Given the masses of various atomic particles mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u, mv = 0, md = 2.0141 u, where p proton, n neutron, e electron, v antineutrino and d deuteron. Which of the following process is allowed by momentum and energy conservation? (a) n + n → deuterium atom (electron bound to the nucleus) (b) n + p → d + γ (c) p → n + e+ + v (d) e+ + e- → γ

Answer: (b). A process is allowed only if the final rest mass is not more than the initial mass and momentum can also be conserved. (b) mn + mp = 2.0159 u > md = 2.0141 u: the extra energy goes to the γ and d recoil, which share momentum. Allowed. (a) Two particles fusing into one body: in the CM frame the single product must be at rest, so the released energy has nowhere to go. Not allowed. (c) mn + me > mp: needs energy, so a free proton cannot decay. (d) A single photon cannot have zero momentum, so e⁺ e⁻ → γ fails in the CM frame. So the answer is (b) n + p → d + γ.

Given the masses of various atomic particles mp = 1.0072 u, mn =… | JEE Main 2020 (6 Sep, Shift 2)

Q21JEE Main 2020 · 6 SEP · SHIFT 2Difficult

Radioactive Decays: Alpha, Beta, Gamma

Given the masses of various atomic particles

mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u,

$m_{\bar{v}}$ = 0, md = 2.0141 u, where p $\equiv$ proton, n $\equiv$ neutron,

e $\equiv$ electron, $\bar{v} \equiv$ antineutrino and d $\equiv$ deuteron. Which of the following process is allowed by momentum and energy conservation?

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Answer: (b)

A process is allowed only if the final rest mass is not more than the initial mass and momentum can also be conserved.
(b) $m_n + m_p = 2.0159\ \text{u} > m_d = 2.0141\ \text{u}$ : the extra energy goes to the $\gamma$ and d recoil, which share momentum. Allowed.
(a) Two particles fusing into one body: in the CM frame the single product must be at rest, so the released energy has nowhere to go. Not allowed.
(c) $m_n + m_e > m_p$ : needs energy, so a free proton cannot decay. (d) A single photon cannot have zero momentum, so $e^+ e^- \to \gamma$ fails in the CM frame.
So the answer is (b) $n + p \rightarrow d + \gamma$ .

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Radioactive Decays: Alpha, Beta, Gamma question from JEE Main 2020 (6 Sep, Shift 2)

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