How many questions from Nuclei appear in JEE?

Nuclei has appeared in 116 of the last 186 JEE Main and JEE Advanced papers — about 62% of them — contributing 140 questions in total across those papers.

Is Nuclei an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 62% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Nuclei questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Nuclei JEE Previous Year Questions with Answers

Q1·PhysicsSingle correctJEE Advanced 2026

A nuclear reactor starts producing a radioactive nuclide

X

from

t = 0

, at a constant rate of

\alpha

per second. Each decay of

X

produces energy

E_{0}

, which is utilized to heat a liquid of mass

m

and specific heat

s

. Assuming no heat loss from the liquid and taking

\lambda

as the decay constant of

X

, the rate of increase in the temperature of the liquid is:

(A) $\frac{\alpha E_{0}}{ms}\left(1 - e^{-\lambda t}\right)$
(B) $\frac{\alpha E_{0}}{ms}\left(e^{\lambda t} - 1\right)$
(C) $\frac{\lambda E_{0}}{ms}\left(1 - e^{-\lambda t}\right)$
(D) $\frac{E_{0}}{ms}\left(\alpha - \lambda e^{-\lambda t}\right)$

Q2·PhysicsSingle correctJEE Main 2026

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous

\alpha

-decay with same

Q

value of 1 MeV. The ratio of energies of

\alpha

-rays produced by A and B is ________.

(A) $\dfrac{2548}{2650}$
(B) $\dfrac{2706}{2646}$
(C) $\dfrac{2597}{2600}$
(D) $\dfrac{2862}{2499}$

Q3·PhysicsNumericalJEE Main 2026

The energy released when

\frac{7}{17.13}

kg of

^{7}_{3}

Li is converted into

^{4}_{2}

He by proton bombardment is

\alpha \times 10^{32}

eV. The value of

\alpha

is _______. (Nearest integer) (Mass of

^{7}_{3}

Li = 7.0183 u, mass of

^{4}_{2}

He = 4.004 u, mass of proton = 1.008 u and 1 u = 931 MeV/c

^{2}

and Avogadro number =

6.0 \times 10^{23}

)

Q4·PhysicsSingle correctJEE Main 2026

The energy released if hydrogen atoms are combined to form

{}^{4}_{2}

He is __________ MeV. (Take binding energies per nucleon of

{}^{2}_{1}

H and

{}^{4}_{2}

He as 1.1 MeV and 7.2 MeV, respectively)

(A)6.1
(B)24.4
(C)26.6
(D)5

Q5·PhysicsSingle correctJEE Main 2026

Assuming the experimental mass of

^{12}_{6}C

as 12 u, the mass defect of

^{12}_{6}C

atom is ________ MeV/

c^2

. (Mass of proton

= 1.00727

u, mass of neutron

= 1.00866

u, 1 u

= 931.5

MeV/

c^2

and

c

is the speed of the light in vacuum).

(A)127.5
(B)89.03
(C)272.0
(D)92.0

Q6·PhysicsSingle correctJEE Main 2026

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10 . If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process,

\Delta Mc^2 =

_____ MeV.

(A)6.9
(B)7.9
(C)2.2
(D)4.3

Q7·PhysicsSingle correctJEE Main 2026

The binding energy per nucleon of

^{209}_{83}Bi

is ________ MeV.

[

Take

m(^{209}_{83}Bi) = 208.980388\,u

,

m_p = 1.007825\,u

,

m_n = 1.008665\,u

,

1\,u = 931\,\mathrm{MeV}/c^2]

(A)7.48
(B)7.84
(C)8.79
(D)6.94

Q8·PhysicsSingle correctJEE Main 2026

A nucleus has mass number α and radius

R_{\alpha}

. Another nucleus has mass number β and radius

R_{\beta}

. If β = 8α then

R_{\alpha}/R_{\beta}

is :

(A)2
(B)8
(C)1
(D)0.5

Q9·PhysicsSingle correctJEE Main 2026

Given below are two statements: Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon. Statement II : For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon. In the light of the above statements, choose the correct answer from the options given below:

(A)Both Statement I and Statement II are true
(B)Statement I is true but Statement II is false
(C)Both Statement I and Statement II are false
(D)Statement I is false but Statement II is true

Q10·PhysicsSingle correctJEE Main 2026

The binding energy for the following nuclear reactions are expressed in MeV.

_2\text{He}^3 + _0\text{n}^1 \rightarrow _2\text{He}^4 + 20

MeV

_2\text{He}^4 + _0\text{n}^1 \rightarrow _2\text{He}^5 - 0.9

MeV If

X_3

,

X_4

,

X_5

denote the stability of

_2\text{He}^3

,

_2\text{He}^4

and

_2\text{He}^5

, respectively, then the correct order is :

(A) $X_4 > X_5 > X_3$
(B) $X_4 = X_5 = X_3$
(C) $X_4 > X_5 < X_3$
(D) $X_4 < X_5 < X_3$

Q11·PhysicsNumericalJEE Main 2026

The average energy released per fission for the nucleus of

^{235}_{92}

U is 190 MeV. When all the atoms of 47 g pure

^{235}_{92}

U undergo fission process, the energy released is

\alpha \times 10^{23}

MeV. The value of α is ________. (Avogadro Number =

6 \times 10^{23}

per mole)

Q12·PhysicsSingle correctJEE Main 2026

Which of the following pair of nuclei are isobars of the element ?

(A) $^{2}_{1}\mathrm{H}$ and $^{3}_{1}\mathrm{H}$
(B) $^{236}_{92}\mathrm{U}$ and $^{238}_{92}\mathrm{U}$
(C) $^{198}_{80}\mathrm{Hg}$ and $^{197}_{79}\mathrm{Au}$
(D) $^{3}_{1}\mathrm{H}$ and $^{3}_{2}\mathrm{H}$

Q13·PhysicsSingle correctJEE Main 2026

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4α particles is ____ kHz. [mass of He nucleus = 4.002 amu, 1 amu =

1.66 \times 10^{-27}

kg, h =

6.6 \times 10^{-34}

J.s and c =

3 \times 10^{8}

m/s]

(A) $9 \times 10^{19}$
(B) $9 \times 10^{20}$
(C) $14.94 \times 10^{20}$
(D) $14.94 \times 10^{19}$

Q14·PhysicsSingle correctJEE Main 2025

For a nucleus of mass number

A

and radius

R

, the mass density of nucleus can be represented as:

(A) $A^{3}$
(B) $A^{1/3}$
(C) $A^{2/3}$
(D)Independent of $A$

Q15·PhysicsSingle correctJEE Main 2025

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The density of the copper

\left({}^{64}_{29}\mathrm{Cu}\right)

nucleus is greater than that of the carbon

\left({}^{12}_{6}\mathrm{C}\right)

nucleus. Reason (R): The nucleus of mass number A has a radius proportional to

A^{1/3}

. In the light of the above statements, choose the most appropriate answer from the options given below:

(A)(A) is correct but (R) is not correct
(B)(A) is not correct but (R) is correct
(C)Both (A) and (R) are correct and (R) is the correct explanation of (A)
(D)Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Q16·PhysicsSingle correctJEE Main 2025

A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents the time dependent mass of P, Q and R?

