The inteisity of gamma radiation from a given source is `I_(0) ` . On passing throug 37.5 mm of lead it is reduced to `I_(0) // 8.` the thickness of lead which will reduce It to `I_(0) //2` is -

Options

A. `(37.5)^(1//3)` mm
B. `(37.5)^(1//4)` mm
C. `37.5 //3` mm
D. `(37.5//4)` mm

Answer

C

Explanation

As `(I)/(I_(0)) = e^(-mu x) therefore (1)/(8) = e^(-mu 37.5) " " … (i)`
and `(1)/(2) = e^(-mu x) " " …. (ii)`
Put (ii) in (i) , `e^(-3 mu x) = e^(-mu (37.5))`
`x = (37.5)/(3) = 12.5` mm