One gram of radium is reduced by `2` miligram in `5` yers by `alpha`-decay. Calculate the half-life of radium.

Options

A. 1700 yr
B. 1000 yr
C. 1115 yr
D. 979 yr

Answer

1

Explanation

`N_(0) = gm`
`N=1 g-2 mg=0.998 g`
`t=5 yr`
`use,N = N_(0)e^(-lambdat)`
`(N_(0))/(N)=e^(5 lambda)`
`(1)/(0.9989) = e^(5lambda)`
"taking log both sides"
`5lamda =ln(1.0020)`
and T=(0.693)/(lambda)=1672 yr`