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q17·PhysicsSingle correctJEE Main 2025

Match the LIST-I (Nuclear / chemical reaction) with LIST-II (Type of reaction). Choose the correct answer from the options given below:

LIST-I (Nuclear / chemical reaction)	LIST-II (Type of reaction)
A. ${}^{1}_{0}n+{}^{235}_{92}U\to{}^{140}_{54}Xe+{}^{94}_{38}Sr+2{}^{1}_{0}n$	I.Chemical reaction
B. $2H_2+O_2\to 2H_2O$	II.Fusion with +ve Q value
C. ${}^{2}_{1}H+{}^{2}_{1}H\to{}^{3}_{2}He+{}^{1}_{0}n$	III.Fission
D. ${}^{1}_{1}H+{}^{3}_{1}H\to{}^{2}_{1}H+{}^{2}_{1}H$	IV.Fusion with -ve Q value

(A)(A)-II, (B)-I, (C)-III, (D)-IV
(B)(A)-III, (B)-I, (C)-II, (D)-IV
(C)(A)-II, (B)-I, (C)-IV, (D)-III
(D)(A)-III, (B)-I, (C)-IV, (D)-II

Q18·PhysicsSingle correctJEE Main 2025

Energy released when two deuterons

(_1H^2)

fuse to form a helium nucleus

(_2He^4)

is: (Given: Binding energy per nucleon of

_1H^2=1.1

MeV and binding energy per nucleon of

_2He^4=7.0

MeV)

(A)8.1 MeV
(B)5.9 MeV
(C)23.6 MeV
(D)26.8 MeV

Q19·PhysicsSingle correctJEE Main 2025

Choose the correct nuclear process from the below options [p: proton, n: neutron,

e^-

: electron,

e^+

: positron,

\nu

: neutrino,

\bar{\nu}

: antineutrino]

(A) $n\to p+e^-+\bar{\nu}$
(B) $n\to p+e^-+\nu$
(C) $n\to p+e^++\bar{\nu}$
(D) $n\to p+e^++\nu$

Q20·PhysicsSingle correctJEE Main 2025

A radioactive nucleus

n_2

has 3 times the decay constant as compared to the decay constant of another radioactive nucleus

n_1

. If initial number of both nuclei are the same, what is the ratio of number of nuclei of

n_2

to the number of nuclei of

n_1

, after one half-life of

n_1

?

(A) $\dfrac{1}{4}$
(B) $\dfrac{1}{8}$
(C)4
(D)8

Q21·PhysicsSingle correctJEE Main 2025

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170. Reason (R) : Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below :

(A)(A) is false but (R) is true
(B)(A) is true but (R) is false
(C)Both (A) and (R) are true and (R) is the correct explanation of (A)
(D)Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

Q22·PhysicsSingle correctJEE Main 2024

The energy released in the fusion of 2 kg of hydrogen deep in the sun is

E_{H}

and the energy released in the fission of 2 kg of

^{235}

U is

E_{U}

. The ratio

\dfrac{E_{H}}{E_{U}}

is approximately: (Consider the fusion reaction as

4\,^{1}_{1}H+2e^{-}\rightarrow\,^{4}_{2}He+2\nu+6\gamma+26.7

MeV; energy released in the fission reaction of

^{235}

U is 200 MeV per fission and

N_{A}=6.023\times10^{23}

)

(A)9.13
(B)5.04
(C)7.62
(D)25.6

Q23·PhysicsSingle correctJEE Main 2024

The energy equivalent of 1g of substance is:

(A) $11.2 \times 10^{24}$ MeV
(B) $5.6 \times 10^{12}$ MeV
(C)5.6 eV
(D) $5.6 \times 10^{26}$ MeV

Q24·PhysicsNumericalJEE Main 2024

A star has 100% helium composition. It starts to convert three

^{4}\mathrm{He}

into one

^{12}\mathrm{C}

via triple alpha process as

^{4}\mathrm{He}+{}^{4}\mathrm{He}+{}^{4}\mathrm{He}\to{}^{12}\mathrm{C}+Q

. The mass of the star is

2.0\times10^{32}

kg and it generates energy at the rate of

5.808\times10^{30}

W. The rate of converting these

^{4}\mathrm{He}

to

^{12}\mathrm{C}

is

n\times10^{42}\ \mathrm{s^{-1}}

, where

n

is ______. [Take, mass of

^{4}\mathrm{He}=4.0026

u, mass of

^{12}\mathrm{C}=12

u]

Q25·PhysicsSingle correctJEE Main 2024

In a hypothetical fission reaction

_{92}X^{236}\to\,_{56}Y^{141}+\,_{36}Z^{92}+3R

. The identity of emitted particles (R) is:

(A)Proton
(B)Electron
(C)Neutron
(D) $\gamma$ -radiations

Q26·PhysicsSingle correctJEE Main 2024

If

M_o

is the mass of isotope

_5^{12}B

,

M_p

and

M_n

are the masses of proton and neutron, then nuclear binding energy of the isotope is:

(A) $(5M_p+7M_n-M_o)C^2$
(B) $(M_o-5M_p)C^2$
(C) $(M_o-12M_n)C^2$
(D) $(M_o-5M_p-7M_n)C^2$

Q27·PhysicsSingle correctJEE Main 2024

Binding energy of a certain nucleus is

18\times10^8

J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

(A) $0.02\,\mu g$
(B) $20\,\mu g$
(C) $2\,\mu g$
(D) $10\,\mu g$

Q28·PhysicsNumericalJEE Main 2024

If three helium nuclei combine to form a carbon nucleus, then the energy released in this reaction is ___

\times10^{-2}

MeV. (Given

1\ \text{u} = 931\ \text{MeV}/c^2

; atomic mass of helium = 4.002603 u; mass of carbon-12 = 12 u.)

Q29·PhysicsNumericalJEE Main 2024

The disintegration energy Q for the nuclear fission of

^{235}\text{U}\to{}^{140}\text{Ce}+{}^{94}\text{Zr}+2n

is ______ MeV. Given atomic masses are:

^{235}\text{U}:235.0439\,u

,

^{140}\text{Ce}:139.9054\,u

,

^{94}\text{Zr}:93.9063\,u

,

n:1.00866\,u

. Value of

c^2=931\ \text{MeV/u}

.

Q30·PhysicsSingle correctJEE Main 2024

Which of the following nuclear fragments corresponding to nuclear fission between neutron

({}^1_0n)

and uranium isotope

({}^{235}_{92}U)

is correct:

(A) ${}^{144}_{56}Ba+{}^{89}_{36}Kr+4{}^1_0n$
(B) ${}^{140}_{54}Xe+{}^{94}_{38}Sr+3{}^1_0n$
(C) ${}^{153}_{51}Sb+{}^{99}_{41}Nb+3{}^1_0n$
(D) ${}^{144}_{56}Ba+{}^{89}_{36}Kr+3{}^1_0n$

Q31·PhysicsNumericalJEE Main 2024

The radius of a nucleus of mass number

64

is

4.8

fermi. Then the mass number of another nucleus having radius of

4

fermi is

\dfrac{1000}{x}

, where

x

is ___

Q32·PhysicsSingle correctJEE Main 2024

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:

(A)24
(B)32
(C)40
(D)20

Q33·PhysicsNumericalJEE Main 2024

The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is

n\times10^7

kWh, where

n=

______. (speed of light =

3\times10^8

m/s)

