Atoms and Nuclei: JEE Mains Previous Year Questions (2021-2024) | Physics for JEE Main & Advanced PDF Download

 Page 1


Q1 - 2024 (01 Feb Shift 1) 
The minimum energy required by a hydrogen atom in ground state to emit radiation in 
Balmer series is nearly: 
(1) 1.5eV 
(2) 13.6eV 
(3) 1.9eV 
(4) 12.1eV 
Solution: (4) 
Transition from ?? = 1 to ?? = 3?E = 12.1eV 
 
Q2 - 2024 (01 Feb Shift 2) 
A particular hydrogen - like ion emits the radiation of frequency 3×10
15
Hz when it 
makes transition from ?? = 2to ?? = 1. The frequency of radiation emitted in transition from 
n = 3 to n = 1is 
?? 9
×10
15
Hz, when x = 
Solution: 32 
?? = -13.6?? 2
 
1
?? ?? 2
-
1
?? ?? 2
  
E = C 
1
n
f
2
-
1
n
i
2
  
h?? = ?? 
1
?? ?? 2
-
1
?? ?? 2
  
?? 1
?? 2
=
 
1
?? ?? 2
-
1
?? ?? 2
 
2-1
 
1
?? ?? 2
-
1
?? ?? 2
 
3-1
 
=
 
1
1
-
1
4
 
 
1
1
-
1
9
 
=
3/4
8/9
 
=
3
4
×
9
8
 
?? 1
?? 2
=
27
32
 
?? 2
=
32
27
?? 1
=
32
27
×3×10
15
Hz =
32
9
×10
15
Hz 
 
Q3 - 2024 (27 Jan Shift 1) 
The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth 
stationary orbit will be: 
Page 2


Q1 - 2024 (01 Feb Shift 1) 
The minimum energy required by a hydrogen atom in ground state to emit radiation in 
Balmer series is nearly: 
(1) 1.5eV 
(2) 13.6eV 
(3) 1.9eV 
(4) 12.1eV 
Solution: (4) 
Transition from ?? = 1 to ?? = 3?E = 12.1eV 
 
Q2 - 2024 (01 Feb Shift 2) 
A particular hydrogen - like ion emits the radiation of frequency 3×10
15
Hz when it 
makes transition from ?? = 2to ?? = 1. The frequency of radiation emitted in transition from 
n = 3 to n = 1is 
?? 9
×10
15
Hz, when x = 
Solution: 32 
?? = -13.6?? 2
 
1
?? ?? 2
-
1
?? ?? 2
  
E = C 
1
n
f
2
-
1
n
i
2
  
h?? = ?? 
1
?? ?? 2
-
1
?? ?? 2
  
?? 1
?? 2
=
 
1
?? ?? 2
-
1
?? ?? 2
 
2-1
 
1
?? ?? 2
-
1
?? ?? 2
 
3-1
 
=
 
1
1
-
1
4
 
 
1
1
-
1
9
 
=
3/4
8/9
 
=
3
4
×
9
8
 
?? 1
?? 2
=
27
32
 
?? 2
=
32
27
?? 1
=
32
27
×3×10
15
Hz =
32
9
×10
15
Hz 
 
Q3 - 2024 (27 Jan Shift 1) 
The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth 
stationary orbit will be: 
(1) 
4
3
R 
(2) 
16
9
?? 
(3) 
3
4
?? 
(4) 
9
16
R 
Solution: (2) 
?? ?
?? 2
?? 
?? 4
?? 3
=
4
2
3
2
 
?? 4
=
16
9
?? 
 
