Two samples X and Y contain equal amounts of radioactive substances. If `1/16 th` of a sample X and `1/256 th` of sample Y remain after 8h, then the ratio of half periods of X and Y is

Options

A. `2:1`
B. `1:2`
C. `1:4`
D. `1:16`

Answer

A

Explanation

Since, `(N)/(N_(0))= ((1)/(2))^((t)/(T_(1//2)))`
For X – sample `(1)/(16)= ((1)/(2))^((8)/((T_(1//2)x)) rArr 4= (8)/((T_(1//2)_(x))`
For Y- sample
`(1)/(256) = ((1)/(2))^((8)/((T_(1//2))_(Y))) rArr 8= (8)/((T_(1//2))_(Y))`
Now, `(4)/(8) = (8)/((T_(1//2))_(X)) xx ((T_(1//2))_(Y))/(8)`
`rArr ((T_(1//2))_(X))/((T_(1//2))_(Y)) = (2)/(1)`