Q34·PhysicsNumericalJEE Main 2024

A nucleus has mass number

A_1

and volume

V_1

. Another nucleus has mass number

A_2

and volume

V_2

. If relation between mass number is

A_2=4A_1

, then

\dfrac{V_2}{V_1}=

______.

Q35·PhysicsSingle correctJEE Main 2024

In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect

\Delta M

will be:

(A) $\sqrt{\dfrac{2c\Delta M}{M}}$
(B) $\dfrac{\Delta Mc^2}{3}$
(C) $c\sqrt{\dfrac{2\Delta M}{M}}$
(D) $c\sqrt{\dfrac{3\Delta M}{M}}$

Q36·PhysicsSingle correctJEE Main 2024

The explosive in a Hydrogen bomb is a mixture of

_1H^2

,

_1H^3

and

_3Li^6

in some condensed form. The chain reaction is given by

_3Li^6+_0n^1\to{}_2He^4+_1H^3

;

_1H^2+_1H^3\to{}_2He^4+_0n^1

. During the explosion the energy released is approximately [Given : M(

_3Li^6

) = 6.01690 amu. M(

_1H^2

) = 2.01471 amu. M(

_2He^4

) = 4.00388 amu, and 1 amu = 931.5 MeV]

(A) $28.12$ MeV
(B) $12.64$ MeV
(C) $16.48$ MeV
(D) $22.22$ MeV

Q37·PhysicsNumericalJEE Main 2024

In a nuclear fission process, a high mass nuclide (

A\approx 236

) with binding energy 7.6 MeV/Nucleon dissociated into middle mass nuclides (

A\approx 118

), having binding energy of 8.6 MeV/Nucleon. The energy released in the process would be __________ MeV.

Q38·PhysicsSingle correctJEE Main 2024

The atomic mass of

_6\text{C}^{12}

is 12.000000 u and that of

_6\text{C}^{13}

is 13.003354 u. The required energy to remove a neutron from

_6\text{C}^{13}

, if mass of neutron is 1.008665 u, will be :

(A)62.5 MeV
(B)6.25 MeV
(C)4.95 MeV
(D)49.5 MeV

Q39·PhysicsIntegerJEE Advanced 2023

In a radioactive decay process, the activity is defined as

A = -\frac{dN}{dt}

, where N(t) is the number of radioactive nuclei at time t. Two radioactive sources,

S_1

and

S_2

have same activity at time

t

= 0. At a later time, the activities of

S_1

and

S_2

are

A_1

and

A_2

, respectively. When

S_1

and

S_2

have just completed their 3

^{rd}

and 7

^{th}

half-lives, respectively, the ratio

A_1/A_2

is ___________.

Q40·PhysicsSingle correctJEE Advanced 2023

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.

List-I	List-II
P. ${}^{238}_{92}\mathrm{U} \rightarrow {}^{234}_{91}\mathrm{Pa}$	1.one $\alpha$ particle and one $\beta^{+}$ particle
Q. ${}^{214}_{82}\mathrm{Pb} \rightarrow {}^{210}_{82}\mathrm{Pb}$	2.three $\beta^{-}$ particles and one $\alpha$ particle
R. ${}^{210}_{81}\mathrm{T}\ell \rightarrow {}^{206}_{82}\mathrm{Pb}$	3.two $\beta^{-}$ particles and one $\alpha$ particle
S. ${}^{228}_{91}\mathrm{Pa} \rightarrow {}^{224}_{88}\mathrm{Ra}$	4.one $\alpha$ particle and one $\beta^{-}$ particle
	5.one $\alpha$ particle and two $\beta^{+}$ particles

(A)P $\rightarrow$ 4, Q $\rightarrow$ 3, R $\rightarrow$ 2, S $\rightarrow$ 1
(B)P $\rightarrow$ 4, Q $\rightarrow$ 1, R $\rightarrow$ 2, S $\rightarrow$ 5
(C)P $\rightarrow$ 5, Q $\rightarrow$ 3, R $\rightarrow$ 1, S $\rightarrow$ 4
(D)P $\rightarrow$ 5, Q $\rightarrow$ 1, R $\rightarrow$ 3, S $\rightarrow$ 2

Q41·PhysicsSingle correctJEE Main 2023

The half-life of a radioactive nucleus is 5 years, The fraction of the original sample that would decay in 15 years is :

(A) $\frac{1}{8}$
(B) $\frac{1}{4}$
(C) $\frac{7}{8}$
(D) $\frac{3}{4}$

Q42·PhysicsSingle correctJEE Main 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170. Reason R: Nuclear force is short ranged. In the light of the above statements, choose the correct answer from the options given below

(A)Both A and R are true but R is NOT the correct explanation of A
(B)A is true but R is false
(C)A is false but R is true
(D)Both A and R are true and R is the correct explanation of A

Q43·PhysicsSingle correctJEE Main 2023

^{238}_{92}U\to ^{234}_{90}\!Th+^{4}_{2}\!D+Q

. In the above nuclear reaction, the approximate amount of energy released will be: [Given, mass of

^{238}_{92}U=238.05079\times 931.5\,MeV/c^{2}

, mass of

^{234}_{90}Th=234.04363\times 931.5\,MeV/c^{2}

, mass of

^{4}_{2}D=4.00260\times 931.5\,MeV/c^{2}

]

(A) $3.82\,MeV$
(B) $5.9\,MeV$
(C) $2.12\,MeV$
(D) $4.25\,MeV$

Q44·PhysicsNumericalJEE Main 2023

Consider an example of alpha decay

_{92}^{238}U\rightarrow{}_{90}^{234}Th+{}_2^4He+Q

. Given:

_{92}^{238}U=238.05060u

,

_{90}^{234}Th=234.04360u

,

_2^4He=4.00260u

, and

1u=931.5\,\dfrac{MeV}{c^2}

. The energy released (Q) during the alpha decay of

_{92}^{238}U

is _________ MeV.

Q45·PhysicsSingle correctJEE Main 2023

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.

(A) $\lambda_A = \lambda_B$
(B) $\lambda_A = 2\lambda_B$
(C) $\lambda_A = \lambda_B \ln 2$
(D) $\lambda_A \ln 2 = \lambda_B$

Q46·PhysicsNumericalJEE Main 2023

A nucleus disintegrates into two nuclear parts, in such a way that the ratio of their nuclear sizes is

1:2^{1/3}

. Their respective speeds have a ratio of

n:1

. The value of n is ____.

Q47·PhysicsSingle correctJEE Main 2023

The half-life of a radioactive substance is T. The time taken for disintegrating

\tfrac{7}{8}

th part of its original mass will be:

(A) $3T$
(B) $8T$
(C) $T$
(D) $2T$

Q48·PhysicsNumericalJEE Main 2023

The decay constant for a radioactive nuclide is

1.5\times10^{-5}

s

^{-1}

. Atomic weight of the substance is 60 g mole

^{-1}

,

(N_A=6\times10^{23})

. The activity of 1.0 µg of the substance is _________

\times10^{10}

Bq.

