Two samples X and Y contain equal amount of radioactive substances. If `1^(th)/16` of the sample Y , remain after 8 hours, then the ratio of half life periods of X and Y is

Options

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

Answer

A

Explanation

As `N/N_0=(1/2)^n`
where, number of half lives , `n=t/T`
T is the half life period
For sample X
`1/16=(1/2)^(8//T_X)` or `(1/2)^4 =(1/2)^(8//T_X)`
`rArr 4=8/T_X` ….(i)
For sample Y
`(1/256)=(1/2)^(8//T_Y)` or `(1/2)^8=(1/2)^(8//T_Y)`
`8=8/T_Y` ...(ii)
Dividing (i) by (ii) , we get
`4/8=8/T_X xx T_Y/8`
`1/2=T_Y/T_X` or `T_X/T_Y=2/1`