Q4 - 2024 (27 Jan Shift 2) 
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be 
?? 7?? , where ?? = 
Solution: 144 
Longest wavelength corresponds to transition between n = 3 and n = 4 
1
?? = RZ
2
 
1
3
2
-
1
4
2
 = RZ
2
 
1
9
-
1
16
  
=
7RZ
2
9×16
 
? ?? =
144
7R
forZ= 1 ? ?? = 144 
 
Q5 - 2024 (29 Jan Shift 1) 
When a hydrogen atom going from n = 2 to n= 1 emits a photon, its recoil speed is 
x
5
m/s. Where x = . (Use : mass of hydrogen atom = 1.6×10
-27
kg ) 
Solution: 17 
Page 3


Q1 - 2024 (01 Feb Shift 1) 
The minimum energy required by a hydrogen atom in ground state to emit radiation in 
Balmer series is nearly: 
(1) 1.5eV 
(2) 13.6eV 
(3) 1.9eV 
(4) 12.1eV 
Solution: (4) 
Transition from ?? = 1 to ?? = 3?E = 12.1eV 
 
Q2 - 2024 (01 Feb Shift 2) 
A particular hydrogen - like ion emits the radiation of frequency 3×10
15
Hz when it 
makes transition from ?? = 2to ?? = 1. The frequency of radiation emitted in transition from 
n = 3 to n = 1is 
?? 9
×10
15
Hz, when x = 
Solution: 32 
?? = -13.6?? 2
 
1
?? ?? 2
-
1
?? ?? 2
  
E = C 
1
n
f
2
-
1
n
i
2
  
h?? = ?? 
1
?? ?? 2
-
1
?? ?? 2
  
?? 1
?? 2
=
 
1
?? ?? 2
-
1
?? ?? 2
 
2-1
 
1
?? ?? 2
-
1
?? ?? 2
 
3-1
 
=
 
1
1
-
1
4
 
 
1
1
-
1
9
 
=
3/4
8/9
 
=
3
4
×
9
8
 
?? 1
?? 2
=
27
32
 
?? 2
=
32
27
?? 1
=
32
27
×3×10
15
Hz =
32
9
×10
15
Hz 
 
Q3 - 2024 (27 Jan Shift 1) 
The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth 
stationary orbit will be: 
(1) 
4
3
R 
(2) 
16
9
?? 
(3) 
3
4
?? 
(4) 
9
16
R 
Solution: (2) 
?? ?
?? 2
?? 
?? 4
?? 3
=
4
2
3
2
 
?? 4
=
16
9
?? 
 
Q4 - 2024 (27 Jan Shift 2) 
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be 
?? 7?? , where ?? = 
Solution: 144 
Longest wavelength corresponds to transition between n = 3 and n = 4 
1
?? = RZ
2
 
1
3
2
-
1
4
2
 = RZ
2
 
1
9
-
1
16
  
=
7RZ
2
9×16
 
? ?? =
144
7R
forZ= 1 ? ?? = 144 
 
Q5 - 2024 (29 Jan Shift 1) 
When a hydrogen atom going from n = 2 to n= 1 emits a photon, its recoil speed is 
x
5
m/s. Where x = . (Use : mass of hydrogen atom = 1.6×10
-27
kg ) 
Solution: 17 
 
??? = 10.2eV 
Recoil speed (v) =
?E
mc
 
=
10.2eV
1.6×10
-27
×3×10
8
 
=
10.2×1.6×10
-19
1.6×10
-27
×3×10
8
 
v = 3.4m/s=
17
5
m/s 
Therefore, ?? = 17 
 
Q6 - 2024 (29 Jan Shift 2) 
Given below are two statements : 
Statement I : Most of the mass of the atom and all its positive charge are concentrated in 
a tiny nucleus and the electrons revolve around it, is Rutherford's model. 
Statement II : An atom is a spherical cloud of positive charges with electrons embedded 
in it, is a special case of Rutherford's model. 
In the light of the above statements, choose the most appropriate from the options given 
below. 
(1) Both statement I and statement II are false 
(2) Statement I is false but statement II is true 
(3) Statement I is true but statement II is false 
(4) Both statement I and statement II are true 
Solution: (3) 
According to Rutherford atomic model, most of mass of atom and all its positive charge 
is concentrated in tiny nucleus & electron revolve around it. 
According to Thomson atomic model, atom is spherical cloud of positive charge with 
electron embedded in it. 
Hence, 
Statement I is true but statement II false. 
Q7 - 2024 (29 Jan Shift 2) 
Hydrogen atom is bombarded with electrons accelerated through a potential different of 
V, which causes excitation of hydrogen atoms. If the experiment is being formed at 
Page 4


