Show that the density of nucleus over a wide range of nuclei is constant

CBSE Class 12 CBSE Class 12 Physics
1

Show that the density of nucleus over a wide range of nuclei is constant independent of mass number.

2

We have
$R={{R}{0}}{{A}^{\frac{1}{3}}}$
Density $\rho =\frac{mA}{\frac{4}{3}\pi {{({{R}{0}}{{A}^{\frac{1}{3}}})}^{3}}}$
$=\frac { m }{ \frac { 4 }{ 3 } \pi { { R }_{ 0 }^{ 3 } } }$
Hence p is independent of A.
(Here m is the mass ol Lite nucleus.)