The intensity of gamma radiation from a given source is I. On passing through&#x

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Question

The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to

\frac{I}{8}

. The thickness of lead which will reduce the intensity to

\frac{l}{2}

will be

Options:

A . 18 mm

B . 12 mm

C . 6 mm

D . 9 mm

Answer: Option B
:
B

I^{'} = I e^{- μ x} \Rightarrow x = \frac{1}{μ} l o g_{e} \frac{I}{I^{'}}

(where l= original intensity, I'= changed intensity)

36 = \frac{1}{μ} l o g_{e} \frac{I}{\frac{I}{8}} = \frac{3}{μ} l o g_{e} 2

......(i)

x = \frac{1}{μ} l o g_{e} \frac{I}{\frac{I}{2}} = \frac{1}{μ} l o g_{e} 2

......(ii)
From equation (i) and (ii), x=12mm.

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