Question

+-/3 points SerCP11 29.1.P.006. Consider the Szn nucleus. Find approximate values for its radius, volume, and density. (a) radius fm (b) volume m3 (c) density kg/m3

Answer 1

The average radius of a nucleus with A nucleons is R = R ₀ A ^1/3, where R ₀ = 1.2$\times$10^-15 m

For $_{30}^{65}\textrm{Zn}$ A=65   

So

Part a.

Radius,R=1.2$\times$10^-15(65)^1/3=4.82$\times$10^-15 m

Radius=4.82 fm

Part b.

Volume of nucleus is=(4/3)$\pi$R³=(4/3)$\pi$(4.82$\times$10^-15)³=4.7$\times$10^-43 m³

Part c.

Mass of nucleus=No of nucleons$\times$mass of 1 nucleon=65$\times$1.67$\times$10^-27=1.0855$\times$10^-25 kg

Density of nucleus=mass/volume=1.0855$\times$10^-25/4.7$\times$10^-43 kg/m³

Density=2.31$\times$10^-21 kg/m³