The intensity of gamma radiation from a given source is `I`
On passing through `36 mm` of lead , it is reduced to `(1)/(8)` . The thickness of lead which will reduce the intensity to `(1)/(2)` will be

Options

A. 6 mm
B. 9 mm
C. 18 mm
D. 12 mm

Answer

D

Explanation

Intensity of gamma radiation when it passes through `x` is `I = I_(0) e^(-mu x)`
`rArr (I_(0))/(8) = I_(0) e^(-mu(36))` ....(i) and `(I_(0))/(2) = I_(0) e^(-mu (x))` ......(ii)
`(1)/(8) = e^(-36mu)` and `(1)/(2) = e^(-mu x) rArr e^(3 mu x) = e^(-36 mu) rArr x = 12 mm`