Question

The activity of a freshly prepared radioactive sample is `10^(10)` disintegrations per second , whose mean life is `10^(9)s` The mass of an atom of this radioisotope is `10^(-25) kg ` The mass (in mg) of the radioactive sample is

Answer 1

Correct Answer - 1
`N=N_0 e^(-lambda t)`
`(dN)/(dt)=10^(10)=N_0(lambda)e^(-10^(-9)t)`
At `(t=0)`
`10^(10)=N_(0) 10^(-9)`
Mass of sample `=N_0 =10^(-25)`
=`N_0` (mass of the atom)
`=10^(-6) kg`
`=10^(-6) xx 10^(3) g`
`=10^(-3) g`
`=1 mg` .