Question

From the relation R = R₀ A^1/3 , Where R₀ is a constant and A is the mass number of a nucleus show that the nuclear matter density is nearly constant (i.e. Independent of A).

Answer 1

Density of nucleus(p) It is defined as the nuclear mass per unit volume.

i.e ρ = \(\frac{mass\,of\,one\,nucleus}{volume\,of\,nucleus}\)

= \(\frac{mass\,of\,one\,nucleon\times number\,of\,nucleons}{\frac{4}{3}\pi r^3}\)

= \(\frac{1.66\times10^{-27}A}{\frac{4}{3}\pi (R_0A^{1/3})^3}\) = \(\frac{3\times1.66\times10^{-27}A}{4\times3.142\times(1.2\times10^{-15})^3\times A}\)

= 2.29 x 10¹⁷Kgm^-3

Thus the nuclear density is of the order of 10¹⁷kgm^-3 and is independent of its mass number. Therefore, all nuclei have the same approximate density.