Assume that a neutron breaks into a proton and an electron. The energy released during this process is: (mass of neutron = 1.6725 × 10⁻²⁷ kg, mass of proton = 1.6725 × 10⁻²⁷ kg, mass of electron = 9 × 10⁻³¹ kg). (a) 0.51 MeV (b) 7.10 MeV (c) 6.30 MeV (d) 5.4 MeV

Answer: (a). Energy released = Δ m c² with Δ m = mn - (mp + me). The given mn and mp are misprinted as equal; the intended energy is the electron's rest energy, E = me c². E = 9 × 10⁻³¹ × (3 × 10⁸)² = 8.1 × 10⁻¹⁴ J E = 8.1 × 10⁻¹⁴1.6 × 10⁻¹³ MeV ≈ 0.51 MeV So the answer is (a) 0.51 MeV.

Assume that a neutron breaks into a proton and an electron. The… | JEE Main 2012 (AIEEE)

Q26JEE Main 2012 · AIEEEMedium

Radioactive Decays: Alpha, Beta, Gamma

Assume that a neutron breaks into a proton and an electron. The energy released during this process is: (mass of neutron $= 1.6725 \times 10^{-27}\text{ kg},$ mass of proton $= 1.6725 \times 10^{-27}\text{ kg},$ mass of electron $= 9 \times 10^{-31}\text{ kg}$ ).

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Answer: (a)

Energy released $= \Delta m\, c^2$ with $\Delta m = m_n - (m_p + m_e)$ .
The given $m_n$ and $m_p$ are misprinted as equal; the intended energy is the electron's rest energy, $E = m_e c^2$ .
$E = 9 \times 10^{-31} \times (3 \times 10^8)^2 = 8.1 \times 10^{-14}\text{ J}$
$E = \dfrac{8.1 \times 10^{-14}}{1.6 \times 10^{-13}}\text{ MeV} \approx 0.51\text{ MeV}$
So the answer is (a) $0.51\text{ MeV}$ .

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