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. `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 X sample
`(1)/(16)=((1)/(2))^(8//T_(X)) or ((1)/(2))^(4)=((1)/(2))^(8//T_(X)) or 4=(8)/(T_(X))" ….(i)"`
For Y sample
`((1)/(256))=((1)/(2))^(8//T_(Y)) or ((1)/(2))^(8)=((1)/(2))^(8)=((1)/(2))^(8//T_(Y)) or 8=(8)/(T_(Y))" ....(ii)"`
Divide (i) by (ii) we get
`(4)/(8)=(8)/(T_(X))xxT_(Y))/(8) rArr (1)/(2)=(T_(Y))/(T_(X)) or (T_(X))/(T_(Y))=(2)/(1)`