from the relation `R=R_0A^(1//3)`, where `R_0` 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 ).

Explanation

we have the expression for nuclear radius as:
`R= R_(@)A^(1)//^(3)`
where ,
A = mass number of the nucleus
Nuclea matter density ` rho =("mass of the nucleus")/("Volume of the nucleus ")`
Let mBe average mass of the nucleus .
Hence ,mass of the nucleus -mA
`therefore rho =(mA)/((4)/(3)piR^(3))=9(3mA)/(4pi (r_(@)A^((1)/(3)))^(3))=(3mA )/(4piR_(@)^(3)A) =(3m)/(4piR_(0)^(3))`
Hence , the nuclear matter density is independent of A it Is neraly constant .