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

Step-by-step solution

aligned & I=I₀ e^ -k x I I₀ =e^ -k x & ( I I₀ )=-k x aligned In first case aligned & ( 1 8 )=-k 36 & (2⁻³ )=-k 36 & or 3 2=k 36 aligned In second case, ( 1 2 )=-k x or (2⁻¹ )=-k x or 2=k x From (i) and (ii) 3 (k x)=k 36 or x=12 ~mm .