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From the table of atomic masses determin...

From the table of atomic masses determine the velocity of a nucleus appearing as a result of `K`-capture in a `Be^(7)` atom provided the daughter nucleus turns out to be in the ground state.

Text Solution

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The process is
`e_(k)^(-)Be^(7) rarrLi^(7)+v`
The energy available in the process is
`Q=c^(2) ("Mass of " Be^(7) "atom-Mass of " li^(7) "atom")`
`= 0.00092xx931MeV= 0.86MeV`
The momentum of a `K` electron is negligible. So in the rest frame of the `Be^(7)` atom, most of the energy is taken by neutrino whose momentum is very nearly `0.86MeV//c`
The momentum of the recoiling nucleus is equal and opposite. The velocity of recoil is
`(0.86MeV//c)/(M_(Li))=cxx(0.86)/(7xx931)= 3.96xx10^(6)cm//s`
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