Nuclear Physics | Physics JEE previous year questions with Solutions

Q 1 :

From the statements given below:

(A) The angular momentum of an electron in $n$ th orbit is an integral multiple of $h$ .

(B) Nuclear forces do not obey inverse square law.

(C) Nuclear forces are spin dependent.

(D) Nuclear forces are central and charge independent.

(E) Stability of nucleus is inversely proportional to the value of packing fraction.

Choose the correct answer from the options given below: [2024]

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

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Q 2 :

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is [2024]

24
32
40
20

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(1)

$R_{1} = \frac{R_{2}}{2}$

$R_{0} {(A_{1})}^{1 / 3} = \frac{R_{0}}{2} {(A_{2})}^{1 / 3}$

$A_{1} = \frac{1}{8} A_{2}$

$A_{1} = \frac{192}{8} = 24$

Q 3 :

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 $A_{2} = 4 A_{1}$ , then $V_{2} / V_{1} =$ ___________ . [2024]

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(4) For a nucleus

Volume: $V = \frac{4}{3} π R^{3}$

$R = R_{0} {(A)}^{1 / 3}$

$V = \frac{4}{3} π R_{0}^{3} A \Rightarrow \frac{V_{2}}{V_{1}} = \frac{A_{2}}{A_{1}} = 4$

Q 4 :

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 $\frac{1000}{x},$ where $x$ is ______ . [2024]

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(27) $R = R_{0} A^{1 / 3}$

$4.8 = R_{0} {(64)}^{1 / 3}$

$4.8 = R_{0} 4$ ...(i)

$4 = R_{0} {(A)}^{1 / 3}$ ...(ii)

$(i) divided by (i i), 1.2 = \frac{4}{{(A)}^{1 / 3}}$

$A = \frac{64}{1.728} = \frac{1000}{x}$

$x = \frac{1728}{64} = 27$

Q 5 :

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). [2025]

Assertion (A): The density of the copper $({}_{29}^{64}C u)$ nucleus is greater than that of the carbon $({}_{6}^{12}C)$ 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) is correct but (R) is not correct
(A) is not correct but (R) is correct
Both (A) and (R) are correct and (R) is the correct explanation of (A)
Both (A) and (R) are correct but (R) is not the correct explanation of (A)

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(2)

$ρ = \frac{M}{V} = \frac{m_{n} \times A}{\frac{4}{3} π R^{3}} = \frac{m_{n} \times A}{\frac{4}{3} π A R_{0}^{3}}$

So $ρ$ is almost constant, density of nucleus is independent of mass number.

$R = R_{0} A^{1 / 3} \Rightarrow R \propto A^{1 / 3}$

Radius is proportional to $A^{1 / 3}$ .

Q 6 :

For a nucleus of mass number A and radius R, the mass density of the nucleus can be represented as [2025]

$A^{3}$
$A^{\frac{1}{3}}$
$A^{\frac{2}{3}}$
Independent of $A$

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(4)

$R = R_{0} A^{1 / 3}$

$Density = \frac{Mass number}{Volume} = \frac{A}{\frac{4}{3} π R_{0}^{3} A} = constant$

Q 7 :

The ratio of the density of oxygen nucleus $({}_{8}^{16}O)$ and helium nucleus $({}_{2}^{4}{He})$ is [2023]

4 : 1
1 : 1
8 : 1
2 : 1

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(2)

Density of any nucleus is same.

Q 8 :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. [2023]

Assertion A: The nuclear density of nuclides ${}_{5}^{10}B,_{3}^{6} Li,_{26}^{56} O,_{10}^{20} Ne$ and ${}_{83}^{209}{Bi}$ can be arranged as

$ρ_{Bi}^{N} > ρ_{Fe}^{N} > ρ_{Ne}^{N} > ρ_{B}^{N} > ρ_{Li}^{N} .$

Reason R: The radius R of 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 statement, choose the correct answer from the options given below:

Both A and R are true and R is the correct explanation of A
A is false but R is true
A is true but R is false
Both A and R are true but R is NOT the correct explanation of A

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(2)

$R = R_{0} A^{1 / 3}, using this$

$ρ = \frac{M}{\frac{4}{3} π R^{3}} = \frac{A m_{p}}{\frac{4}{3} π R_{0}^{3} A} = \frac{m_{p}}{\frac{4}{3} π R_{0}^{3}}$

$ρ is independent of mass number.$

$∴$ $A is false.$

Q 9 :

For a nucleus ${}_{Z}^{A}X$ 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 $b_{c} = - a_{2} \frac{Z (Z - 1)}{A^{4 / 3}}$

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: [2023]

B, C, E only
C, D only
A, B, C, D only
B, C only

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(2)

$Surface energy per nucleon \propto \frac{r^{2}}{A} \propto \frac{A^{2 / 3}}{A} \propto \frac{1}{A^{1 / 3}}$
$(Mass number A \propto r^{3} \Rightarrow r \propto A^{1 / 3})$

$A is incorrect$

$Contribution to binding energy by coulombic forces is$

$= \frac{- a_{2} Z (Z - 1)}{A^{1 / 3}}$

$B is incorrect$

$Volume energy \propto A$

$C is correct$

$For (D), if we consider only surface energy contribution then option is correct.$

$For (E) only 3 interactions contribute to surface energy.$

Q 10 :

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{- 27} kg$ and radius of nucleus is $1.5 \times 10^{- 15} A^{1 / 3} m$ . The approximate ratio of the nuclear density and water density is $n \times 10^{13}$ . The value of $n$ is _______. [2023]

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(11)

$Density of nuclei = \frac{mass of nuclei}{volume of nuclei}$

$ρ = \frac{1.6 \times 10^{- 27} A}{\frac{4}{3} π {(1.5 \times 10^{- 15})}^{3} A} = 0.113 \times 10^{18} {kg/m}^{3}$

$ρ_{w} = 10^{3} {kg/m}^{3}$

$Hence \frac{ρ}{ρ_{w}} = 11.31 \times 10^{13}$

Topic Question Set

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Q 2 :

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is [2024]

Q 3 :

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 $A_{2} = 4 A_{1}$ , then $V_{2} / V_{1} =$ ___________ . [2024]

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Q 4 :

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 $\frac{1000}{x},$ where $x$ is ______ . [2024]

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Q 6 :

For a nucleus of mass number A and radius R, the mass density of the nucleus can be represented as [2025]

Q 7 :

The ratio of the density of oxygen nucleus $({}_{8}^{16}O)$ and helium nucleus $({}_{2}^{4}{He})$ is [2023]

Q 10 :

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{- 27} kg$ and radius of nucleus is $1.5 \times 10^{- 15} A^{1 / 3} m$ . The approximate ratio of the nuclear density and water density is $n \times 10^{13}$ . The value of $n$ is _______. [2023]

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