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  • (a) Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon 

(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)


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

Posted by

Safeer PP

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