Q49·PhysicsSingle correctJEE Main 2023

A radioactive material is reduced to

\dfrac{1}{8}

of its original amount in 3 days. If

8\times10^{-3}

kg of the material is left after 5 days, the initial amount of the material is

(A)64 g
(B)40 g
(C)32 g
(D)256 g

Q50·PhysicsNumericalJEE Main 2023

A nucleus with mass number 242 and binding energy per nucleon as

7.6\,\text{MeV}

breaks into fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as

8.1\,\text{MeV}

, the total gain in binding energy is ______

\text{MeV}

Q51·PhysicsSingle correctJEE Main 2023

For a nucleus

^{A}_{Z}X

having mass number A and atomic number Z: A. The surface energy per nucleon

(b_{s}) = a_{1}A^{2/3}

. B. The Coulomb contribution to the binding energy

b_{c} = -a_{2}\dfrac{Z(Z-1)}{A^{4/3}}

. C. The volume energy

b_{v} = a_{3}A

. D. Decrease in the binding energy is proportional to surface area. E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons,

(a_{1}, a_{2}

and

a_{3}

are constants). Choose the most appropriate answer from the options given below:

(A)C, D only
(B)B, C, E only
(C)A, B, C, D only
(D)B, C only

Q52·PhysicsSingle correctJEE Main 2023

The mass of proton, neutron and helium nucleus are respectively

1.0073u

,

1.0087u

and

4.0015u

. The binding energy of helium nucleus is:

(A) $28.4$ MeV
(B) $56.8$ MeV
(C) $14.2$ MeV
(D) $7.1$ MeV

Q53·PhysicsNumericalJEE Main 2023

Nucleus A having

Z=17

and equal number of protons and neutrons has

1.2

MeV binding energy per nucleon. Another nucleus B of

Z=12

has total

26

nucleons and

1.8

MeV binding energy per nucleons. The difference of binding energy of B and A will be _________ MeV.

Q54·PhysicsSingle correctJEE Main 2023

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

(A)proton is a charged particle
(B)neutron is an uncharged particle
(C)neutron is a composite particle made of a proton and an electron
(D)neutron has larger rest mass than proton

Q55·PhysicsNumericalJEE Main 2023

A radioactive nucleus decays by two different processes. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be

\dfrac{\alpha}{11}

s. The value of

\alpha

is _______.

Q56·PhysicsSingle correctJEE Main 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The nuclear density of nuclides

^{10}_{5}B

,

^{6}_{3}Li

,

^{56}_{26}Fe

,

^{20}_{10}Ne

and

^{209}_{83}Bi

can be arranged as

\rho^{N}_{Bi}>\rho^{N}_{Fe}>\rho^{N}_{Ne}>\rho^{N}_{B}>\rho^{N}_{Li}

. Reason R: The radius R of a nucleus is related to its mass number A as

R=R_0 A^{1/3}

, where

R_0

is a constant. In the light of the above statements, choose the correct answer from the options given below:

(A)A is false but R is true
(B)A is true but R is false
(C)Both A and R are true but R is NOT the correct explanation of A
(D)Both A and R are true and R is the correct explanation of A

Q57·PhysicsNumericalJEE Main 2023

A radioactive element

_{92}^{242}X

emits two

\alpha

-particles, one electron and two positrons. The product nucleus is represented by

_{P}^{234}Y

. The value of

P

is ________ .

Q58·PhysicsSingle correctJEE Main 2023

If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min will be:

(A) $\dfrac{1}{8}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{1}{4}$
(D) $\dfrac{1}{16}$

Q59·PhysicsSingle correctJEE Main 2023

Substance

A

has atomic mass number

16

and half-life of

1

day. Another substance

B

has atomic mass number

32

and half life of

\dfrac12

day. If both

A

and

B

simultaneously start undergo radio activity at the same time with initial mass

320\,g

each, how many total atoms of

A

and

B

combined would be left after

2

days.

(A) $3.38\times10^{24}$
(B) $1.69\times10^{24}$
(C) $6.76\times10^{24}$
(D) $6.76\times10^{23}$

Q60·PhysicsSingle correctJEE Main 2023

The ratio of the density of oxygen nucleus (

^{16}_{8}O

) and helium nucleus (

^{4}_{2}He

) is:

(A) $4:1$
(B) $2:1$
(C) $1:1$
(D) $8:1$

Q61·PhysicsNumericalJEE Main 2023

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio

3:2

. The ratio of their nuclear sizes will be

\left(\frac{x}{3}\right)^{\frac{1}{3}}

. The value of '

x

' is:

Q62·PhysicsSingle correctJEE Main 2023

Consider the following radioactive decay process:

{}^{218}_{84}A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^-} A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^+} A_5 \xrightarrow{\gamma} A_6

. The mass number and the atomic number of

A_6

are given by:

(A)210 and 84
(B)210 and 82
(C)211 and 80
(D)210 and 80

Q63·PhysicsNumericalJEE Main 2023

Assume that protons and neutrons have equal masses. Mass of a nucleon is

1.6\times10^{-27}

kg and radius of nucleus is

1.5\times10^{-15}A^{1/3}

m. The approximate ratio of the nuclear density and water density is

n\times10^{13}

. The value of

n

is _______ .

Q64·PhysicsNumericalJEE Main 2023

The energy released per fission of nucleus of

^{240}X

is

200

MeV. The energy released if all the atoms in

120

g of pure

^{240}X

undergo fission is _________

\times10^{25}

MeV (Given

N_A=6\times10^{23}

)

Q65·PhysicsNumericalJEE Advanced 2022

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction

^{16}_{7}N + ^{4}_{2}He \rightarrow ^{1}_{1}H + ^{19}_{8}O

in a laboratory frame is n (in MeV). Assume that

^{16}_{7}N

is at rest in the laboratory frame. The masses of

^{16}_{7}N

,

^{4}_{2}He

,

^{1}_{1}H

and

^{19}_{8}O

can be taken to be 16.006 u, 4.003 u, 1.008 u and 19.003 u, respectively, where 1 u = 930 MeVc

^{-2}

. The value of n is __________.

Q66·PhysicsIntegerJEE Advanced 2022

In a radioactive decay chain reaction,

^{230}_{90}Th

nucleus decays into

^{214}_{84}Po

nucleus. The ratio of the number of α to number of β

^{-}

particles emitted in this process is__________

Q67·PhysicsMultiple correctJEE Advanced 2022

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be

E_b^p

and the binding energy of a neutron be

E_b^n

in the nucleus. Which of the following statement(s) is(are) correct?

(A) $E_b^p - E_b^n$ is proportional to $Z(Z-1)$ where Z is the atomic number of the nucleus.
(B) $E_b^p - E_b^n$ is proportional to $A^{-\frac{1}{3}}$ where A is the mass number of the nucleus.
(C) $E_b^p - E_b^n$ is positive.
(D) $E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.

Q68·PhysicsSingle correctJEE Main 2022

Read the following statements: (A) Volume of the nucleus is directly proportional to the mass number. (B) Volume of the nucleus is independent of mass number. (C) Density of the nucleus is directly proportional to the mass number. (D) Density of the nucleus is directly proportional to the cube root of the mass number. (E) Density of the nucleus is independent of the mass number. Choose the correct option from the following options.

(A)(A) and (D) only.
(B)(A) and (E) only.
(C)(B) and (E) only.
(D)(A) and (C) only

Q69·PhysicsNumericalJEE Main 2022

Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time

\frac{1}{a\lambda}

. The value of a is________.

Q70·PhysicsNumericalJEE Main 2022

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be ________ hours.

