Question 331: Atoms & Nuclei

Question

The intensity of gamma radiation from a given source is $$L$$. On passing through $$36$$ $$mm$$ of lead, it is reduced to $${{\rm I} \over 8}.$$ The thickness of lead which will reduce the intensity to $${{\rm I} \over 2}$$ will be

Accepted Answer

KEY CONCEPT :
Intensity $$I = {I_0}.{e^{ - \mu d}},$$
Applying logarithm on both sides,
$$ - \mu d = \log \left( {{I \over {{I_0}}}} ight)$$
$$ - \mu  	imes 36 = \log \left( {{{I/8} \over I}} ight).........\left( i ight)$$
$$ - \mu  	imes d = \log \left( {{{I/2} \over I}} ight).........\left( {ii} ight)$$
Dividing $$(i)$$ by $$(ii),$$
$${{36} \over d} = {{\log \left( {{1 \over 8}} ight)} \over {\log \left( {{1 \over 2}} ight)}}$$
$$ = {{3\log \left( {{1 \over 2}} ight)} \over {\log \left( {{1 \over 2}} ight)}} = 3$$
or $$\,\,\,d = {{36} \over 3} = 12\,mm$$

Answer

$$9mm$$

Answer

$$6mm$$

Answer

$$12mm$$

Answer

$$18mm$$

Atoms & Nuclei

The intensity of gamma radiation from a given source is $L. On passing through 36 mm of lead, it is reduced to {{\rm I} \over 8}. The thickness of lead which will reduce the intensity to {{\rm I} \over 2}$ will be

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