question_answer

When \[{{U}^{238}}\] nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is                                                [AIEEE 2003]

A) \[\frac{4\,u}{238}\]

B) \[-\frac{4\,u}{238}\]

C) \[\frac{4\,u}{234}\]

D) \[-\frac{4\,u}{238}\]

Correct Answer: C

Solution :

[c]

Apply conservation of linear momentum, we get  (-ve sign is for opposite direction)

The residual nucleus will recoil with a velocity of  unit.

Recoil speed of residual nucleus is .

NOTE If they ask the recoil velocity, then answer remains same i. e.,  and not  as the word recoil itself is signifying the direction of motion of residual nucleus.