From the relation `R=R_(0)A^(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.

Explanation

Given : `R=R_(0)A^(1//3)`
Assuming the nucleus to be spherical,
Volume of the nucleus
`V=(4)/(3)pi R^(3)`
`=(4)/(3)pi R_(0)^(3)A`
Nuclear density `=("mass")/("volume")`
`rho=(3cancelAm_(rho))/(4 pi R_(0)^(3)cancelA) " where" m_(rho)="mass of the proton"`
Since `m_(rho)=1.67xx10^(-17)` kg is a constant, `R_(0)=1.3fm`
Nuclear density is independent of atomic mass number . In other words, nuclear density is independent of the size of the nucleus.