Two radioactive elements X and Y have half - lives of 6 min and 15 min respectively . An experiment starts with 8 times as many atoms of X as Y . How long it takes for the number of atoms of X left equals the number of atoms of Y left ?

Options

A. a) 6 min
B. b) 12 min
C. c) 48 min
D. d) 30 min

Answer

D

Explanation

Let the initial amount of Y=1
So , the initial amount of X=8
X decomposes as ,
`8overset(1)to4overset(2)to2overset(3)to1overset(4)to(1)/(2)overset(5)to(1)/(4)`
Number of half - lives of X = 5
Y decomposes as 1 `overset(1)to(1)/(2)overset(2)to(1)/(4)`
Number of half - lives of Y=2
So , total time `T=nxxt_(1//2)`
`=5xx6=30` min
or `T=nxxt_(1//2)=2xx15=30` min