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A .^7Li target is bombarded with a proto...

A `.^7Li` target is bombarded with a proton beam current of `10^-4` A for `1` hour to produce `.^7 Be` of activity `1.8xx10^8` disintegrations per second.
Assuming that `.^7Be` radioactive nucleus is produced by bombarding `1000` protons, determine its half-life.

Text Solution

Verified by Experts

The totla number of protons bombarded
`=("it")/(lamda)=(10^(-4)xx3600)/(1.6xx10^(-19))=22.5xx10^(17)`
Numebr of `.""^(7)Be` produced
`N=(22.5xx10^(17))/1000=22.5xx10^(14)`
We know that activity
`A=lamdaN`
or `A=(0.693/(t_(1//2)))N`
`:.t_(1//2)=0.693N/A`
`=0.693xx(22.5xx10^(14))/(1.8xx10^(8))`
`=8.63xx10^(6)s`
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