Q71·PhysicsSingle correctJEE Main 2022

The half life period of a radioactive substance is 60 days. The time taken for

\frac{7}{8}

th of its original mass to disintegrate will be :

(A)120 days
(B)130 days
(C)180 days
(D)20 days

Q72·PhysicsSingle correctJEE Main 2022

What is the half-life period of a radioactive material if its activity drops to

1/16^{\text{th}}

of its initial value of 30 years ?

(A)9.5 years
(B)8.5 years
(C)7.5 years
(D)10.5 years

Q73·PhysicsSingle correctJEE Main 2022

The activity of a radioactive material is

6.4 \times 10^{-4}

curie. Its half life is 5 days. The activity will become

5 \times 10^{-6}

curie after :

(A)7 days
(B)15 days
(C)25 days
(D)35 days

Q74·PhysicsSingle correctJEE Main 2022

Mass numbers of two nuclei are in the ratio of 4:3. Their nuclear densities will be in the ratio of

(A)4:3
(B) $\left(\frac{3}{4}\right)^{\frac{1}{3}}$
(C)1 : 1
(D) $\left(\frac{4}{3}\right)^{\frac{1}{3}}$

Q75·PhysicsNumericalJEE Main 2022

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:

^{2}_{1}X + {}^{2}_{1}X = {}^{4}_{2}Y

The binding energies per nucleon

^{2}_{1}X

and

^{4}_{2}Y

are 1.1 MeV and 7.6 MeV respectively. The energy released in this process is________ . MeV.

Q76·PhysicsSingle correctJEE Main 2022

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is : (Take log

_{10}

1.88 = 0.274)

(A)0.02 min $^{-1}$
(B)2.7 min $^{-1}$
(C)0.063 min $^{-1}$
(D)6.3 min $^{-1}$

Q77·PhysicsSingle correctJEE Main 2022

The activity of a radioactive material is

2.56 \times 10^{-3}

Ci. If the half life of the material is 5 days, after how many days the activity will become

2 \times 10^{-5}

Ci?

(A)30 days
(B)35 days
(C)40 days
(D)25 days

Q78·PhysicsSingle correctJEE Main 2022

In the following nuclear rection,

D \xrightarrow{\ \alpha\ } D_1 \xrightarrow{\ \beta^-\ } D_2 \xrightarrow{\ \alpha\ } D_3 \xrightarrow{\ \gamma\ } D_4

Mass number of D is 182 and atomic number is 74. Mass number and atomic number of

D_4

respectively will be____.

(A)174 and 71
(B)174 and 69
(C)172 and 69
(D)172 and 71

Q79·PhysicsNumericalJEE Main 2022

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gest reduced to 6.25% of its initial value of x is ________.

Q80·PhysicsSingle correctJEE Main 2022

The Q-value of a nuclear reaction and kinetic energy of the projectile particle,

K_{p}

are related as :

(A) $Q = K_{p}$
(B) $(K_{p} + Q) < O$
(C) $Q < K_{p}$
(D) $(K_{p} + Q) > 0$

Q81·PhysicsSingle correctJEE Main 2022

Following statements related to radioactivity are given below: (A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions. (B) The number of un–decayed nuclei in the radioactive sample decays exponentially with time. (C) Slope of the graph of log

_e

(no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ). (D) Product of decay constant (λ) and half–life time (T

_{1/2}

) is not constant. Choose the most appropriate answer from the options given below:

(A)(A) and (B) only
(B)(B) and (D) only
(C)(B) and (C) only
(D)(C) and (D) only

Q82·PhysicsSingle correctJEE Main 2022

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half- life of the nucleus will be :

(A)3.75 hours
(B)0.56 hours
(C)0.26 hours
(D)1.80 hours

Q83·PhysicsSingle correctJEE Main 2022

How many alpha and beta particles are emitted when Uranium

_{92}U^{238}

decays to lead

_{82}Pb^{206}

?

(A)3 alpha particles and 5 beta particles
(B)6 alpha particles and 4 beta particles
(C)4 alpha particles and 5 beta particles
(D)8 alpha particles and 6 beta particles

Q84·PhysicsSingle correctJEE Main 2022

Which of the following figure represents the variation of

\ln\left(\frac{R}{R_0}\right)

with ln A(If R = radius of a nucleus and A = its mass number)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q85·PhysicsSingle correctJEE Main 2022

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :

(A)0.8 MeV
(B)275 MeV
(C)220 MeV
(D)176 MeV

Q86·PhysicsNumericalJEE Main 2022

A sample contains 10

^{-2}

kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of then atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is

\dfrac{x}{100}

. the value of x is ______.

Q87·PhysicsMultiple correctJEE Advanced 2021

A heavy nucleus

N

, at rest, undergoes fission

N \rightarrow P + Q

, where

P

and

Q

are two lighter nuclei. Let

\delta = M_N - M_P - M_Q

, where

M_P

,

M_Q

and

M_N

are the masses of

P

,

Q

and

N

, respectively.

E_P

and

E_Q

are the kinetic energies of

P

and

Q

, respectively. The speed of

P

and

Q

are

v_P

and

v_Q

, respectively. If

c

is the speed of light, which of the following statement(s) is(are) correct ?

(A) $E_P + E_Q = c^2 \delta$
(B) $E_P = \left( \frac{M_P}{M_P + M_Q} \right) c^2 \delta$
(C) $\frac{v_P}{v_Q} = \frac{M_Q}{M_P}$
(D)The magnitude of momentum for $P$ as well as $Q$ is $c\sqrt{2\mu\delta}$ , where $\mu = \frac{M_P M_Q}{\left( M_P + M_Q \right)}$

Q88·PhysicsSingle correctJEE Advanced 2021

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

(A)50
(B)75
(C)350
(D)525

Q89·PhysicsSingle correctJEE Main 2021

The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :

(A)x–will decay faster than y.
(B)y– will decay faster than x.
(C)x and y have same decay rate initially and later on different decay rate.
(D)x and y decay at the same rate always.

Q90·PhysicsSingle correctJEE Main 2021

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B vesus time is : (Assume that at t = 0, there are no B atoms in the sample)

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q91·PhysicsSingle correctJEE Main 2021

There are

10^{10}

radioactive nuclei in a given radioactive element, Its half-life time is 1 minute. How many nuclei will remain after 30 seconds ?

\left(\sqrt{2} = 1.414\right)

(A) $2 \times 10^{10}$
(B) $7 \times 10^{9}$
(C) $10^{5}$
(D) $4 \times 10^{10}$

Q92·PhysicsSingle correctJEE Main 2021

At time t = 0, a material is composed of two radioactive atoms A and B, where

N_{A}(0) = 2N_{B}(0)

. The decay constant of both kind of radioactive atoms is

\lambda

. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of

N_{B}(t)

/

N_{B}(0)

with respect to time t ?

\left[\begin{array}{l} N_{A}\left(0\right) = \text{No. of A atoms at } t = 0 \\\\ N_{B}\left(0\right) = \text{No. of B atoms at } t = 0 \end{array}\right]

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q93·PhysicsNumericalJEE Main 2021

A radioactive sample has an average life of 30ms and is decaying. A capacitor of capacitance 200 μF is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be ____ Ω .

