A nucleus mass no- 238 initially at rest decay into another nucleus mass no- 234 emitting an - particle mass no- 4 with the speed of 1-17-107 m-sec- Find the recoil speed of the remaining nucleus-

Given, #10; #10;Mass of nucleus, M_2=234 u #10; #10;Mass of alpha, m=4 and velocity of alpha, v=1.17× #10;10^7 m/s #10; #10;Fr ...

A nucleus mas...

Question

A nucleus (mass no. $238$ ) initially at rest decay into another nucleus (mass no. $234$ ) emitting an $α$ particle (mass no. $4$ ) with the speed of $1.17 \times 10^{7} m / s e c$ . Find the recoil speed of the remaining nucleus.

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Solution

Given,

Mass of nucleus, $M_{2} = 234 u$

Mass of alpha, $m = 4$ and velocity of alpha, $v = 1.17 \times 10^{7} m / s$

From conservation of momentum

Initial momentum = final momentum

$M V_{i n i t i a l} = M_{2} V + m v$

$\Rightarrow 0 = 234 \times V + 4 \times 1.17 \times 10^{7}$

$\Rightarrow V = 2 \times 10^{5} m / s$

Recoil speed is $2 \times 10^{5} m / s$

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