In a typical unclear reaction, e.g.
`""_(1)^(2)H+""_(1)^(2)H to ""_(2)^(3)He + n +3.27 Me V`,
although number of nucleons is conserved is conserved, yet energy is released. How ? Explain.
(b) Show that nuclear dendity in a given nucleus is independent of mass number A.

Explanation

(a) In a nuclear reaction, the sum of the masses of the target nucleus `(""_(1)^(2)H)`, and the bombarding particle `(""_(1)^(2)H)` may be greater or less than the sum of the masses of the product nucleus `(""_(1)^(3)He)` and the outgoing particle `(""_(0)^(1)n)`. So, from the law of conservation of mass energy, some energy (3.27 MeV) is evolved or involved in a nuclear reaction. This energy is called Q-value of the nuclear reaction.
(b) Density of the nucleus `=("mass of nucleus")/("volume of nucleus")`
Mass of the nucleus = a amu `= A xx 1.66 xx 10^(-27) `kg
Volume of the nucleus `=(4)/(3) pi R^(3)`
`=(4)/(3) pi (R_(0)A^(1//3))^(3) =(4)/(3) pi R_(0)^(3) A`
Thus, ` " density"= (Axx1.66xx 10^(-27))/(((4)/(3)piR_(0)^(3))A)=(1.66 xx 10^(-27))/(((4)/(3)piR_(0)^(3)))`
which shows that the density is independent of mass number A.
Using `R_(0)=1.1 xx 10^(-15)m` and density ` =2.97 xx 10^(17) kg//m^(3)`