- Home
- Standard 12
- Physics
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
twice that of $\operatorname{Sn}^{119}$
thrice that of $Sn ^{119}$
same as that of $Sn ^{119}$
half that of $Sn ^{119}$
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 $Sn ^{119}$.