Q94·PhysicsSingle correctJEE Main 2021

If 'f' denotes the ratio of the number of nuclei decayed (

N_d

) to the number of nuclei at t = 0 (

N_0

) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as : [ λ is the radioactive decay constant ]

(A) $\lambda e^{-\lambda t}$
(B) $\lambda\left(1-e^{-\lambda t}\right)$
(C) $-\lambda\left(1-e^{-\lambda t}\right)$
(D) $-\lambda e^{-\lambda t}$

Q95·PhysicsSingle correctJEE Main 2021

Consider the following statements : (A) Atoms of each element emit characteristics spectrum. (B) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. (C) The density of nuclear matter depends on the size of the nucleus. (D) A free neutron is stable but a free proton decay is possible. (E) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below :

(A)B and D only
(B)A, C and E only
(C)A, B, C, D and E
(D)A, B and E only

Q96·PhysicsNumericalJEE Main 2021

The nuclear activity of a radioactive element becomes

\left(\frac{1}{8}\right)^{\text{th}}

of its initial value in 30 years. The half –life of radioactive element is ________ years.

Q97·PhysicsNumericalJEE Main 2021

From the given data, the amount of energy required to break the nucleus of aluminium

^{27}_{13}\text{Al}

is ________

x \times 10^{-3}

J. Mass of neutron = 1.00866u Mass of proton = 1.00726 u Mass of Aluminium nucleus = 27.18846 u (Assume 1 u corresponds to x J of energy) (Round off to the nearest integer)

Q98·PhysicsSingle correctJEE Main 2021

The half-life of

^{198}

Au is 3 days. If atomic weight of

^{198}

Au is 198 g /mol then the activity of 2 mg of

^{198}

Au is [ in disintegration / second ] :

(A) $6.06 \times 10^{18}$
(B) $2.67 \times 10^{12}$
(C) $16.18 \times 10^{12}$
(D) $32.36 \times 10^{12}$

Q99·PhysicsSingle correctJEE Main 2021

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as : (where

\lambda

is the decay constant)

(A) $\frac{\ell n \frac{3}{2}}{\lambda}$
(B) $\frac{\ell n 2}{\lambda}$
(C) $\frac{2 \ell n 2}{\lambda}$
(D) $\frac{1}{2}\ \frac{\ell n 2}{\lambda}$

Q100·PhysicsSingle correctJEE Main 2021

A nucleus with number 184 initially at rest emits an

\alpha-

particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the

\alpha-

particle.

(A)5.5 MeV
(B)5.38 MeV
(C)5.0 MeV
(D)0.12 MeV

Q101·PhysicsSingle correctJEE Main 2021

For a certain radioactive process the graph between

\ell n(R)

and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately :

(A)2.62 sec
(B)9.15 sec
(C)4.62 sec
(D)6.93 sec

Q102·PhysicsNumericalJEE Main 2021

A radioactive substance decays to

\left(\frac{1}{16}\right)^{th}

of this initial activity in 80 days. The half life of the radioactive substance expressed in days is ____________.

Q103·PhysicsSingle correctJEE Main 2021

A nucleus of mass M emits γ − ray photon of frequency 'ν'. The loss of internal energy by the nucleus is : [Take 'c' as the speed of electromagnetic wave ]

(A) $h\nu\left[1+\frac{h\nu}{2Mc^2}\right]$
(B)0
(C) $h\nu\left[1-\frac{h\nu}{2Mc^2}\right]$
(D) $h\nu$

Q104·PhysicsSingle correctJEE Main 2021

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains? (Take ln 3 = 1.1)

(A)340 years
(B)1110 years
(C)700 years
(D)740 years

Q105·PhysicsSingle correctJEE Main 2021

The decay of a proton to neutron is :

(A)not possible as proton mass is less than the neutron mass
(B)possible only inside the nucleus
(C)not possible but neutron to proton conversion is possible
(D)always possible as it is associated only with β $^{+}$ decay

Q106·PhysicsSingle correctJEE Main 2021

A radioactive sample disintegrates via two independent decay processes having half lives

T_{1/2}^{(1)}

and

T_{1/2}^{(2)}

respectively. The effective half-life

T_{1/2}

of the nuclei is :

(A)None of the above
(B) $T_{1/2} = T_{1/2}^{(1)} + T_{1/2}^{(2)}$
(C) $T_{1/2} = \dfrac{T_{1/2}^{(1)}T_{1/2}^{(2)}}{T_{1/2}^{(1)} + T_{1/2}^{(2)}}$
(D) $T_{1/2} = \dfrac{T_{1/2}^{(1)} + T_{1/2}^{(2)}}{T_{1/2}^{(1)} - T_{1/2}^{(2)}}$

Q107·PhysicsSingle correctJEE Main 2021

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.

(A)60 minutes
(B)20 minutes
(C)40 minutes
(D)13 minutes

Q108·PhysicsSingle correctJEE Main 2021

The half-life of Au

^{198}

is 2.7 days. The activity of 1.50 mg of Au

^{198}

if its atomic weight is 198 g mol

^{-1}

is, (N

_{A}

= 6 × 10

^{23}

/mol)

(A)240 Ci
(B)357 Ci
(C)535 Ci
(D)252 Ci

Q109·PhysicsSingle correctJEE Main 2021

A radioactive sample is undergoing α decay. At any time t

_{1}

, its activity is A and another time t

_{2}

, the activity is

\frac{A}{5}

. What is the average life time for the sample?

(A) $\frac{t_{2}-t_{1}}{\ln 5}$
(B) $\frac{\ln\left(t_{2}+t_{1}\right)}{2}$
(C) $\frac{t_{1}-t_{2}}{\ln 5}$
(D) $\frac{\ln 5}{t_{2}-t_{1}}$

Q110·PhysicsSingle correctJEE Main 2021

Two radioactive substances X and Y originally have

N_1

and

N_2

nuclei respectively. Half life of X is half of the half life of Y. After there half lives of Y, number of nuclei of both are equal. The ratio

\dfrac{N_1}{N_2}

will be equal to :

(A) $\dfrac{8}{1}$
(B) $\dfrac{1}{8}$
(C) $\dfrac{3}{1}$
(D) $\dfrac{1}{3}$

Q111·PhysicsSingle correctJEE Main 2020

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?

(A)n + n → deuterium atom (electron bound to the nucleus)
(B) $p → n + e^{+} + \bar{v}$
(C) $n + p → d + γ$
(D) $e^{+} + e^{-} → γ$

Q112·PhysicsSingle correctJEE Main 2020

You are given that Mass of

^7_2\text{Li} = 7.0160\text{u}

Mass of

^4_2\text{He} = 4.0026\text{u}

and

^1_1\text{H} = 1.0079\text{u}

. When 20 g of

^7_3\text{Li}

is converted into

^4_2\text{He}

by proton capture, the energy liberated, (in kWh), is [Mass of nucleon

=\dfrac{1\text{Gev}}{c^2}

]

(A) $4.5\times10^5$
(B) $8\times10^6$
(C) $6.82\times10^5$
(D) $1.33\times10^6$

Q113·PhysicsSingle correctJEE Main 2020

Activities of three radioactive substances A, B and C are represented by the curves A, B and C in the figure. Then their half lives

T_{1/2}(A) : T_{1/2}(B) : T_{1/2}(C)

are in the radio:

(A)3:2:1
(B)2:1:3
(C)4:3:1
(D)2:1:1

Q114·PhysicsSingle correctJEE Main 2020

A radioactive nucleus decays by two difference processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is closes to:

(A)6 sec.
(B)9 sec.
(C)12 sec.
(D)55 sec.

