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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(3)

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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4

(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]

0%

(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)

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

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

Topic Question Set

(3)

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]

0%

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]

0%

Q 6 :
For a nucleus of mass number A and radius R, the mass density of the nucleus can be represented as [2025]

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Topic Question Set

(3)

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 A1 and volume V1. Another nucleus has mass number A2 and volume V2. If relation between mass number is A2=4A1, then V2/V1= ___________ . [2024]

0%

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 1000x, where x is ______ . [2024]

0%

Q 6 : For a nucleus of mass number A and radius R, the mass density of the nucleus can be represented as [2025]

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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]

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]

Q 6 :
For a nucleus of mass number A and radius R, the mass density of the nucleus can be represented as [2025]