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JEE Main

Explore popular questions from Atoms and Nuclei for JEE Main. This collection covers Atoms and Nuclei previous year JEE Main questions hand picked by experienced teachers.

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Atoms and Nuclei

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Q 1. The energy that should be added to an electron, to reduce its de-Broglie wavelengths from {tex} 10 ^ { - 10 } \mathrm { m } {/tex} to {tex} 0.5 \times 10 ^ { - 10 } \mathrm { m } , {/tex} will be

A

four times the initial energy.

thrice the initial energy.

C

equal to the initial energy.

D

twice the initial energy.

Explanation

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Q 2. A proton with kinetic energy {tex} K {/tex} describes a circle of radius {tex} r {/tex} in a uniform magnetic field. An {tex} \alpha {/tex} -particle with kinetic energy {tex} K {/tex} moving in the same magnetic field will describe a circle of radius

A

{tex} \frac { r } { 2 } {/tex}

r

C

2{tex} r {/tex}

D

4{tex} r {/tex}

Explanation

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Q 3. If the binding energy per nucleon is {tex}^{7}_{3}Li{/tex} and {tex}^{4}_{2}He{/tex} nuclei are 5.60 MeV and 7.06 MeV respectively, then in the reaction {tex}^{1}_{1}H + ^{7}_{3} Li \rightarrow 2 ^{4}_{2}He{/tex} energy of proton must be

A

39.2{tex} \mathrm { MeV } {/tex}

B

28.24{tex} \mathrm { MeV } {/tex}

17.28{tex} \mathrm { MeV } {/tex}

D

1.46{tex} \mathrm { MeV } {/tex}

Explanation

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Q 4. In hydrogen like atoms the ratio of difference of energies {tex} E _ { 4 n } - E _ { 2 n } {/tex} and {tex} E _ { 2 n } - E _ { n } {/tex} varies with atomic number {tex} z {/tex} and principle quantum number {tex} n {/tex} as

A

{tex} \frac { z ^ { 2 } } { n ^ { 2 } } {/tex}

B

{tex} \frac { z ^ { 4 } } { n ^ { 4 } } {/tex}

C

{tex} \frac { z } { n } {/tex}

None of these

Explanation

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Q 5. The ratio of de Broglie wavelength of {tex} \alpha {/tex} -particle to that of a proton being subjected to the same magnetic field so that the radii of their paths are equal to each other assuming the field induction vector {tex} \vec { B } {/tex} is perpendicular to the velocity vectors of the {tex} \alpha {/tex} -particle and the proton is

A

1

B

{tex} \frac { 1 } { 4 } {/tex}

{tex} \frac { 1 } { 2 } {/tex}

D

2

Explanation

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Q 6. The speed of an electron having a wavelength of the order of 1{tex} {\text{Å}} {/tex} will be

{tex} 7.25 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s } {/tex}

B

{tex} 6.26 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s } {/tex}

C

{tex} 5.25 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s } {/tex}

D

{tex} 4.24 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s } {/tex}

Explanation

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Q 7. In certain element the {tex} K {/tex} -shell electron energy is {tex} - 18.525 \mathrm { keV } {/tex} and the {tex} L {/tex} -shell electron energy is {tex} - 3 \mathrm { keV } {/tex} . When an electron jumps from the {tex} L {/tex} -shell to {tex} K {/tex} shell, an {tex} x {/tex} -ray photon is emitted. The wavelength of the emitted {tex} x {/tex} -rays is

0.8{tex} {\text{Å}}{/tex}

B

1{tex} {\text{Å}}{/tex}

C

0.6{tex}{\text{Å}} {/tex}

D

1.2{tex} {\text{Å}} {/tex}

Explanation

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Q 8. An electron moves along a metal tube with variable section. The velocity of the electron when it approaches the neck of tube, is

greater than {tex} v _ { 0 } {/tex}

B

equal to {tex} v _ { 0 } {/tex}

C

less than {tex} v _ { 0 } {/tex}

D

not defined

Explanation

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Q 9. Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron {tex} = 1.6725 \times 10 ^ { - 27 } \mathrm { kg }{/tex}, mass of proton {tex} = 1.6725 \times 10 ^ { - 27 } \mathrm { kg } , {/tex} mass electron {tex} \left. = 9 \times 10 ^ { - 31 } \mathrm { kg } \right) {/tex}

