of the velocity of light to the velocity of electron in the first orbit of a

hydrogen atom.

h . rg – s m . g r . m) a. 1 b. 137 c. 6 d. 225

10. What is the ratio of time periods of an electron revolving in the second orbit of a

hydrogen atom to another electron revolving in the third orbit of : a. 8 : 27 b. 32 : 27 c. 27 : 32 d. None o these

11. What is the energy in eV required to excite the electron from n = 1 to n =2 energy level

in a hydrogen atom? (n = principal quantum number) a. 13.6 b. 3.4 c. 17 d. 10.2



12. Th n rgy of n l tron in th s on n th thir Bohr’s orbits of th hy rog n atom is . erg and . erg respectively. Calculate the wavelength of the emitted radiation when the electron drops from the third orbit to the second orbit.

a. . b. .

c. . d. .

13. The ionization enthalpy of hydrogen atom is . mol . The energy required

to excite the atom from n = 1 to n = 2 is: a. . mol b. . mol c. . mol d. . mol

14. Bohr’s th ory is ppli bl to whi h of th following s t of sp i s?

a. i B b. i B c. i B d. For all these sets

15. Match the following:

List - I List – II I. Ground state energy of

(P) 6.04 eV

II. Potential energy of I orbit of H-atom

(Q) – 27.2 eV

III. Kinetic energy of II excited state of

(R) .

IV. Ionisation energy of in ground state

(S) – 54.4 eV

a. I – (P), II-(Q), III – (S), IV – (R) b. I – (S), II-(P), III – (Q), IV – (R) c. I – (S), II-(Q), III – (P), IV – (R) d. I – (S), II-(Q), III – (R), IV – (P)

16. If the energy difference between two electronic states is 46.12 l mol and the

frequency of the light emitted when the electrons drop from a higher state to lower states is x what is the value of x? ( . h . l s mol wh r is th Avog ro’s numb r n h is th Pl n ’s onst nt



17. The longest wavelength (in cm) of light that is required to remove an electron from n = 2 orbit of hydrogen atom is y . What is the value of y?

18. An electromagnetic radiation of wavelength 242 nm is sufficient to ionise a sodium atom. Calculate the ionisation energy in mol Pl n onst nt h . s

19. The velocity of an electron in the first Bohr orbit of a hydrogen atom is equal to the velocity of the electron in the nth Bohr orbit of atom. Find the value of n. a. 1 b. 2 c. 3 d. 4

20. The energy of an electron in the first Bohr orbit of H atom is –13.6 eV. The possible

energy value(s) for the electron in the excited state(s) is (are): a. – 3.40 eV b. – 4.20 eV c. – 6.81 eV d. – 1.51 eV



Answer Key

Question number

1 2 3 4 5

Correct answer

(b) (a, d) (d) (b) (d)

Question number

6 7 8 9 10

Correct answer

(a) (b) (d) (b) (b)

Question number

11 12 13 14 15

Correct answer

(d) (a) (d) (b) (c)

Question number

16 17 18 19 20

Correct answer

(4.84) (36.51) (493.80) (b) (a, d)



Solutions

1. (b) Bohr’s r ius for nth orbit,

r . *

+

where n n rgy l v l Atomi numb r For H atom: n = 1, Z = 1

r . [

]

or ion: n

r . [

]

or i ion: n

r . [

]

pon t ing r tio

: r : r :

:

n simplifying w g t th r tio s:

:

:

i. . : :

2. (a, d)

Let, initial state (1) have orbit number = n Final state (2) have orbit number = n Bohr’s r ius for n orbit,

r . *

+

where, n rbit numb r Atomi numb r Given: Difference in orbit radius r r r ius of Bohr orbit

As the element taken is hydrogen, hence Z = 1 For 1st Bohr orbit, n = 1

Radius for first Bohr orbit, r .

Hence, r r r .

For n ,

r . *

+ . n

...(i)



For n

r . *

+ . n

...(ii)

Taking the difference of equations 1 and 2, we get r r . n

. n

. n n

. . n n

n n

.

.

n n n n Now there are 3 possibilities: 1. n n n n 2. n n n n 3. n n n n For case (1), Let n n n n n Upon solving, we get n n n Hence the transition would be For case (2), Let n n n n n Upon solving, we get n n n Hence the transition would be For case (3), Let n n n n n Upon solving, we get n . n n . which are not possible Only n transitions are the correct answers.

3. (d) Bohr’s r ius for nth orbit,

r . *

+

where n n rgy l v l Atomi numb r For 1st Bohr orbit of hydrogen atom, n = 1 and Z = 1

Radius of H atom r . For ion: n = 2, Z = 2



r . *

+ r

For i ion: n = 2, Z = 3

r . *

+

r

For i ion: n = 3, Z = 3

r . *

+ r

For B ion: n = 2, Z = 4

r . *

+ r

B n has the same radius as that of the 1st Bohr’s orbit of hy rog n tom.

4. (b)

Energy of an in any excited state is given by: .

tom

For H atom .

tom

Since, . tom is giv n th v lu of ‘n’ orr spon ing to this v lu from above expression will be n = 2.

