The unit of length on the nuclear scale is a Fermi: 1 f = 10^-15 m. nuclear sizes obey roughly the following empirical relation:
r = r₀ A^1/3

where r is the radius of the nucleus, A its mass number, and r₀ is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.

Question

The unit of length on the nuclear scale is a Fermi: 1 f = 10^-15 m. nuclear sizes obey roughly the following empirical relation:
r = r₀ A^1/3

where r is the radius of the nucleus, A its mass number, and r₀ is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.

Philoid · Accepted Answer

The equation for the radius of the nucleus is given by,

r = r₀ A^1/3

∴ Volume on the nucleus, V =

=

Mass number is given in the problem as, A.

Thus,

M = Mass number× Mass of single Nucleus

= A×1.67×10^-27 kg

(∵ Mass of single Nucleus = 1.67×10^-27 kg)

∴ Density, ρ =

= = kg/m³

This equation doesn’t have Mass number A and it has only one variable, Radius of the atom (r). Since, every atom has same radius then the density of sodium atom nuclei remains constant.

∴ Density of sodium atom nucleus, ρ _nucleus = kg/m³

2.29×10¹⁷ kg/m³