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The half-life of "(92)^(238)U against al...

The half-life of `"_(92)^(238)U` against `alpha`-decay is `4.5xx10^(9)` yr. Calculate the activity of 1g sample of `"_(92)^(238)U`.

Text Solution

Verified by Experts

We have to apply formula for activity `(R=lamdaN)`
and half-life `(T_(1//2)=0.693/(lamda))`.
According to the question,
Half-life, `T_(1//2)=4.5xx10^(9)` yr
`=4.5xx10^(9)xx3.11xx10^(7)s`
`because1" yr"=3.1x10^(7)s`
Mass = 1g, M = 238 amu
`therefore` Number of atoms in 1 g uranium
`N=m/(n)xxNA=(1xx6.02xx10^(23))/(238)`
Activity of radioactive sample `R=lamdaN`
`=0.693/(T_(1//2))xxN`
`=0.693/(4.5xx10^(9)xx3.1xx10^(7))xx(6.02xx10^(23))/(238)`
`=1.25xx10^(4)"Bq"`
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