(a) Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon (BE/A) versus the mass number A.
(b) A radioactive isotope has a hald -life of 10 years. How long will it take for the activity to reduce to 3.125%.

Explanation

(a) The atom curve shows that:
(i) when a heavy nucleus breaks into the two medium sized nuclie (in nucler fission). The BE/nucleon increases resulting in the release of energy. (ii) When two small nuclei combine to from a relatively bigger nuclues fusion BE/nucles increases, resulting in the resulting in the relase of energy.

(b) Half life of the radioactive isotope = 10 years.
After decays , the amount of the release of energy.
(b) Half life of the radioactive isotope = 10 years.
After decay, the amount of the radioactive isotope = N.
Given 3.125% of `N_(0)` remains after decay tehn
`(N)/(N_(0)) = 3.125% = (3.125)/(100) = (1)/(32)`
But `(N)/(N_(0)) = e^(-n)`
Where, `lambda` = Decay constant .
t = time .
`- lambda t = (1)/(32)`
`- lambda t = In 1 - In 32`
`- lambda t = 0 - 3.4567`
`t = (3.4567)/(lambda)`
`sin clambda = (0.693)/(T) = (0.693)/(10)`
`(((3.466)/(0.693)))/(10) = 50`
Thus , the isotope will take about 50 years to reduce to 3.125% of its original value.