Now, Angular momentum mvr

5. (d)

As per the question, for H atom r r r ...(i) Where r ius of Bohr’s nth energy level

As p r Bohr’s th ory r .

For H atom, r . n Similarly, r . n r . n Putting these values in equation (i), we get . n . n . n n n n n n n n n or n Since n = 0 is not possible, the only possible value is n = 4.



6. (a) As p r qu stion th m ximum v lo ity will b ‘ ’. Since the question has asked about highest atomic number which can exist, as per -Bohr’s th ory.

v . (

)

Data of first orbit of hydrogen is given. Hence, expression becomes: v . Here v m s Hence, .

7. (b)

As p r Bohr’s th ory T

where, T Time period of revolution, n = orbit number

and Z = atomic number of element For Z = 2, n = 2

T

Where, K is the proportionality constant Similarly, for i Z = 3, n = 4

T

Taking the ratio of time period of and i

8. (d)

Number of revolutions per second

...(i)

In case of Hydrogen atom, (Z = 1, n = 1)

v .

m s

v .

m s

r n . . m umb r of r volutions p r s on from q.

.

. . .

9. (b)

A or ing to Bohr’s postul t v lo ity of n l tron in Bohr orbit n b giv n by:

v .

n m s



Since for H, Z = 1. Putting up the values v . m s The ratio of the velocity of light (c) to the velocity of electron in the first orbit of a hydrogen atom (v)

v

.

10. (b)

We know that time period of an electron in the nth orbit of Hydrogen like atom is:

T

11. (d)

We know that, energy of an electron .

As the atom is hydrogen, Z = 1 To excite an electron from n = 1 to n = 2, energy would be absorbed. Taking the difference between two energy states, we get Therefore putting n = 1 and n = 2 and Z = 1,

. (

) ( .

)

. (

)

. . . 12. (a)

Energy of an electron in the nth orbit is denoted as . So, the energies of orbits 3 and 2 can be written as and respectively. is the difference between these energies. If is the wavelength of the emitted radiation, we can say that:

Given . rg and . rg We know that m s.

.

. .

.

. . m .

13. (d)

Given,

The ionization energy enthalpy of hydrogen atom .

mol



Again, Ionization energy (IE)

Energy, .

mol

Hence, The energy required to excite an electron in an atom of hydrogen from n = 1 to n = 2 is the energy difference between the two energy levels, which is given by

( .

) ( .

)

. (

)

. mol . mol

14. (b) Bohr’s mo l is only ppli bl to uni-electronic species.

15. (c)

(I) We know that the energy of an electron in a Bohr orbit .

As the atom is helium, Z = 2 We have to find the energy of ground state. Hence n = 1

– . . Hence energy of ground state of is – 54.4 eV. (II) We know that

T.

P.

T. E = – K. E P. T. . T. So the energy of an electron

T. .

n

Given that Z = 1 (for H-atom) and n = 1 (for orbit 1 or ground state) T. . As P. E = 2 T. E P. . . Hence potential energy of 1 orbit of H (III) We know that energy of an electron

T. .

n



Given that Z= 2 (for He –atom) and n=1 (it is excited sate)

T. .

. T.

. .

= 6.044 eV

Hence kinetic energy of II excited state of is +6.044 eV

(IV) Now, Ionization Energy = - energy of an electron .

.

J)

We have to calculate ionization energy of in the ground state. Hence, n=1 and Z=2 (for He atom)

Ioniz tion n rgy of .

J

.

J

= . J

16. (4.84) rom Pl n ’s quantum theory, h where is the frequency

v

h

.

. . s

17. (36.51)

Here, We know that,

.

( .

)

.

.

Again, . Thus, . . .

Energy of the photon absorbed during this transition

( . )

. .

. m . m

18. (493.80)



According to Pl n ’s qu ntum th ory the energy of radiation is inversely proportional

to its wavelength which is given by,

Given, m h . s As the electromagnetic radiation is just sufficient to ionize the sodium atom, Ionization energy = Energy of the photon

.

. . tom Thus, for the ionisation of 1 atom, energy . is required. n rgy r quir p r mol . . . mol

19. (b) The velocity of an electron in the nth Bohr orbit of a hydrogen like atom is given by:

v .

m s

Z = 1 and n = 1 for H, Z = 2 and n is unknown for Equating the values, we get

n

20. (a, d) The energy of an electron on Bohr orbits of hydrogen atoms is given by the expression

.

where, n takes only integral values. For the first Bohr orbit n = 1, energy of electron is – 13.6 eV. Apart from that, only – 3.4 eV and – 1.51 eV can be obtained by substituting n = 2 and n = 3 respectively in the above expression. As the other options are between – 13.6 eV and – 1.5 eV, it is not possible for these energy values to have integral values of n.

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BYJU’S Home Learning Programcdn1.byjus.com/wp-content/uploads/2020/07/Atomic-Structure-S5-Worksheet-july...Atomic Structure (Session - 5) – JEE Page | 4 17. The longest wavelength