Q19 of 26 Page 1

(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% ?

a) The plot of binding energy per nucleon (BE/A) versus the mass number A is given below:



From the plot we note that


i) During nuclear fission


A heavy nucleus in the larger mass region ( A>200) breaks into two middle level nuclei, resulting in an increase in B.E/ nucleon. This results in a release of energy.


Example:


92U235 + n1→ 56Ba144 + 36Kr89 + 30n1 + energy


ii) During nuclear fusion


Light nuclei in the lower mass region (A<20 ) fuse to form a nucleus having higher B.E / nucleon. Hence Energy gets released.


Example:


1H2 + 1H2→ 2He4 + energy


b) Let the initial activity be Ao.


Let the time taken for the activity to reduce = t.


Half live is given T1/2 = 10years


If we take Ao = 100, then activity after time t will be


At = 3.125 (given)


We know the law of radioactivity decay is given as


At = Ao e-λt ….(i)


Where λ = decay constant.



Therefore, substituting the values of At Ao and λ in equation (i),


3.125 = 100e-0.0693t



Taking natural logarithm on both sides of above equation





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


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