A nucleus zAX emits an -particle with velocity v- The recoil speed of the daughter nucleus is-

The correct option is B 4v/A 4 Let the daughter nucleus by Y . _Z^AX→ _Z 2^A 4Y + (_2^4α )^++ + 2β^ #160; Let recoil velocity of Y be ...

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Standard X

Physics

Alpha Decay

A nucleus z...

Question

A nucleus $_{z}^{A} X$ emits an $α$ -particle with velocity $v$ . The recoil speed of the daughter nucleus is:

\frac{A - 4}{4 v}

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\frac{4 v}{A - 4}

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v

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\frac{v}{4}

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Solution

The correct option is B $\frac{4 v}{A - 4}$
Let the daughter nucleus by $Y$ .
$_{Z}^{A} X \to_{Z - 2}^{A - 4} Y + (_{2}^{4} α)^{+ +} + 2 β^{-}$

Let recoil velocity of $Y$ be $- v_{r}$ .

Using conservation of momentum:
$p_{i} = p_{f}$
$0 = (A - 4) v_{r} - 4 v$
$v_{r} = \frac{4 v}{A - 4}$

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A nucleus AzX emits an α-particle with velocity v. The recoil speed of the daughter nucleus is:

The correct option is B 4vA−4Let the daughter nucleus by Y.AZX→A−4Z−2Y+(42α)+++2β−Let recoil velocity of Y be −vr.Using conservation of momentum:pi=pf0=(A−4)vr−4vvr=4vA−4

A nucleus $_{z}^{A} X$ emits an $α$ -particle with velocity $v$ . The recoil speed of the daughter nucleus is:

The correct option is B $\frac{4 v}{A - 4}$
Let the daughter nucleus by $Y$ .
$_{Z}^{A} X \to_{Z - 2}^{A - 4} Y + (_{2}^{4} α)^{+ +} + 2 β^{-}$

Let recoil velocity of $Y$ be $- v_{r}$ .

Using conservation of momentum:
$p_{i} = p_{f}$
$0 = (A - 4) v_{r} - 4 v$
$v_{r} = \frac{4 v}{A - 4}$