Gujarati
13.Nuclei
medium

The nuclear radius is given by $R=r_0 A^{1 / 3}$, where $r_0$ is constant and $A$ is the atomic mass number. Then, the nuclear mass density of $U^{238}$ is

A

twice that of $\operatorname{Sn}^{119}$

B

thrice that of $Sn ^{119}$

C

same as that of $Sn ^{119}$

D

half that of $Sn ^{119}$

(KVPY-2019)

Solution

(c)

Given, nuclear radius is

$R=r_0 A^{\frac{1}{3}}$

Here, atomic mass number of nucleus $=A$

$\therefore$ Nuclear density $d$ is given by

$d=\frac{\text { Mass number }}{\text { Volume }}$

$\Rightarrow \quad d=\frac{A}{\frac{1}{3} \pi R^3}=\frac{4}{3} \pi\left(r_0 A^{\left.\frac{1}{3}\right)^3}\right.$

$\Rightarrow \quad d=\frac{A}{\frac{1}{3} \pi r_0^3 \cdot A}=\frac{3}{4 \pi r_0^3}$

As $r_0=$ a constant, so nuclear density is a constant quantity.

$\therefore$ Nuclear mass density of $U^{238}$ is same as that of $Sn ^{119}$.

Standard 12
Physics

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(AIPMT-1990)

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