Assertion A: The nuclear density of nuclides and can be arranged as Reason R: The radius R of nucleus is related to its mass number A as , where is a constant. [2023]

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Solution

Q.
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:

1 Both A and R are true and R is the correct explanation of A

2 A is false but R is true

3 A is true but R is false

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

Ans.
(2)

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

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

$ρ is independent of mass number.$

$∴$ $A is false.$

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