Answer
The density of the nucleus is $2.3\times 10^{17}~kg/m^3$
Work Step by Step
We can find the volume of the nucleus as:
$V = \frac{4}{3}\pi~R^3$
$V = \frac{4}{3}\pi~(7.5\times 10^{-15}~m)^3$
$V = 1.767\times 10^{-42}~m^3$
We can find the density of the nucleus as:
$\rho = \frac{m}{V}$
$\rho = \frac{4.0\times 10^{-25}~kg}{1.767\times 10^{-42}~m^3}$
$\rho = 2.3\times 10^{17}~kg/m^3$
The density of the nucleus is $2.3\times 10^{17}~kg/m^3$.
