Question

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.

Answer 1

(T_1/2)_A = 20 minutes

(T_1/2)_B = 40 minutes

t = 80 minutes

n = `"t"/("T"_(1/2))` N = `"N"_circ (1/2)^"n" = "t"/("T"_(1/2))`

For A : n_A = `80/20 = 4`

`"N"_"A" = "N"_circ (1/2)^4 = "N"_circ/16`

Number of A Nucleided decayed = 

`"N"_circ - "N"_circ/16 = (15"N"_circ)/16`

For B : n_B = `80/40 = 2`

`"N"_"B" = "N"_circ (1/2)^2 = "N"_circ/4`

Number of A Nucleided decayed = 

`"N"_circ - "N"_circ/4 = (3"N"_circ)/4`

`"N"_"A"/"N"_"B" = (15"N"_circ)/16 xx 4/(3 "N"_circ) = 5/4`

`"N"_"A"/"N"_"B" =` 5 : 4