Two samples X and Y contain equal amount of radioactive substance. If `(1)/(16)` th of the sample X and `(1)/(256)` th of the sample Y, remain after 8 h, 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

For X radioactive substances
`N = N_(0)((1)/(2))^(t//T_(X))`
`(N)/(N_(0)) = ((1)/(2))^(8//T_(X))`
`(1)/(16) = ((1)/(2))^(8//T_(X))`
`rArr ((1)/(2))^(4) = ((1)/(2))^(8//T_(X))`
`T_(X) = 2`
For Y radioactive substances
`(N)/(N_(0)) = ((1)/(2))^(8//T_(Y))`
`(1)/(256) = ((1)/(2))^(8//T_(Y))`
`((1)/(2))^(8) = ((1)/(2))^(8//T_(Y))`
or `T_(Y) = 1`
`therefore (T_(X)) = (2)/(1)`