(i) What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number ′A′ lying 30<A<170?
(ii) Show that the density of nucleus over a wide range of nuclei is constant-independent of mass number A.
(i)The approximate constancy of
BEA over most of the range is saturation property of nuclear force.
In heavy nuclei, nuclear size > range of the nuclear force.
So a nuclear sense approximately a constant number of neighbors and thus the nuclear BEA levels off at high A. This saturation of the nuclear force.
(ii)
The mass of the nucleus of the atom of the mass number A
A= A a.m.u.
= A ×1.660565×10−27kg
The volume of the nucleus is 4πr33=4π3(R0A−3)3=4πR30A3
∴Volume=4π3(1.1×10−15)3×Am3
Now the density of the nucleus= mV; where m is mass and V is the volume of the nucleus.
ρ=A×1.660565×10−274π3(1.1×10−15)3×A=2.97×1017Kgm−3
Thus, we can see the density of the nuclei is independent of mass number and it is constant for all nuclei .