Calculate `t_(3//2)` for `Am^(241)` in years given that it emits `1.2 xx 10^(11) alpha`-particles per gram per second

Explanation

1 gram of `An` contains `N_(A)//241` nuclei `= N_(0)`.
Using the equation,
Rate of decay `= 1.2 xx 10^(11) s^(-1)`
`= K xx N_(0)`
`= K xx N_(A)//241`
`= K xx 6.02 xx 10^(23)//241`
` K = 1.2 xx 10^(11) xx 241//6.02 xx 10^(23)`
`= 4.8 xx 10^(-11) s^(-1)`
and `t_(1//2) = In 2//K = 0.693//K`
`= (0.693)//4.8 xx 10^(-11)`
`= 1.40 xx 10^(10) s = 458` years