question_answer

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     AIEEE  Solved  Paper-2005

A) 6mm                     

B) 9mm     

C)        18mm  

D)        12mm

Correct Answer: D

Solution :

The intensity is given by \[l'=l\,{{e}^{-\mu \,\,x}}\] where, \[l=\] intensity of radiation \[-\mu \,x\,=\log \,\frac{l'}{l}\] \[-\mu \,(0.36)=\log \,\frac{l}{8\,l}\]                                    ...(i) Now, intensity is \[\frac{l}{2}\] and thickness is x', then \[-\mu \,x'\,=\log \,\frac{l}{2\,l}\]                                           ...(ii) From Eqs. (i) and (ii), we get \[\therefore \]