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Standard XII

Physics

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A small quant...

Question

A small quantity of a solution containing $N a^{24}$ radio – nuclide of half life T and activity $R_{0}$ is injected into blood of a person. $1 c m^{3}$ of sample of blood taken from the blood of the person shows activity $R_{1}$ . If the total volume of the blood in the body of the person is V, find the time after which sample is taken:

\frac{T}{2 I n (2)} [I n (\frac{R_{0}}{V R_{1}})]

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\frac{T}{I n (2)} [I n (\frac{V R_{0}}{R_{1}})]

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\frac{T}{I n (2)} [I n (\frac{V R_{1}}{R_{0}})]

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\frac{T}{I n (2)} [I n (\frac{R_{1}}{V R_{0}})]

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Solution

The correct option is A $\frac{T}{2 I n (2)} [I n (\frac{R_{0}}{V R_{1}})]$
Total volume of blood,
$V = \frac{T o t a l a c i t i v i t y R}{(A c t i v i t y p e r c m^{3} R_{1})} = \frac{R_{0} e^{- λ t}}{R_{1}} O r, \frac{V R_{1}}{R_{0}} = e^{- λ t} O r, - I n (\frac{V R_{1}}{R_{0}}) = λ t = \frac{I n (2) t}{T} T = \frac{T}{I n (2)} I n (\frac{R_{0}}{V R_{1}})$

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The correct option is A T2 In(2)[In(R0VR1)]Total volume of blood, V=Total acitivity R(Activity per cm3R1)=R0e−λtR1Or,VR1R0=e−λtOr,−In(VR1R0)=λt=In(2)tTT=TIn(2)In(R0VR1)