Question

From the relation R = R₀A¹/³, 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

We have the expression for nuclear radius as:

R = R₀A¹/³

Where,

R₀ = Constant.

A = Mass number of the nucleus

Nuclear matter density, `rho = "Mass of the nucleus"/"Volume of the nucleus"`

Let m be the average mass of the nucleus.

Hence, mass of the nucleus = mA

`therefore rho = "mA"/(4/3  pi"R"^3) = "3mA"/(4pi ("R"_0 "A"^(1/3))^3) = (3"mA")/(4pi"R"_0^3 "A") = "3m"/(4pi"R"_0^3)`

Hence, the nuclear matter density is independent of A. It is nearly constant.