Q1 - 2024 (01 Feb Shift 1) 
The minimum energy required by a hydrogen atom in ground state to emit radiation in 
Balmer series is nearly: 
(1) 1.5eV 
(2) 13.6eV 
(3) 1.9eV 
(4) 12.1eV 
Solution: (4) 
Transition from ?? = 1 to ?? = 3?E = 12.1eV 
 
Q2 - 2024 (01 Feb Shift 2) 
A particular hydrogen - like ion emits the radiation of frequency 3×10
15
Hz when it 
makes transition from ?? = 2to ?? = 1. The frequency of radiation emitted in transition from 
n = 3 to n = 1is 
?? 9
×10
15
Hz, when x = 
Solution: 32 
?? = -13.6?? 2
 
1
?? ?? 2
-
1
?? ?? 2
  
E = C 
1
n
f
2
-
1
n
i
2
  
h?? = ?? 
1
?? ?? 2
-
1
?? ?? 2
  
?? 1
?? 2
=
 
1
?? ?? 2
-
1
?? ?? 2
 
2-1
 
1
?? ?? 2
-
1
?? ?? 2
 
3-1
 
=
 
1
1
-
1
4
 
 
1
1
-
1
9
 
=
3/4
8/9
 
=
3
4
×
9
8
 
?? 1
?? 2
=
27
32
 
?? 2
=
32
27
?? 1
=
32
27
×3×10
15
Hz =
32
9
×10
15
Hz 
 
Q3 - 2024 (27 Jan Shift 1) 
The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth 
stationary orbit will be: 
(1) 
4
3
R 
(2) 
16
9
?? 
(3) 
3
4
?? 
(4) 
9
16
R 
Solution: (2) 
?? ?
?? 2
?? 
?? 4
?? 3
=
4
2
3
2
 
?? 4
=
16
9
?? 
 
Q4 - 2024 (27 Jan Shift 2) 
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be 
?? 7?? , where ?? = 
Solution: 144 
Longest wavelength corresponds to transition between n = 3 and n = 4 
1
?? = RZ
2
 
1
3
2
-
1
4
2
 = RZ
2
 
1
9
-
1
16
  
=
7RZ
2
9×16
 
? ?? =
144
7R
forZ= 1 ? ?? = 144 
 
Q5 - 2024 (29 Jan Shift 1) 
When a hydrogen atom going from n = 2 to n= 1 emits a photon, its recoil speed is 
x
5
m/s. Where x = . (Use : mass of hydrogen atom = 1.6×10
-27
kg ) 
Solution: 17 
 
