Question

(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 half-life of 10 years. How long will it take for the activity to reduce to 3.125% ?

Answer 1

(a) Graph of binding energy per nucleon versus mass number:

When we move from the heavy nuclei region to the middle region of the plot, there is a gain in the overall binding energy and hence release of energy. This indicates that energy can be released when a heavy nucleus (A $\approx$ 240) breaks into two roughly equal fragments. This process is called nuclear fission.

Similarly, when we move from lighter nuclei to heavier nuclei, we again find that there is a gain in the overall binding energy and hence release of energy. This indicates that energy can be released when two or more lighter nuclei fuse together to form a heavy nucleus. This process is called nuclear fusion.


(b) We know that, $\frac{R}{R_0}={\left(\frac{1}{2}\right)}^n$

Given, $\frac{R}{R_0}=3.125\%=\frac{3.125}{100}$

$\therefore \frac{3.125}{100}={\left(\frac{1}{2}\right)}^n$

or $\frac{1}{32}={\left(\frac{1}{2}\right)}^n$

$\Rightarrow {\left(\frac{1}{2}\right)}^5={\left(\frac{1}{2}\right)}^n$

$\Rightarrow n=5$

Given, T = 10 years

As n = $\frac{t}{T}$

$\therefore \frac{t}{T}=5$

or $t=5\times 10=50$ years