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

Options

A. `1 : 4`
B. `5 : 4`
C. `1 : 16`
D. `4 : 1`

Answer

B

Explanation

For `A_(t (1)/(2)) = 20` min t = 80 min , number of half lifes n = 4
`therefore` Nuclei remaining = `(N_(0))/(2^(4))` . Therefore nuclei decayed = `N_(0) - (N_(0))/(2^(4))`
For `B_(t (1)/(2)) = 40` min , t = 80 min , number of half lifes n = 2
`therefore ` Nuclei remaining = `(N_(0))/(2^(2))` . Therefore nuclei decayed `= N_(0) - (N_(0))/(2^(2))`
`therefore` Required ratio = `(N_(0) - (N_(0))/(2^(4)))/(N_(0) - (N_(0))/(2^(2))) = (1 - (1)/(16))/(1 - (1)/(4)) = (15)/(16) xx (4)/(3) = (5)/(4)`