The binding energies per nucleon for a deuteron and an α -particle are x₁ and x₂ respectively. The energy Q released in the reaction ²H₁ + ²H₁ → ⁴He₂ + Q, is (a) 4(x₁ + x₂) (b) 4(x₂ - x₁) (c) 2(x₂ - x₁) (d) 2(x₁ + x₂)

Answer: (b). Total BE of each deuteron = 2x₁, so two deuterons have 4x₁; total BE of ⁴He = 4x₂. Q = 4x₂ - 4x₁ = 4(x₂ - x₁). So the answer is (b) 4(x₂ - x₁).

The binding energies per nucleon for a deuteron and an α -particle… | NEET 1995 (AIPMT)

Q42NEET 1995 · AIPMTEasy

Nuclear Fission & Fusion

The binding energies per nucleon for a deuteron and an $\alpha$ -particle are $x_{1}$ and $x_{2}$ respectively. The energy $Q$ released in the reaction

${}^{2}\text{H}_{1} + {}^{2}\text{H}_{1} \rightarrow {}^{4}\text{He}_{2} + Q,$

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Answer: (b)

Total BE of each deuteron $= 2x_1$ , so two deuterons have $4x_1$ ; total BE of ${}^4\text{He} = 4x_2$ .
$Q = 4x_2 - 4x_1 = 4(x_2 - x_1)$ .
So the answer is (b) $4(x_2 - x_1)$ .

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