Correct Answer - Option 4 : Energy of 9.72 MeV has to be supplied
Note:
For this question in Jee paper, there was no correct option given, hence one of the options is replaced by the correct one.
Concept:
Energy absorbed or released in a nuclear reaction is given by;
ΔQ = Binding energy of products – Binding energy of reactants.
If energy is absorbed, ΔQ is negative and if it is positive then energy is released.
Also, Binding energy = Binding energy per nucleon × number of nucleons.
Calculation:
Given reaction is
Ne20 → 2He4 + C12
Binding energy per nucleon of Ne20 is 8.03 MeV
Number of nucleon in Ne20 is 20
Binding energy per nucleon of He4 is 7.07 MeV
Number of nucleon in He4 is 4
Binding energy per nucleon of C12 is 7.86 MeV
Number of nucleon in C12 is 12
Here, binding energy of products i.e., 2(He)4 + C12 is
= 2 × (B.E of He4) + (B.E of C12)
= 2(4 × 7.07) + (12 × 7.86)
= 2 × 28.28 + 94.32
= 56.56 + 94.32
= 150.88 MeV
And binding energy of reactants, i.e., Ne20 is
= 20 × 8.03 = 160.6 MeV
So, ΔQ = (B.E)Products – (B.E)reactants
= 150.88 – 160.6 = -9.72 MeV
As ΔQ is negative,
∴ Energy of 9.72 MeV is absorbed in the reaction.