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The intensity of gamma radiation from a ...

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

A

`9 mm `

B

`6 mm `

C

`12mm`

D

`18 mm`

Text Solution

Verified by Experts

The correct Answer is:
C
KEY CONCEPT : intensity `I = I_(0)e^(-mu d)`
Applying logrithm on both sides ,
`- mu d = log ((I)/(I_(0)))`
`- mu xx = log ((I//8)/(I))`……(i)
`- mu xx d= log ((I//2)/(I))`……(ii)
Dividing (i) by(ii)
`(36)/(d) = (log((1)/(8)))/(log((1)/(2))) = ( 3 log((1)/(2)))/(log((1)/(2))) = 3 or d = (36)/(3) = 12 mm`
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