{tex} 0.51 {/tex} {tex}\mathrm { MeV } {/tex}

B

{tex} 7.10 {/tex} {tex}\mathrm { MeV } {/tex}

C

{tex}6.30 {/tex} {tex}\mathrm { MeV } {/tex}

D

{tex} 5.4 {/tex} {tex}\mathrm { MeV } {/tex}

Explanation


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Q 10.
The above is a plot of binding energy per nucleon {tex} \mathrm { E } _ { \mathrm { b } } {/tex} , against the nuclear mass {tex} M ; A , B , C , D , E , F {/tex} correspond to different nuclei. Consider four reactions:
(i) {tex} A + B \rightarrow C + \varepsilon \quad {/tex}
(ii) {tex} C \rightarrow A + B + \varepsilon {/tex}
(iii) {tex} D + E \rightarrow F + \varepsilon {/tex} and
(iv) {tex} F \rightarrow D + E + \varepsilon {/tex}
where {tex} \varepsilon {/tex} is the energy released? In which reactions is {tex} \varepsilon {/tex} positive?

A

(i) and (iii)

B

(ii) and (iv)

C

(ii) and (iii)

(i) and (iv)

Explanation



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Q 11. A radioactive nucleus (initial mass number {tex} A {/tex} and atomic number {tex} Z {/tex} emits 3{tex} \alpha {/tex} - particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

A

{tex} \frac { A - Z - 8 } { Z - 4 } {/tex}

{tex} \frac { A - Z - 4 } { Z - 8 } {/tex}

C

{tex} \frac { A - Z - 12 } { Z - 4 } {/tex}

D

{tex} \frac { A - Z - 4 } { Z - 2 } {/tex}

Explanation





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Q 12. If in a {tex} p - n {/tex} junction diode, a square input signal of 10{tex} \mathrm { V } {/tex} is applied as shown

Then the output signal across {tex} R _ { L } {/tex} will be

B

C

D

Explanation

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Q 13. A nucleus of mass {tex} M + \Delta m {/tex} is at rest and decays into two daughter nuclei of equal mass {tex} \frac { M } { 2 } {/tex} each. Speed of light is {tex} c . {/tex}
The speed of daughter nuclei is

A

{tex} c \frac { \Delta m } { M + \Delta m } {/tex}

{tex} c \sqrt { \frac { 2 \Delta m } { M } } {/tex}

C

{tex} c \sqrt { \frac { \Delta m } { M } } {/tex}

D

{tex} c \sqrt { \frac { \Delta m } { M + \Delta m } } {/tex}

Explanation









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Q 14. The radiation corresponding to {tex}3 \rightarrow 2 {/tex} transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of {tex} 3 \times 10 ^ { - 4 }\mathrm{T} {/tex} . If the radius of the largest circular path followed by these electrons is {tex}10.0 \mathrm { mm } {/tex} , the work function of the metal is close to:

A

{tex}1.8 \mathrm { eV } {/tex}

{tex} 1.1\mathrm { eV } {/tex}

C

{tex} 0.8\mathrm { eV } {/tex}

D

{tex}1.6 \mathrm { eV } {/tex}

Explanation









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Q 15. This question contains Statement- 1 and statement- {tex} - 2 {/tex} . Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and
Statement-2: For heavy nuclei, binding energy per nucleon increases with increasing {tex} Z {/tex} while for light nuclei it decreases with increasing {tex} Z {/tex} .

A

Statement-1 is false, Statement- 2 is true

B

Statement-1 is true, Statement-2 is true; Statement- 2 is a correct explanation for Statement- 1

C

Statement-1 is true, Statement-2 is true; Statement- 2 is not a correct explanation for Statement-1

Statement-1 is true, Statement- 2 is false

Explanation



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Q 16. Suppose an electron is attracted towards the origin by a force {tex} \frac { k } { r } {/tex} where {tex} ' k '{/tex} is a constant and {tex}' r' {/tex} is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the {tex} n ^ { \text {th } } {/tex} orbital of the electron is found to be {tex} ' {r _ { n }} '{/tex} and the kinetic energy of the electron to be {tex} ' { T _ { n } }' {/tex}. Then which of the following is true?

