Question: Q. 1. (i) Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon $(B E / A)$ versus the mass number $A$.
(ii) A radioactive isotope has a half life of $\mathbf{1 0}$ years. How long will it take for the activity to reduce to $3.125 %$ ?
U] A [CBSE SQP 2018]
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Solution:
Ans. (i)
$1 / 2$
From the above graph, it’s clear that binding energy per nucleon is low for very light and for very heavy nuclei. If a nucleus of lower binding energy is converted into higher binding energy nucleuśs then energy is released. There are two methods of converting lower binding energy into higher binding energy.
Fission : A heavy nucleus (low BEN is broken into two lower nuclei (higher BEN) and energy is released. This process is known as Fission.
Fusion : Two light nuclei (bom BEN) are joined and formed one nucleus of higher BEN, energy is released. This process is known as Fusion.
(ii)
$$ \begin{aligned} \frac{N}{N_{0}} & =\frac{3.125}{100} \ & =(1 / 2)^{5} \end{aligned} $$
Comparing this with the following standard equation
We may write $\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{n}$ where, $n=\frac{t}{T_{1 / 2}}$
$$ \left(\frac{1}{2}\right)^{5}=\left(\frac{1}{2}\right)^{n} ; \text { hence } n=5 \quad 1 / 2 $$
Half life of the radioisotope is given 10 years.
Putting the value of $n$ and $T_{1 / 2}$ in $\left[n=\frac{t}{T_{1 / 2}}\right]$
$$ \begin{aligned} 5 & =\frac{t}{10} \ t & =50 \text { years } \end{aligned} $$
(Please note that part (ii) is from second topic of the chapter. Kindly refer ‘revision notes’ of second topic for more clarity. )
