A radioactive nucleus of mass number A, initi | vedclass

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(C) According to the law of conservation of linear momentum, the initial momentum of the system is zero because the nucleus is initially at rest.Let $

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$\frac{4 v}{A-4}$

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(C) According to the law of conservation of linear momentum, the initial momentum of the system is zero because the nucleus is initially at rest.Let $M$ be the mass of the parent nucleus, which is proportional to the mass number $A$. Thus, $M = kA$.The mass of the $\alpha$-particle is $4$ (in atomic mass units), and the mass of the daughter nucleus is $(A-4)$.Let $V_r$ be the recoil speed of the daughter nucleus.By conservation of momentum: $P_{	ext{initial}} = P_{	ext{final}}$$0 = m_{\alpha} v + m_{	ext{daughter}} V_r$$0 = 4v + (A-4) V_r$$V_r = -\frac{4v}{A-4}$The magnitude of the recoil speed is $\frac{4v}{A-4}$.

$A$ radioactive nucleus of mass number $A$, initially at rest, emits an $\alpha$-particle with a speed $v$. The recoil speed of the daughter nucleus will be

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