Half-life of radium is 1500 y. In how many years will 1 g of pure radium reduce by 1 mg ?

Explanation

Let time in which 1g radium will reduce by 1 mg =t
So, remaining mass of radium =1-0.001 = 0.999 g
Now, assuming initial mass is `N_0` , and in time t mass becomes N then,
`N/N_0=0.999/1=0.999`
Again, `N=N_0 e^(-lambdat)`
or , `e^(lambdat) = N_0/N=1/0.999 `=1.001 (approx.)
`therefore lambdat =log_e(1.001)` =0.001 (approx.)
or , `0.693/T . t=0.001` [ `because` half-life , `T=0.693/lambda`]
or , `t=T/0.693xx0.001=1500/693` y =2.16 y (approx. )