The radius $R$ of a nucleus of mass number $A$ can be estimated by the formula $R = (1.3 \times {\rm{1}}{{\rm{0}}^{ - 15}}){A^{1/3}}m.$ It follows that the mass density of a nucleus is of the order of $({M_{proton}} \cong {M_{neutron}} \simeq 1.67 \times {10^{ - 27}}{\rm{\,\,kg)}}$

${10^{17}}{\rm{\,\,kg}}\,{{\rm{m}}^{ - 3}}$

${10^{24}}{\rm{\,\,kg}}\,{{\rm{m}}^{ - 3}}$

${10^{10}}{\rm{\,\,kg}}\,{{\rm{m}}^{ - 3}}$

${10^3}{\rm{\,\,kg}}\,{{\rm{m}}^{ - 3}}$

The penetrating powers of ${\rm{\alpha }},\,\,{\rm{\beta }}\,\,{\rm{and}}\,\,{\rm{\gamma }}$ radiations, in decreasing order are

${\rm{\gamma }},\,\,{\rm{\alpha }},\,\,{\rm{\beta }}$

${\rm{\alpha }},\,\,{\rm{\beta }},\,\,{\rm{\gamma }}$

${\rm{\beta }},\,\,{\rm{\gamma }},\,\,{\rm{\alpha }}$

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JEE • PHYSICS • NUCLEI

Nuclei practice · Mixed difficulty

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 380 questions

1 Medium

1 of 380

Application +4 | -1

The radius of a nucleus with atomic mass number

\mathrm{7}

\mathrm{2}\,\,\mathrm{fermi}

. Find the radius of nucleus with atomic number

\mathrm{189}

View answer and explanation

Correct option: D

\mathrm{6}\,\,\mathrm{fermi}

Option D (6 fermi) is correct because the nuclear radius is proportional to the cube root of the mass number.

2 Medium

2 of 380

Understanding +4 | -1

Which one is correct about fission?

View answer and explanation

Correct option: A

Approx.

0.1 \%

mass converts into energy

Option A (Approx.

0.1 \%

mass converts into energy) is correct because in nuclear fission, a small fraction of the mass is converted into energy according to Einstein's mass-energy equivalence.

3 Medium

3 of 380

Application +4 | -1

N{e^{22}}

nucleus, after absorbing energy, decays into two

\alpha -

particles and an unknown nucleus. The unknown nucleus is

View answer and explanation

Correct option: B

Carbon

Option B (Carbon) is correct because the atomic number and mass number balance in the nuclear reaction.

4 Medium

4 of 380

Understanding +4 | -1

A moderator is used in nuclear reactors in order to

View answer and explanation

Correct option: A

Slow down the speed of the neutrons

The correct answer is A (Slow down the speed of the neutrons) because moderators are used to reduce the kinetic energy of neutrons to increase the probability of nuclear fission.

5 Medium

5 of 380

Remembering +4 | -1

Nuclear forces are

View answer and explanation

Correct option: D

All the above

Option D (All the above) is correct because nuclear forces exhibit all the listed properties: they are non-central, saturated, and spin-dependent.

6 Medium

6 of 380

Understanding +4 | -1

For uranium nucleus how does its mass vary with volume?

View answer and explanation

Correct option: A

m \propto V

Option A (

m \propto V

) is correct because nuclear density is constant, implying mass is directly proportional to volume.

7 Medium

7 of 380

Application +4 | -1

The half-life of a radioactive isotope ‘x’ is 60 years. It decays to another element ‘y’ which is stable. Two elements x and y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be

View answer and explanation

Correct option: D

240 years

Option A (5 m) is correct because the distance is calculated by finding the time it takes for the box to fall off the trolley and then using the lorry's acceleration to find the distance covered.

8 Medium

8 of 380

Understanding +4 | -1

Statement-I: The fusion process is achived by raising the temperature of the system.

Statement-II: The fusion particles have enough K.E to overcome the coulomb repulsive behaviour.

View answer and explanation

Correct option: A

Statement-I and Statement-II are true

Option A is correct because both statements are true: fusion requires high temperatures to overcome Coulomb repulsion.

9 Easy

9 of 380

Understanding +4 | -1

Assertion: For an element generally

N \geq Z(N=

number of neutrons,

Z=

atomic number)
Reason: Neutrons always experience attractive nuclear force.

View answer and explanation

Correct option: B

If both Assertion and Reason are true, but Reason is not the correct explanation of Assertion

Option B (If both Assertion and Reason are true, but Reason is not the correct explanation of Assertion) is correct because both the assertion about neutron-proton ratio and the reason about attractive nuclear force are true, but the latter doesn't explain the former.