??? = 10.2eV 
Recoil speed (v) =
?E
mc
 
=
10.2eV
1.6×10
-27
×3×10
8
 
=
10.2×1.6×10
-19
1.6×10
-27
×3×10
8
 
v = 3.4m/s=
17
5
m/s 
Therefore, ?? = 17 
 
Q6 - 2024 (29 Jan Shift 2) 
Given below are two statements : 
Statement I : Most of the mass of the atom and all its positive charge are concentrated in 
a tiny nucleus and the electrons revolve around it, is Rutherford's model. 
Statement II : An atom is a spherical cloud of positive charges with electrons embedded 
in it, is a special case of Rutherford's model. 
In the light of the above statements, choose the most appropriate from the options given 
below. 
(1) Both statement I and statement II are false 
(2) Statement I is false but statement II is true 
(3) Statement I is true but statement II is false 
(4) Both statement I and statement II are true 
Solution: (3) 
According to Rutherford atomic model, most of mass of atom and all its positive charge 
is concentrated in tiny nucleus & electron revolve around it. 
According to Thomson atomic model, atom is spherical cloud of positive charge with 
electron embedded in it. 
Hence, 
Statement I is true but statement II false. 
Q7 - 2024 (29 Jan Shift 2) 
Hydrogen atom is bombarded with electrons accelerated through a potential different of 
V, which causes excitation of hydrogen atoms. If the experiment is being formed at 
T = 0K. The minimum potential difference needed to observe any Balmer series lines in 
the emission spectra will be 
?? 10
V, where ?? = 
Solution: (121) 
For minimum potential difference electron has to make transition from ?? = 3 to ?? = 2 
state but first electron has to reach to n = 3 state from ground state. So, energy of 
bombarding electron should be equal to energy difference of ?? = 3 and ?? = 1 state. 
?E = 13.6 1 -
1
3
2
 e = eV 
13.6×8
9
= V 
V = 12.09V ˜ 12.1V 
So, ?? = 121 
 
Q8 - 2024 (30 Jan Shift 1) 
The ratio of the magnitude of the kinetic energy to the potential energy of an electron in 
the 5
th 
 excited state of a hydrogen atom is: 
(1) 4 
(2) 
1
4
 
(3) 
1
2
 
(4) 1 
Solution: (3) 
1
2
|?? ?? | = ?? ?? for each value of n (orbit) 
?
?? ?? |?? ?? |
=
1
2
 
 
Q9 - 2024 (30 Jan Shift 1) 
A electron of hydrogen atom on an excited state is having energy E
n
= -0.85eV. The 
maximum number of allowed transitions to lower energy level is 
Solution: 6 
?? ?? = -
13.6
?? 2
= -0.85 
? ?? = 4 
No of transition 
Page 5


Q1 - 2024 (01 Feb Shift 1) 
The minimum energy required by a hydrogen atom in ground state to emit radiation in 
Balmer series is nearly: 
(1) 1.5eV 
(2) 13.6eV 
(3) 1.9eV 
(4) 12.1eV 
Solution: (4) 
Transition from ?? = 1 to ?? = 3?E = 12.1eV 
 
Q2 - 2024 (01 Feb Shift 2) 
A particular hydrogen - like ion emits the radiation of frequency 3×10
15
Hz when it 
makes transition from ?? = 2to ?? = 1. The frequency of radiation emitted in transition from 
n = 3 to n = 1is 
?? 9
×10
15
Hz, when x = 
Solution: 32 
?? = -13.6?? 2
 
1
?? ?? 2
-
1
?? ?? 2
  
E = C 
1
n
f
2
-
1
n
i
2
  
h?? = ?? 
1
?? ?? 2
-
1
?? ?? 2
  
?? 1
?? 2
=
 
1
?? ?? 2
-
1
?? ?? 2
 
2-1
 
1
?? ?? 2
-
1
?? ?? 2
 
3-1
 
=
 
1
1
-
1
4
 
 
1
1
-
1
9
 
=
3/4
8/9
 
=
3
4
×
9
8
 
?? 1
?? 2
=
27
32
 
?? 2
=
32
27
?? 1
=
32
27
×3×10
15
Hz =
32
9
×10
15
Hz 
 
Q3 - 2024 (27 Jan Shift 1) 
The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth 
stationary orbit will be: 
(1) 
4
3
R 
(2) 
16
9
?? 
(3) 
3
4
?? 
(4) 
9
16
R 
Solution: (2) 
?? ?
?? 2
?? 
?? 4
?? 3
=
4
2
3
2
 
?? 4
=
16
9
?? 
 
