Half lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially, the samples have equal number of nuclei. Calculate the ratio of decayed numbers of A and B nuclei after 80 minutes.

Explanation

80 minutes = 4 half lives of A = 2 half live of B
Let the initial number of nuclei in each sample be N.
`N_(A)` after 80 minutes = `(N)/(2^(4))`
Number of A nuclides decayed = `(15)/(16)N`
`N_(B)` after 80 minutes =` (N)/(2^(4))`
Number of B nuclides decayed = `(3)/(4)N`
Required ratio = `(15)/(16) xx (4)/(3) = (5)/(4)`
`N_(A) : N_(B) = 5 : 4`