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A radioactive nucleus, initially at rest...

A radioactive nucleus, initially at rest, decays by emitting a `beta`-particle and a neutrino (n) in mutually prependicular directions. The momentum `P_(N)` of recoil nucleus will be

A

`p_(n) + p_(beta)`

B

`sqrt(p_(n)^(2) + p_(beta)^(2))`

C

`(p_(n) p_(beta))/(p_(n) + p_(beta))`

D

`((p_(n) + p_(beta))p_(beta))/(p_(n))`

Text Solution

Verified by Experts

The correct Answer is:
B
Resolve momentum `p_(N)` into two perpendicular components and equate with momenta of neutrino (n) and `beta`- particle

`therefore p_(N) sin theta= p_(N), p_(N) cos theta= p_(beta), therefore (p_(N))^(2)= (p_(n))^(2) + (p_(beta))^(2)`, or momentum of recoil nucleus `= sqrt(p_(n)^(2) + p_(beta)^(2))`
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