10 Medium

10 of 380

Application +4 | -1

Two radioactive elements

A

and

B

initially have same number of atoms. The half life of

A

is same as the average life of

B

. If

\lambda_A

and

\lambda_B

are decay constants of

A

and

B

respectively, then choose the correct relation from the given options.

View answer and explanation

Correct option: C

\lambda_A=\lambda_B \ln 2

Option C (

\lambda_A=\lambda_B \ln 2

) is correct because it relates the decay constants based on the given half-life and average life relationship.

11 Medium

11 of 380

Application +4 | -1

In an

\alpha -

decay, the kinetic energy of

\alpha -

particle is 48 MeV and Q value of the reaction is 50 MeV. The mass number of the mother nucleus is [assume that daughter nucleus is in ground state]

View answer and explanation

Correct option: B

100

Option B (100) is correct because the mass number of the mother nucleus can be calculated using the kinetic energy of the alpha particle and the Q value of the reaction.

12 Medium

12 of 380

Understanding +4 | -1

A free neutron decays into a proton, an electron and

View answer and explanation

Correct option: B

An antineutrino

Option B (An antineutrino) is correct because a free neutron decays into a proton, an electron, and an antineutrino to conserve lepton number.

13 Hard

13 of 380

Analyzing +4 | -1

Let

{A}_{{n}}

be the area enclosed by the

{n}

th orbit in a hydrogen atom. The graph of

\ln \left(\frac{{A_n}}{{A_1}}\right)

against

\ln {(n})

View answer and explanation

Correct option: A

Will pass through the origin

Option A (Will pass through the origin) is correct because the area enclosed by the nth orbit is proportional to n⁴, and the logarithmic relationship will pass through the origin.

14 Medium

14 of 380

Analyzing +4 | -1

Assertion: A free neutron decays to a proton but a free proton
does not decay to a neutron.
Reason: Neutron has larger rest mass than the proton.

View answer and explanation

Correct option: D

If both assertion and reason are false

Option D is correct. A free neutron decays into a proton, an electron, and an antineutrino. A free proton cannot decay into a neutron because it violates energy conservation. The neutron has a larger rest mass than the proton, so the reason is correct, but the assertion is false.

15 Medium

15 of 380

Application +4 | -1

In order to decrease radioactive nuclei to one million of its initial number, number of half – lives required is

View answer and explanation

Correct option: A

Option A (20) is correct because it takes 20 half-lives to reduce a radioactive sample to one millionth of its original amount.

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16 Easy

16 of 380

Understanding +4 | -1

Which of the following are suitable for the fusion process?

View answer and explanation

Correct option: A

Light nuclei.

Option A (Light nuclei) is correct because nuclear fusion involves combining light nuclei to form heavier ones, releasing energy.

17 Medium

17 of 380

Understanding +4 | -1

Statement-I: Nuclear forces arise from strong coulombic interactions between protons and neutrons.

Statement-II: Nuclear forces are independent of charge of the nucleons.

View answer and explanation

Correct option: D

Statement-I is false and Statement-II is true

Option D is correct because nuclear forces are not Coulombic and are independent of the charge of the nucleons.

18 Medium

18 of 380

Remembering +4 | -1

The element used for radioactive carbon dating for more than

\mathrm{56000 }\,\mathrm{yr}

View answer and explanation

Correct option: A

\mathrm{C - 14}

Option A (

\mathrm{C - 14}

) is correct because Carbon-14 is the isotope used for radioactive dating of organic materials up to around 50,000 years.

19 Easy

19 of 380

Understanding +4 | -1

F_{p p}, F_{n n}

and

F_{n p}

are the nuclear forces between proton -proton, neuron-neuron and neuron- proton respectively. Then relation between them is

View answer and explanation

Correct option: C

F_{p p}=F_{n n}=F_{n p}

Option C is correct because nuclear forces are charge-independent, meaning the force between any two nucleons (protons or neutrons) is the same.

20 Medium

20 of 380

Remembering +4 | -1

M

is the atomic mass and

A

is the mass number, packing fraction is given by

View answer and explanation

Correct option: B

\frac{{M - A}}{A}

The correct answer is B (

\frac{{M - A}}{A}

) because packing fraction is defined as the ratio of mass excess to the mass number.

