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A radioactive nucleus of mass number A, ...

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

A

`(2v)/(A - 4)`

B

`(2v)/(A + 4)`

C

`(4v)/(A - 4)`

D

`(4v)/(A + 4)`

Text Solution

Verified by Experts

The correct Answer is:
C
`alpha`-particle has 4 units of mass. Therefore mass of the daughter nucleus after the emission of `alpha`-particle = (A - 4)
Let v' be the speed of daughter nucleus.
According to law of conservation of linear momentum, `A xx 0 = 4v + (A - 4)v'`
`rArr" "v' = - (4v)/(A - 4)`
-ve sign shows the recoil of the daughter nucleus.
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