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

Half life period of element A`t_(1//2)` = 20 min.
Half life period of element B`t_(1//2)` = 40 min.
Number of nuclei in terms of half life
`N=(N_(0))/(2^((1)/(t_(1/2))))`
For element A`t_(1//2)` = 20 min.
`N_(A)=(N_(0))/(2^((1)/(t_(1/2))))`, at t = 80 min.
`N_(A)=N_(0)/2^(80/40)=N_(0)/2^(4)=N_(0)/16`
Decayed No. of A = `N_(0)-N_(0)/16=15/16*N_(0)`
For element B. `t_(1//2)` = 40 min.
t = 80 min.
`N_(B)=N_(0)/2^(80/40)=N_(0)/2^(2)=N_(0)/4`
Decayed No. of B = `N_(0)-N_(0)/4=3/4*N_(0)`
Ratio of decayed no. of A & B = `(15/16N_(0))/(3/4N_(0))`
= `5/4` i.e. 5 : 4.