A radio active substance has a half life period of 30 days. Calculate (i) time taken for `3//4` of original number of atoms to disintegrate, (ii) time taken for `1//8` of the original number of atoms to remain unchanged.

Explanation

Here, T=30days,t=?
No. of atoms disitingrated =`(3//4)N_0`
No. of atoms left after time t,
`N=N_0-3/4N_0=1/4N_0`
No. half lives in time t days,
`n=t/T=t/30`
No. of nuclei left after n half lives is given by
`N=N_0(1/2)^n`
`:. (N_0)/4=N_0(1/2)^(t//30) or (2)^(t//30)=4=2^2`
or`t/30=2 or t=60 days`
(ii) `t=? ,N=N_0//8`
As `N=N_0(1/2)^n :. (N_0)/8=N_0(1/2)^(t//30)`
or `(2)^(t//30)=8=(2)^3 or t/30 =3`
or `t=90 days `