From the relation R = R0A1/3, where R0is a constant and A is themass number of a nucleus, show that the nuclear matter density isnearly constant (i.e. independent of A).

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Solution

The relation given for the nuclear radius is,

R= R 0 A 1 3
Here, R 0 is a constant and A is the mass number of the nucleus.

Let the nuclear matter density be ρ, then,

ρ= mass of the nucleus volume of the nucleus (i1)

If mbe the average mass of the nucleus, then the mass of the nucleus is mA.

Substituting the values in the equation (1), we get:

ρ= mA 4 3 π R 3 = 3mA 4π ( R 0 A 1 3 ) 3 = 3mA 4π R 0 3 A = 3m 4π R 0 3

So, the nuclear matter density is independent of A. Hence, it can be concluded that nuclear density is nearly constant.

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