# 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.

## Mathematics

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. The probability of a radioactive atom for not disintegrating till 3 times of its half-life is

A

{tex} \frac { 1 } { 3 } {/tex}

B

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

{tex} \frac { 1 } { 8 } {/tex}

D

{tex} \frac { 7 } { 8 } {/tex}

##### Explanation

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Q 3. The wavelength of a certain line in the ray spectrum for tungsten {tex} ( Z = 74 ) {/tex} is 200 A. What would be the wavelength of the same line for platinum {tex} ( Z = 78 ) ? {/tex} The screening constant {tex} a {/tex} is unity.

179.76{tex} {\text{Å}} {/tex}

B

189.76{tex} {\text{Å}} {/tex}

C

289.76{tex} {\text{Å}} {/tex}

D

379.76{tex} {\text{Å}} {/tex}

##### Explanation

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Q 4. Two electrons of kinetic energy 2.5 eV fall on a metal plate, which has work function of 4.0 eV. Number of electrons ejected from the metal surface is

A

One

B

Two

Zero

D

More than two

##### Explanation

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Q 5. 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 6. 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 7. 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 8. 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 9. 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 10. 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 11. 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 12. The probability of nucleus to decay in two mean lives is

A

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

{tex} \frac { \mathrm { e } ^ { 2 } - 1 } { \mathrm { e } ^ { 2 } } {/tex}

C

{tex} \frac { 3 } { 4 } {/tex}

D

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

##### Explanation

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Q 13. A sample of radioactive material decays simultaneously by two processes {tex}\mathrm A {/tex} and {tex}\mathrm B {/tex} with half lives {tex} \frac { 1 } { 2 } {/tex} and {tex} \frac { 1 } { 4 } {/tex} hr respectively. For first half hr it decays with the process {tex} \mathrm A {/tex}, next one hr with the process {tex}\mathrm B {/tex} and for further half an hour with both {tex}\mathrm A {/tex} and {tex}\mathrm B {/tex}. If originally there were {tex}\mathrm N _ { 0 } {/tex} nuclei, find the number of nuclei after {tex} 2\ h r {/tex}, of such decay.

{tex} \frac { \mathrm { N } _ { 0 } } { ( 2 ) ^ { 8 } } {/tex}

B

{tex} \frac { \mathrm { N } _ { 0 } } { ( 2 ) ^ { 4 } } {/tex}

C

{tex} \frac { \mathrm { N } _ { 0 } } { ( 2 ) ^ { 6 } } {/tex}

D

{tex} \frac { \mathrm { N } _ { 0 } } { ( 2 ) ^ { 5 } } {/tex}

##### Explanation

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Q 14. If {tex} N _ { 0 } {/tex} is the original mass of the substance of half-life period {tex} t _ { 1 / 2 } = 5 {/tex} years, then the amount of {tex} f {/tex} substance left after {tex}15{/tex} years is

{tex} N _ { 0 } / 8 {/tex}

B

{tex} N _ { 0 } / 16 {/tex}

C

{tex} N _ { 0 } / 2 {/tex}

D

{tex} N _ { 0 } / 4 {/tex}

##### Explanation

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Q 15. Which of the following cannot be emitted by radioactive substances during their decay?

Protons

B

Neutrinoes

C

Helium nuclei

D

Electrons

##### Explanation

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Q 16. Starting with a sample of pure {tex} ^{66} \mathrm { Cu } , \frac { 7 } { 8 } {/tex} of it decays into {tex} \mathrm { Zn } {/tex} in {tex}15{/tex} minutes. The corresponding half life is

A

{tex}15{/tex} minutes

B

{tex}10{/tex} minutes

C

{tex} 7 \frac { 1 } { 2 } {/tex} minutes

{tex}5{/tex} minutes

##### Explanation

{tex}[\mathrm {OR}]{/tex}

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Q 17. In gamma ray emission from a nucleus

A

Only the proton number changes

B

Both the neutron number and the proton number change

There is no change in the proton number and the neutron number

D

Only the neutron number changes

##### Explanation

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Q 18. This question contains {tex}\mathrm {Statement-1}{/tex} and {tex}\mathrm {Statement-2}{/tex}. Of the four choices given after the statements, choose the one that best describes the two statements.
{tex}\mathrm {Statement-1}{/tex}: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
{tex}\mathrm {Statement-2}{/tex}: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-l is true, Statement- 2 is false

##### Explanation

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Q 19. The half life of a radioactive substance is {tex}20{/tex} minutes. The approximate time interval {tex} \left( t _ { 2 } - t _ { 1 } \right) {/tex} between the time {tex} t _ { 2 } {/tex} when {tex} \frac { 2 } { 3 } {/tex} of it had decayed and time {tex} t _ { 1 } {/tex} when {tex} \frac { 1 } { 3 } {/tex} of it had decayed is:

A

{tex} 14{/tex} {tex}\mathrm{ min } {/tex}

{tex} 20{/tex} {tex}\mathrm{ min } {/tex}

C

{tex} 28{/tex} {tex}\mathrm{ min } {/tex}

D

{tex} 7{/tex} {tex}\mathrm{ min } {/tex}

##### Explanation

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Q 20. 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}