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).
We have the expression for nuclear radius as:
R = R0A1/3
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
`:. rho = mA/(4/3 piR^3) = "3mA"/(4pi (R_0 A^(1/3))^3) = (3mA)/(4piR_0^3 A) = "3m"/(4piR_0^3)`
Hence, the nuclear matter density is independent of A. It is nearly constant.