Question

A sample of ${}^{14}C{O}_2$ was mixed with ordinary ${}^{12}C{O}_2$ for studying a biological tracer experiment. The 10 mL of this mixture at STP possess the rate of ${10}^4$ disintegration per minute. The number of millicurie of radioactive carbon is needed to prepare 60 litre of such a mixture is :

• A. [0.027 mCi]
• B. [0.081 mCi]
• C. [0.073 mCi]
• D. None of these

Answer 1

The correct option is A [0.027 mCi]

Rate of decay of $10ml$ gas $={10}^{4}dpm=\frac{{10}^4}{60}dps$
Thus rate of decay of $600$ liter gas $=\frac{{10}^4\times 600\times 1000}{60\times 10}={10}^{7}dps$
As we know $3.7\times {10}^{10}dps$ is shown by $2Ci$ of $C^{14}$
${10}^{7}dps$ is shown by $\frac{{10}^7}{3.7\times {10}^{10}}Ci$ of $C^{14}=2.7\times {10}^{-2}=0.027mCi$