Q4 - 2024 (27 Jan Shift 2) 
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be 
?? 7?? , where ?? = 
Solution: 144 
Longest wavelength corresponds to transition between n = 3 and n = 4 
1
?? = RZ
2
 
1
3
2
-
1
4
2
 = RZ
2
 
1
9
-
1
16
  
=
7RZ
2
9×16
 
? ?? =
144
7R
forZ= 1 ? ?? = 144 
 
Q5 - 2024 (29 Jan Shift 1) 
When a hydrogen atom going from n = 2 to n= 1 emits a photon, its recoil speed is 
x
5
m/s. Where x = . (Use : mass of hydrogen atom = 1.6×10
-27
kg ) 
Solution: 17 
 
??? = 10.2eV 
Recoil speed (v) =
?E
mc
 
=
10.2eV
1.6×10
-27
×3×10
8
 
=
10.2×1.6×10
-19
1.6×10
-27
×3×10
8
 
v = 3.4m/s=
17
5
m/s 
Therefore, ?? = 17 
 
Q6 - 2024 (29 Jan Shift 2) 
Given below are two statements : 
Statement I : Most of the mass of the atom and all its positive charge are concentrated in 
a tiny nucleus and the electrons revolve around it, is Rutherford's model. 
Statement II : An atom is a spherical cloud of positive charges with electrons embedded 
in it, is a special case of Rutherford's model. 
In the light of the above statements, choose the most appropriate from the options given 
below. 
(1) Both statement I and statement II are false 
(2) Statement I is false but statement II is true 
(3) Statement I is true but statement II is false 
(4) Both statement I and statement II are true 
Solution: (3) 
According to Rutherford atomic model, most of mass of atom and all its positive charge 
is concentrated in tiny nucleus & electron revolve around it. 
According to Thomson atomic model, atom is spherical cloud of positive charge with 
electron embedded in it. 
Hence, 
Statement I is true but statement II false. 
Q7 - 2024 (29 Jan Shift 2) 
Hydrogen atom is bombarded with electrons accelerated through a potential different of 
V, which causes excitation of hydrogen atoms. If the experiment is being formed at 
T = 0K. The minimum potential difference needed to observe any Balmer series lines in 
the emission spectra will be 
?? 10
V, where ?? = 
Solution: (121) 
For minimum potential difference electron has to make transition from ?? = 3 to ?? = 2 
state but first electron has to reach to n = 3 state from ground state. So, energy of 
bombarding electron should be equal to energy difference of ?? = 3 and ?? = 1 state. 
?E = 13.6 1 -
1
3
2
 e = eV 
13.6×8
9
= V 
V = 12.09V ˜ 12.1V 
So, ?? = 121 
 
Q8 - 2024 (30 Jan Shift 1) 
The ratio of the magnitude of the kinetic energy to the potential energy of an electron in 
the 5
th 
 excited state of a hydrogen atom is: 
(1) 4 
(2) 
1
4
 
(3) 
1
2
 
(4) 1 
Solution: (3) 
1
2
|?? ?? | = ?? ?? for each value of n (orbit) 
?
?? ?? |?? ?? |
=
1
2
 
 
Q9 - 2024 (30 Jan Shift 1) 
A electron of hydrogen atom on an excited state is having energy E
n
= -0.85eV. The 
maximum number of allowed transitions to lower energy level is 
Solution: 6 
?? ?? = -
13.6
?? 2
= -0.85 
? ?? = 4 
No of transition 
=
?? (?? -1)
2
=
4(4 -1)
2
= 6 
 
Q10 - 2024 (30 Jan Shift 2) 
An electron revolving in n
th 
 Bohr orbit has magnetic moment ?? ?? . If ?? ?? ?? ?? ?? , the value of ?? 
is: 
(1) 2 
(2) 1 
(3) 3 
(4) 0 
Solution: (2) 
Magnetic moment = i?? r
2
 
?? =
 evr 
2
 
?? ?? 
1
?? ?? 2
 
?? ?? ?? 
?? =1 
Q11 - 2024 (31 Jan Shift 1) 
The mass defect in a particular reaction is 0.4g. The amount of energy liberated is 
n×10
7
kWh, where n = 
Solution: 1 
E = ?mc
2
= 0.4×10
-3
× 3×10
8
 
2
= 3600×10
7
kWs
=
3600×10
7
3600
kWh = 1×10
7
kWh
 
 (speed of light = 3×10
8
m/s)