A ^238U nucleus decays by emitting an α pa

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A $^{238}U$ nucleus decays by emitting an $\alpha$ particle of speed $v\,m{s^{ - 1}}$. The recoil velocity of the residual nucleus is (in $m{s^{ - 1}}$)

A

$ - 4v/234$

B

$v/4$

C

$ - 4v/238$

D

$4v/238$

A $^{238}U$ nucleus decays by emitting an $\alpha$ particle of speed $v\,m{s^{ - 1}}$. The recoil velocity of the residual nucleus is (in $m{s^{ - 1}}$)

Initially $238\,U$ nucleus was at rest and after decay its part moves in opposite direction.
According to conservation of momentum
$4v + 234V = 238 × 0 $

==> $V = - \frac{{4v}}{{234}}$