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

Answer

B

Explanation

`therefore l=l_(0)e^(-kx) Rightarrow (1)/(l_(0))=e^(-kx)`
`therefore ln((1)/(8))=-kxx36`
`or 3ln 2 =kxx36.....(i)`
In second casse `ln(1/2)=-kxxx`
or `ln (2^(-1))=-kx `
or `ln 2=kx ` .......(ii)
From (i) and (ii)
`3xx(kx)=kxx36`
or x=12mm.