21 Medium

21 of 380

Application +4 | -1

The radius

R

of a nucleus of mass number

A

can be estimated by the formula

R = (1.3 \times \mathrm{1}{\mathrm{0}^{ - 15}}){A^{1/3}}m.

It follows that the mass density of a nucleus is of the order of

({M_{proton}} \cong {M_{neutron}} \simeq 1.67 \times {10^{ - 27}}\mathrm{\,\,kg)}

View answer and explanation

Correct option: A

{10^{17}}\mathrm{\,\,kg}\,{\mathrm{m}^{ - 3}}

Option A (

{10^{17}}\mathrm{\ kg}\,{\mathrm{m}^{ - 3}}

) is correct because it is the approximate mass density of a nucleus, independent of the mass number A.

22 Medium

22 of 380

Remembering +4 | -1

Curie is a unit of

View answer and explanation

Correct option: C

Radioactivity

Option C (Radioactivity) is correct because Curie is the unit used to measure the radioactivity of a substance.

23 Medium

23 of 380

Remembering +4 | -1

According to law of conservation of energy and momentum for β-decay, the existence of a new particle along with electron was predicted, which was

View answer and explanation

Correct option: D

neutrino

Option D (neutrino) is correct because the neutrino's existence was predicted to conserve energy and momentum in beta decay.

24 Medium

24 of 380

Analyzing +4 | -1

Given the masses of various atomic particles

{m_p} = 1.0072\,u,\,\,\,\,{m_n} = 1.0087\,\,u,\,\,\,\,{m_e} = 0.000548\,\,u,\,\,\,\,{m_{\bar v}} = 0,\,\,\,\,{m_d} = 2.0141\,\,u,

Where

p

= proton,

n

= neutron,

e

= electron

\bar v =

antineutrino and

d

= deuteron. Which of the following process is allowed by momentum and energy conservation?

View answer and explanation

Correct option: C

n + p \to d + \bar v

Option B (

p \to n + {e^ + } + \bar v

) is correct because the mass of the proton is less than the combined mass of the neutron, positron, and antineutrino, thus violating energy conservation. Option D (

n + p \to d + \bar v

) is correct because the mass on the reactant side is greater than the product side.

25 Easy

25 of 380

Remembering +4 | -1

Which is used as a neutron absorber in nuclear
reactor:

View answer and explanation

Correct option: C

Cadmium

Option C (Cadmium) is correct because cadmium is commonly used as a neutron absorber in nuclear reactors to control the chain reaction.

26 Medium

26 of 380

Understanding +4 | -1

The mass density of a nucleus varies with mass number

\mathrm{A}

View answer and explanation

Correct option: C

\mathrm{A}^{0}

The correct answer is C (A⁰) because the mass density of a nucleus is approximately constant and independent of the mass number A.

27 Medium

27 of 380

Remembering +4 | -1

The penetrating powers of

\mathrm{\alpha },\,\,\mathrm{\beta }\,\,\mathrm{and}\,\,\mathrm{\gamma }

radiations, in decreasing order are

View answer and explanation

Correct option: B

\mathrm{\gamma },\,\,\mathrm{\beta },\,\,\mathrm{\alpha }

Option B (

\rm{{\gamma}},\,\rm{{\beta}},\,\rm{{\alpha }}

) is correct because gamma rays have the highest penetrating power, followed by beta particles, and then alpha particles.

28 Medium

28 of 380

Understanding +4 | -1

The correct relation between

t_{\mathrm{av}}=

average life and

t_{1 / 2}=

half life for a radioactive nuclei.

View answer and explanation

Correct option: C

0.693 t_{\mathrm{av}}=t_{1 / 2}

Option C (

0.693 t_{\mathrm{av}}=t_{1 / 2}

) is correct because it represents the relationship between average life and half-life derived from radioactive decay equations.

29 Medium

29 of 380

Understanding +4 | -1

A photon of

1.7 \times {10^{ - 13}}\;Joules

is absorbed by a material under special circumference. The correct statement is

View answer and explanation

Correct option: B

Electron and positron pair will be created

Option B (Electron and positron pair will be created) is correct because the energy of the photon is greater than 1.02 MeV, which is the minimum energy required for pair production.

30 Medium

30 of 380

Application +4 | -1

How many neutrons are more than protons in

_{92}{\mathrm{U}^{235}}

nucleus?

View answer and explanation

Correct option: C

Option C (51) is correct because it is the difference between the number of neutrons and protons in the Uranium nucleus.

Revision notes and key takeaways

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Key Takeaways

✓ This set contains 380 single-correct-answer MCQs on NUCLEI.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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