(a) Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon \left ( \frac{BE}{A} \right ) 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%?

 

 

 

 
 
 
 
 

Answers (1)
S safeer


From the graph, we note that
During nuclear fission
    From the graph when we go through from heavy region to the middle region there is a given in binding energy per nucleon which means energy is released 
During nuclear fusion
    From the graph, when we move from lighter nuclei region to heavier nuclei region there is a gain in binding energy per nucleon. Which means energy is released 
 
b)
 Given,
            T_{\frac{1}{2}}= 10\; years
activity after 't' time At = 3.125 %
The law of radioactivity decay is given as A_{t}= A_{0}e^{-\lambda t}

\lambda= \frac{0\cdot 693}{T_{\frac{1}{2}}}

where \lambda = decay constant


\lambda = \frac{0\cdot 693}{10}= 0\cdot 0693
Let A_{0}= 100\, ^{0}/_{0}( initial activity) Then,
3\cdot 125= 100\; e^{-0\cdot 0693t}
\frac{3\cdot 125}{100}= e^{-0\cdot 0693t}
Taking logarithm on both sides
\l_{n}\, \frac{3\cdot 125}{100}= 0\cdot 0693\, t
\l_{n}\, \frac{100}{3\cdot 125}= 0\cdot 0693\, t
t= \frac{l_{n}32}{0\cdot 0693}= 50\; years

Therefore the time taken for the activity to reduce to 3.125 % is 50 years

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