Consider the nuclear fission Ne20 \to 2He4 + C12 Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -

8.3 MeV energy will be released

energy of 11.9 MeV has to be supplied

energy of 12.4 MeV will be supplied

energy of 3.6 MeV will be released

Atoms and Nuclei PYQ — JEE Main 2019 · 10 Jan · Shift 2 · Q72 with Solution

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Correct answer: NONE OF THE GIVEN OPTIONS IS CORRECT., IF THE INTENDED REACTION/DATA WERE DIFFERENT, THE QUESTION LIKELY CONTAINS A TYPO. FOR THE REACTION AS WRITTEN AND THE GIVEN BINDING ENERGIES, THE REQUIRED SUPPLIED ENERGY IS 38.0 MEV.

Use binding energies to find total binding energy of reactants and products

Given binding energy per nucleon:

For $\mathrm{^{20}Ne}$ : $8.03\,\text{MeV/nucleon}$
For $\mathrm{^{4}He}$ : $7.07\,\text{MeV/nucleon}$
For $\mathrm{^{12}C}$ : $7.86\,\text{MeV/nucleon}$

So total binding energies are:

B(\mathrm{^{20}Ne}) = 20 \times 8.03 = 160.6\,\text{MeV}

B(\mathrm{^{4}He}) = 4 \times 7.07 = 28.28\,\text{MeV}

B(\mathrm{^{12}C}) = 12 \times 7.86 = 94.32\,\text{MeV}

Find total binding energy of products

Reaction:

\mathrm{^{20}Ne \rightarrow \, ^4He + \, ^{12}C}

Total binding energy of products:

B_{\text{products}} = 28.28 + 94.32 = 122.60\,\text{MeV}

Compare initial and final binding energies

Initial binding energy:

B_{\text{initial}} = 160.6\,\text{MeV}

Final binding energy:

B_{\text{final}} = 122.6\,\text{MeV}

Change in binding energy:

\Delta B = B_{\text{final}} - B_{\text{initial}} = 122.6 - 160.6 = -38.0\,\text{MeV}

Since the products have less total binding energy, the reaction is less stable after fission. Therefore, energy must be supplied.

Amount of energy required:

E_{\text{required}} = 160.6 - 122.6 = 38.0\,\text{MeV}

Check options

A: $8.3\,\text{MeV}$ released — incorrect
B: $11.9\,\text{MeV}$ supplied — incorrect
C: $12.4\,\text{MeV}$ supplied — incorrect
D: $3.6\,\text{MeV}$ released — incorrect

So, based on the given data, none of the options matches.

Conclusion

The correct physical result is:

\boxed{38.0\,\text{MeV} \text{ must be supplied}}

Hence the stored answer $\mathbf{B}$ does not agree with the calculation. The reaction as written also appears nucleon-number inconsistent because $4 + 12 = 16 \neq 20$ , suggesting there may be a typo in the question.

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View written solutionFree

Use binding energies to find total binding energy of reactants and products

Given binding energy per nucleon:

For $\mathrm{^{20}Ne}$ : $8.03\,\text{MeV/nucleon}$
For $\mathrm{^{4}He}$ : $7.07\,\text{MeV/nucleon}$
For $\mathrm{^{12}C}$ : $7.86\,\text{MeV/nucleon}$

So total binding energies are:

B(\mathrm{^{20}Ne}) = 20 \times 8.03 = 160.6\,\text{MeV}

B(\mathrm{^{4}He}) = 4 \times 7.07 = 28.28\,\text{MeV}

B(\mathrm{^{12}C}) = 12 \times 7.86 = 94.32\,\text{MeV}

Find total binding energy of products

Reaction:

\mathrm{^{20}Ne \rightarrow \, ^4He + \, ^{12}C}

Total binding energy of products:

B_{\text{products}} = 28.28 + 94.32 = 122.60\,\text{MeV}

Compare initial and final binding energies

Initial binding energy:

B_{\text{initial}} = 160.6\,\text{MeV}

Final binding energy:

B_{\text{final}} = 122.6\,\text{MeV}

Change in binding energy:

\Delta B = B_{\text{final}} - B_{\text{initial}} = 122.6 - 160.6 = -38.0\,\text{MeV}

Since the products have less total binding energy, the reaction is less stable after fission. Therefore, energy must be supplied.

Amount of energy required:

E_{\text{required}} = 160.6 - 122.6 = 38.0\,\text{MeV}

Check options

A: $8.3\,\text{MeV}$ released — incorrect
B: $11.9\,\text{MeV}$ supplied — incorrect
C: $12.4\,\text{MeV}$ supplied — incorrect
D: $3.6\,\text{MeV}$ released — incorrect

So, based on the given data, none of the options matches.

Conclusion

The correct physical result is:

\boxed{38.0\,\text{MeV} \text{ must be supplied}}

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