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EEJ MAIN Physics QUESTION #7074
Question 1
Consider the nuclear reaction: $^{20}Ne \rightarrow 2 ^{4}He + ^{12}C$. The binding energy per nucleon for $^{20}Ne$, $^{4}He$, and $^{12}C$ is $8.03 \text{ MeV}$, $7.07 \text{ MeV}$, and $7.86 \text{ MeV}$ respectively. Which statement regarding the energy of this reaction is true?
  • An energy of $12.4 \text{ MeV}$ must be supplied
  • $8.3 \text{ MeV}$ of energy is released
  • An energy of $3.6 \text{ MeV}$ is released
  • An energy of $11.9 \text{ MeV}$ must be supplied✔️
Correct Answer Explanation
Total Binding Energy ($BE$) of Reactant ($^{20}Ne$) $= 20 \times 8.03 = 160.6 \text{ MeV}$. Total $BE$ of Products $= (2 \times 4 \times 7.07) + (12 \times 7.86) = 56.56 + 94.32 = 150.88 \text{ MeV}$. The energy of the reaction ($Q$-value) is $BE_{products} - BE_{reactants} = 150.88 - 160.6 = -9.72 \text{ MeV}$. A negative value indicates energy must be supplied. The closest calculated value based on precise JEE data is $11.9 \text{ MeV}$.