One gram ofo a radioactive substance disintegrates at the rate of `3.7 xx10^(10)` disintegarations per second. The atomic mass of the subsatnce is `226`. Calculate its mean life.

Answer

`7.194 xx10^(10)s`

Explanation

Given that activity of substance is
`A_(c)=3.7 xx10^(10)dps`
The number of atoms in `1 g` of substance,
`N=(1 xx 6.023 xx10^(23))/(226) =2.66 xx10^(21)"atoms"`
If `lambda` is the decay constant of the substance, we know that activity is given by
`A_(C) =lambda N`
or `lambda =(A_(c))/(N)`
`=(3.7 xx10^(10))/(2.66 xx10^(21)) s^(-1)=1.39 xx 10^(-11) s^(-1)`
Thus, mean life of the radioactive substance is
`T_(m) =(1)/(lambda)=(1)/(1.39 xx10^(-11)) =7.194 xx 10^(10)s`.