A

{tex} T _ { n } \propto \frac { 1 } { n ^ { 2 } } , r _ { n } \propto n ^ { 2 } {/tex}

{tex} T _ { n } {/tex} independent of {tex} n , r _ { n } \propto n {/tex}

C

{tex} T _ { n } \propto \frac { 1 } { n } , r _ { n } \propto n {/tex}

D

{tex} T _ { n } \propto \frac { 1 } { n } , r _ { n } \propto n ^ { 2 } {/tex}

Explanation



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Q 17. This question has Statement- 1 and Statement- 2 . Of the four choices given after the statements, choose the one that best describes the two statements.
Statement- 1: A metallic surface is irradiated by a monochromatic light of frequency {tex} v > v _ { 0 } {/tex} (the threshold frequency). The maximum kinetic energy and the stopping potential are {tex} K _ { \max } {/tex} and {tex} V _ { 0 } {/tex} respectively. If the frequency incident on the surface is doubled, both the {tex} K _ { \max } {/tex} and {tex} V _ { 0 } {/tex} are also doubled.
Statement- 2 :The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

A

Statement-1 is true, Statement-2 is true, Statement- 2 is the correct explanation of Statement- 1 .

B

Statement-1 is true, Statement- 2 is true, Statement- 2 is not the correct explanation of Statement- 1 .

Statement- 1 is false, Statement- 2 is true.

D

Statement- 1 is true, Statement- 2 is false.

Explanation





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Q 18. The forward biased diode connection is:

B

C

D

Explanation



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Q 19. The difference in the variation of resistance with temeperature in a metal and a semiconductor arises essentially due to the difference in the

A

crystal sturcture

variation of the number of charge carriers with temperature

C

type of bonding

D

variation of scattering mechanism with temperature

Explanation

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Q 20. If radius of the {tex} _{13} ^ { 27 } { Al } {/tex} nucleus is estimated to be 3.6 fermi then the radius of {tex} ^{ 125 } _{ 52 }Te {/tex} nucleus be nearly

A

8 fermi

6 fermi

C

5 fermi

D

4 fermi

Explanation





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Q 21. In the circuit below, {tex} A {/tex} and {tex} B {/tex} represent two inputs and {tex} C {/tex} represents the output.

The circuit represents

A

NOR gate

B

AND gate

C

NAND gate

OR gate

Explanation





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Q 22. The current voltage relation of a diode is given by {tex} \mathrm { I } = \left( \mathrm { e } ^ { 1000 \mathrm { V } / \mathrm { T } } - 1 \right) \mathrm { mA } , {/tex} where the applied voltage {tex} \mathrm { V } {/tex} is in volts and the temperature {tex} \mathrm { T } {/tex} is in degree kelvin. If a student makes an error measuring {tex} \pm 0.01 \mathrm { V } {/tex} while measuring the current of {tex} 5\mathrm { mA } {/tex} at {tex}300 \mathrm { K } {/tex} , what will be the error in the value of current in {tex} \mathrm { mA } ? {/tex}

{tex} 0.2\mathrm { mA } {/tex}

B

{tex}0.02 \mathrm { mA } {/tex}

C

{tex} 0.5\mathrm { mA } {/tex}

D

{tex}0.05 \mathrm { mA } {/tex}

Explanation





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Q 23. By increasing the temperature, the specific resistance of a conductor and a semiconductor

A

increases for both

B

decreases for both

increases, decreases

D

decreases, increases

Explanation









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Q 24. Two identical photocathodes receive light of frequencies {tex} f _ { 1 } {/tex} and {tex} { f _ { 2 }}{/tex} . If the velocites of the photo electrons (of mass m) coming out are respectively {tex} v _ { 1 } {/tex} and {tex} v _ { 2 } , {/tex} then

{tex} v _ { 1 } ^ { 2 } - v _ { 2 } ^ { 2 } = \frac { 2 h } { m } \left( f _ { 1 } - f _ { 2 } \right) {/tex}

B

{tex} v _ { 1 } + v _ { 2 } = \left[ \frac { 2 h } { m } \left( f _ { 1 } + f _ { 2 } \right) \right] ^ { 1 / 2 } {/tex}

C

{tex} v _ { 1 } ^ { 2 } + v _ { 2 } ^ { 2 } = \frac { 2 h } { m } \left( f _ { 1 } + f _ { 2 } \right) {/tex}

D

{tex} v _ { 1 } - v _ { 2 } = \left[ \frac { 2 h } { m } \left( f _ { 1 } - f _ { 2 } \right) \right] ^ { 1 / 2 } {/tex}

Explanation









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Q 25. In the middle of the depletion layer of a reverse- biased {tex} p-n {/tex} junction, the

electric field is zero

B

potential is maximum

C

electric field is maximum

D

potential is zero

Explanation