Question

The mass (M) and the radius (r) of a nucleus can be expressed in terms of the mass number, A. (a) Show that the density of a nucleus is independent of A. (b) Calculate the density of a gold (Au) nucleus. Compare your answer to that for iron (Fe). 

Answer 1

Mass=M

Radius=r

Mass number =A

Part(a)

$\rho=\frac{M}{V}=\frac{M}{\frac{4 \pi r^3}{3}}$

$r=r_0A^\frac{1}{3}$

$\rho=\frac{M}{4\pi r_0^3 A}$

Part (b)

$$\rho=\frac{1.67\times10^{-27}}{4\times \pi 4.2\times10^{-15}\times{197}}=19.3g/cm^3$$

Iron

$\rho=7.87gm/cm^3$

Difference density of iron and gold

∆$\rho=19.3-7.87=11.7g/cm^3$