Q115·PhysicsSingle correctJEE Main 2020

In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is

(A) $\frac{3}{5}$
(B) $\frac{3}{4}$
(C) $\frac{7}{8}$
(D) $\frac{4}{5}$

Q116·PhysicsSingle correctJEE Main 2020

The radius R of a nucleus of mass number A can be estimated by the formula

R=\left(1.3\times 10^{-15}\right)A^{1/3}m

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

\left(M_{prot}=M_{neut.}\simeq 1.67\times 10^{-27}\,kg\right)

(A) $10^{3}kg\ m^{-3}$
(B) $10^{17}\,kg\ m^{-3}$
(C) $10^{10}\,kg\ m^{-3}$
(D) $10^{24}\,kg\ m^{-3}$

Q117·PhysicsSingle correctJEE Main 2020

The activity of a radioactive sample falls from 700 s

^{-1}

to 500 s

^{-1}

in 30 minutes. Its half life is close to

(A)66 min
(B)52 min
(C)62 min
(D)72 min

Q118·PhysicsSingle correctJEE Advanced 2019

In a radioactive sample

^{40}_{19}

K nuclei either decay into stable

^{40}_{20}

Ca nuclei with decay constant 4.5 ×

10^{-10}

per year or into stable

^{40}_{18}

Ar nuclei with decay constant

0.5 \times 10^{-10}

per year. Given that in this sample all the stable

^{40}_{20}

Ca and

^{40}_{18}

Ar nuclei are produced by the

^{40}_{19}

K nuclei only. In time t ×

10^9

years, if the ratio of the sum of stable

^{40}_{20}

Ca and

^{40}_{18}

Ar nuclei to the radioactive

^{40}_{19}

K nuclei is 99, the value of t will be [Given : ln10 = 2.3]

(A)1.15
(B)4.6
(C)9.2
(D)2.3

Q119·PhysicsNumericalJEE Advanced 2019

Suppose a

^{226}_{88}\mathrm{Ra}

nucleus at rest and in ground state undergoes

\alpha

-decay to a

^{222}_{86}\mathrm{Rn}

nucleus in its excited state. The kinetic energy of the emitted

\alpha

particle is found to be 4.44 MeV.

^{222}_{86}\mathrm{Rn}

nucleus then goes to its ground state by

\gamma

-decay. The energy of the emitted

\gamma

photon is ______keV. [Given: atomic mass of

^{226}_{88}\mathrm{Ra}

= 226.005 u, atomic mass of

^{222}_{86}\mathrm{Rn}

= 222.000 u, atomic mass of

\alpha

particle = 4.000 u, 1 u = 931 MeV/

c^2

, c is speed of the light]

Q120·PhysicsSingle correctJEE Main 2019

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :

(A)9 : 8
(B)1 : 8
(C)8 : 1
(D)3 : 8

Q121·PhysicsSingle correctJEE Main 2019

Two radioactive materials A and B have decay constants

10\lambda

and

\lambda

, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of B will be 1/e after a time:

(A) $\dfrac{1}{11\lambda}$
(B) $\dfrac{1}{10\lambda}$
(C) $\dfrac{1}{9\lambda}$
(D) $\dfrac{11}{10\lambda}$

Q122·PhysicsSingle correctJEE Main 2019

Two radioactive substances A and B have decay constants 5λ and λ respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become

\left(\dfrac{1}{e}\right)^{2}

will be

(A)1/λ
(B)1/4λ
(C)2/λ
(D)1/2λ

Q123·PhysicsSingle correctJEE Main 2019

The ratio of mass densities of nuclei of

^{40}C_a

and

^{16}O

is close to:

(A)0.1
(B)5
(C)2
(D)1

Q124·PhysicsSingle correctJEE Main 2019

In a radioactive decay chain, the initial nucleus is

_{90}^{232}\text{Th}

. At the end there are 6 α-particles and 4 β-particles with are emitted. If the end nucleus is

_{Z}^{A}X

, A and Z are given by :

(A)A = 208; Z = 80
(B)A = 202; Z = 80
(C)A = 208; Z = 82
(D)A = 200; Z = 81

Q125·PhysicsSingle correctJEE Main 2019

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to:

(A)200
(B)150
(C)400
(D)360

Q126·PhysicsSingle correctJEE Main 2019

A sample of radioactive material A, that has an activity of 10 mCi (1 Ci =

3.7 \times 10^{10}

decays/s), has twice the number of nuclei as another sample of different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively:

(A)5 days and 10 days
(B)10 days and 40 days
(C)20 days and 5 days
(D)20 days and 10 days

Q127·PhysicsSingle correctJEE Main 2019

At a given instant, say t = 0, two radioactive substances A and B have equal activates. The ratio

\frac{R_B}{R_A}

of their activities. The ratio

\frac{R_B}{R_A}

of their activates after time t itself decays with time t as

e^{-3t}

. If the half-life of A is

\ell n2

, the half-life of B is:

(A) $4\ell n2$
(B) $\frac{\ell n2}{2}$
(C) $\frac{\ell n2}{4}$
(D) $2\ell n2$

Q128·PhysicsMultiple correctJEE Advanced 2018

In a radioactive decay chain,

^{232}_{90}

Th nucleus decays to

^{212}_{82}

Pb nucleus. Let

N_{\alpha}

and

N_{\beta}

be the number of

\alpha

and

\beta^{-}

particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

(A) $N_{\alpha} = 5$
(B) $N_{\alpha} = 6$
(C) $N_{\beta} = 2$
(D) $N_{\beta} = 4$

Q129·PhysicsIntegerJEE Advanced 2017

^{131}I

is an isotope of Iodine that

\beta

decays to an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with

^{131}I

is injected into the blood of a person. The activity of the amount of

^{131}I

injected was 2.4

\times

10^{5}

Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 hours, 2.5 ml of blood is drawn from the person's body, and gives an activity of 115 Bq. The total volume of blood in the person's body, in liters is approximately (you may use

e^{x} \approx 1 + x

for

|x| \ll 1

and ln 2

\approx

0.7).

Q130·PhysicsSingle correctJEE Advanced 2016

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by

E = \frac{3}{5}\,\frac{Z(Z-1)e^{2}}{4\pi\varepsilon_{0}R}

The measured masses of the neutron,

^{1}_{1}\text{H}

,

^{15}_{7}\text{N}

and

^{15}_{8}\text{O}

are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065u, respectively. Given that the radii of both the

^{15}_{7}\text{N}

and

^{15}_{8}\text{O}

nuclei are same, 1 u = 931.5 MeV/

c^{2}

( c is the speed of light) and

e^{2}/(4\pi\varepsilon_{0})

= 1.44 MeV fm. Assuming that the difference between the binding energies of

^{15}_{7}\text{N}

and

^{15}_{8}\text{O}

is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm =

10^{-15}

m)

(A)2.85 fm
(B)3.03 fm
(C)3.42 fm
(D)3.80 fm

Q131·PhysicsIntegerJEE Advanced 2016

The isotope

^{12}_{5}\text{B}

having a mass 12.014 u undergoes β-decay to

^{12}_{6}\text{C}

.

^{12}_{6}\text{C}

has an excited state of the nucleus (

^{12}_{6}\text{C}^*

) at 4.041 MeV above its ground state. If

^{12}_{5}\text{B}

decays to

^{12}_{6}\text{C}^*

, the maximum kinetic energy of the β-particle in units of MeV is (1 u = 931.5 MeV/

c^{2}

, where

c

is the speed of light in vacuum).

