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

Given : Intensity of the gamma radiation from the source Io=I
Intensity I=Ioe−μx
where x is the thickness of lead
Now for x=36mm, intensity becomes I=I/8
∴I/8=Ie−μ×36
(loge1/8=−2;.079)
⇒μ=0.0578
Now let the thickness of lead be x so that the intensity becomes I=I/2
∴I/2=Ie−0.0578×x
(loge1/2=−0.693)
−0.693=−0.0578x
⇒x=12mm