The half life of a radioactive elements is 10 yrs. Calculate the fraction of the sample left after 20 yrs.

Explanation

Data supplied,
`T_(1//2) = 10 yrs :. t = 20 yrs = 2 xx 10 = 2T_(1//2) :. n = (2T_(1//2))/(T_(1//2))= 2`
`N = N_0 e^(-lambda t) = N_0 (e^(-lambda T_(1//2)))^(t//T_(1//2)) = N_0.(1/2)^(t//T_(1//2))`
Also `N = N_0//2^n`
`:. N_0//2^n = N_0 (1/2)^(1//2)`
`:. N/(N_0) = 1/(2^n) = 1/4`
`:. N = (N_0)/4`
i.e., No. of atoms left after 20 yrs = `(N_0)/(4)`, i.e. `1/4 th`of the original no. of atom.