The half-life of radium is `1500 years`. In how many years will `1 g` of pure radium be reduced to one centigram?

Options

A. `3.927 xx 10^(2)years`
B. `9.927 xx 10^(2)years`
C. `99.927 xx 10^(2)years`
D. `0.927 xx 10^(2)years`

Answer

b

Explanation

Here, half -life of radium,` t=1500` years
Disintegration constant `lambda=(0.693)/(T)=(0.693)/1500 year^(-1)`
`N_(0) =1g N=10 mg = 1 `centigram `=10^(2)g`
`:. N=10 mg`
Now apply `N=N_(0) e^(- lambda t)`.