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

Here, `t=8h, T_(1)//T_(2)=?`
`(A_(1))/(A_(0))=(N_(1))/(N_(0))=(1/2)^(n_(1))=1/16=(1/2)^(4) :. n_(1)=4`
`(A_(2))/(A_(0))=(N_(2))/(N_(0))=(1/2)^(n_(2))=1/256=(1/2)^(8) :. n_(2)=8`
`(T_(1))/(T_(2)) =(t//n_(1))/(t//n_(2))=(n_(2))/(n_(1))=8/4=2:1`