Q132·PhysicsSingle correctJEE Advanced 2016

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

(A)64
(B)90
(C)108
(D)120

Q133·PhysicsIntegerJEE Advanced 2015

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5 % of the electrical power available form the plant at that time. If the plant is able to meet the total power needs of the village for a maximum period of

nT

years, then the value of

n

is

Q134·PhysicsMatrix matchJEE Advanced 2015

Match the nuclear processes given in column I with the appropriate option(s) in column II

Column I	Column II
A.Nuclear fusion	P.Absorption of thermal neutrons by $^{235}_{92}\mathrm{U}$
B.Fission in a nuclear reactor	Q. $^{60}_{27}\mathrm{Co}$ nucleus
C. $\beta$ -decay	R.Energy production in stars via hydrogen conversion to helium
D. $\gamma$ -ray emission	S.Heavy water
	T.Neutrino emission

Q135·PhysicsIntegerJEE Advanced 2015

For a radioactive material, its activity A and rate of change of its activity R are defined as

A = -\dfrac{dN}{dt}

and

R = -\dfrac{dA}{dt}

, where N(t) is the number of nuclei at time t. Two radioactive sources P (mean life

\tau

) and Q (mean life

2\tau

) have the same activity at

t = 0

. Their rates of change of activities at

t = 2\tau

are

R_{P}

and

R_{Q}

, respectively. If

\dfrac{R_{P}}{R_{Q}} = \dfrac{n}{e}

, then the value of n is

Q136·PhysicsMultiple correctJEE Advanced 2015

A fission reaction is given by

^{236}_{92}\mathrm{U} \to {}^{140}_{54}\mathrm{Xe} + {}^{94}_{38}\mathrm{Sr} + x + y

, where x and y are two particles. Considering

^{236}_{92}\mathrm{U}

to be at rest, the kinetic energies of the products are denoted by

K_{Xe}

,

K_{Sr}

,

K_{x}

(2MeV) and

K_{y}

(2MeV), respectively. Let the binding energies per nucleon of

^{236}_{92}\mathrm{U}

,

^{140}_{54}\mathrm{Xe}

and

^{94}_{38}\mathrm{Sr}

be 7.5 MeV, 8.5 MeV and 8.5 MeV respectively. Considering different conservation laws, the correct option(s) is(are)

(A) $x = n$ , $y = n$ , $K_{Sr} = 129$ MeV, $K_{Xe} = 86$ MeV
(B) $x = p$ , $y = e^{-}$ , $K_{Sr} = 129$ MeV, $K_{Xe} = 86$ MeV
(C) $x = p$ , $y = n$ , $K_{Sr} = 129$ MeV, $K_{Xe} = 86$ MeV
(D) $x = n$ , $y = n$ , $K_{Sr} = 86$ MeV, $K_{Xe} = 129$ MeV

Q137·PhysicsSingle correctJEE Advanced 2013

The mass of nucleus

^{A}_{Z}\mathrm{X}

is less than the sum of the masses of

(A-Z)

number of neutrons and

Z

number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass

M

can break into two light nuclei of mass

m_{1}

and

m_{2}

only if

(m_{1} + m_{2}) < M

. Also two light nuclei of masses

m_{3}

and

m_{4}

can undergo complete fusion and form a heavy nucleus of mass

M'

only if

(m_{3} + m_{4}) > M'

. The masses of some neutral atoms are given in the table below: The kinetic energy (in keV) of the alpha particle, when the nucleus

^{210}_{84}\mathrm{Po}

at rest undergoes alpha decay, is

Nuclide	Mass
$^{1}_{1}\mathrm{H}$	1.007825 u
$^{2}_{1}\mathrm{H}$	2.014102 u
$^{3}_{1}\mathrm{H}$	3.016050 u
$^{4}_{2}\mathrm{He}$	4.002603 u
$^{6}_{3}\mathrm{Li}$	6.015123 u
$^{7}_{3}\mathrm{Li}$	7.016004 u
$^{70}_{30}\mathrm{Zn}$	69.925325 u
$^{82}_{34}\mathrm{Se}$	81.916709 u
$^{152}_{64}\mathrm{Gd}$	151.919803 u
$^{206}_{82}\mathrm{Pb}$	205.974455 u
$^{209}_{83}\mathrm{Bi}$	208.980388 u
$^{210}_{84}\mathrm{Po}$	209.982876 u

(A)5319
(B)5422
(C)5707
(D)5818

Q138·PhysicsSingle correctJEE Advanced 2013

The mass of nucleus

^{A}_{Z}\mathrm{X}

is less than the sum of the masses of

(A-Z)

number of neutrons and

Z

number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass

M

can break into two light nuclei of mass

m_{1}

and

m_{2}

only if

(m_{1} + m_{2}) < M

. Also two light nuclei of masses

m_{3}

and

m_{4}

can undergo complete fusion and form a heavy nucleus of mass

M'

only if

(m_{3} + m_{4}) > M'

. The masses of some neutral atoms are given in the table below: The correct statement is

Nuclide	Mass
$^{1}_{1}\mathrm{H}$	1.007825 u
$^{2}_{1}\mathrm{H}$	2.014102 u
$^{3}_{1}\mathrm{H}$	3.016050 u
$^{4}_{2}\mathrm{He}$	4.002603 u
$^{6}_{3}\mathrm{Li}$	6.015123 u
$^{7}_{3}\mathrm{Li}$	7.016004 u
$^{70}_{30}\mathrm{Zn}$	69.925325 u
$^{82}_{34}\mathrm{Se}$	81.916709 u
$^{152}_{64}\mathrm{Gd}$	151.919803 u
$^{206}_{82}\mathrm{Pb}$	205.974455 u
$^{209}_{83}\mathrm{Bi}$	208.980388 u
$^{210}_{84}\mathrm{Po}$	209.982876 u

(A)The nucleus $^{6}_{3}\mathrm{Li}$ can emit an alpha particle
(B)The nucleus $^{210}_{84}\mathrm{Po}$ can emit a proton.
(C)Deuteron and alpha particle can undergo complete fusion.
(D)The nuclei $^{70}_{30}\mathrm{Zn}$ and $^{82}_{34}\mathrm{Se}$ can undergo complete fusion.

Q139·PhysicsSingle correctJEE Advanced 2013

Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists:

List I	List II
P.Alpha decay	1. $^{15}_{8}\mathrm{O} \to {}^{15}_{7}\mathrm{N} + .....$
Q. $\beta^{+}$ decay	2. $^{238}_{92}\mathrm{U} \to {}^{234}_{90}\mathrm{Th} + .....$
R.Fission	3. $^{185}_{83}\mathrm{Bi} \to {}^{184}_{82}\mathrm{Pb} + .....$
S.Proton emission	4. $^{239}_{94}\mathrm{Pu} \to {}^{140}_{57}\mathrm{La} + .....$

(A)P-4, Q-2, R-1, S-3
(B)P-1, Q-3, R-2, S-4
(C)P-2, Q-1, R-4, S-3
(D)P-4, Q-3, R-2, S-1

Q140·PhysicsIntegerJEE Advanced 2013

A freshly prepared sample of a radioisotope of half-life 1386 s has activity

10^{3}

disintegrations per second. Given that

\ln 2 = 0.693

, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is

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