A radioactive element has a half life of 20 days . What amount would be left after 80 days , if the original amount was 8 g?

Explanation

Given, 20 days=1 half life
80 days =4 half lives
Initial mass `m_(0)=8g`
No. of atoms present at any instant is directly proportional to the mass of the sample present at that instant by definition of half life.
No. of atoms left unchanged after n half lives
`N=N_(0)((1)/(2))^(n)`
`n=4`
`m=m_(0)((1)/(2))^(n)=4xx((1)/(2))^(4)=4xx(1)/(16)=0.25g`