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  • If  time is necessary for a radioactive isotope to become <img alt="\frac{1}{3}rd" src="https://

If  t_{1 / 3} time is necessary for a radioactive isotope to become \frac{1}{3}rd of its original amount, What fraction would be left after \frac{t_{1 / 3}}{3} time?

Option: 1

\mathrm{\frac{1}{\sqrt{3}}}


Option: 2

\sqrt{3}


Option: 3

3\sqrt{3}


Option: 4

\frac{1}{3\sqrt{3}}


Answers (1)

best_answer

\mathrm{t=\frac{1}{\lambda} \ln \frac{\left[N_{0}\right]}{[N]}}

\mathrm{\frac{t_{1 / 3}}{3}=\frac{1}{\lambda} \ln 3 }

Divide by 3 in both sides.
\mathrm{ \frac{t_{1 / 3}}{3}=\frac{1}{\lambda}\frac{1}{3}ln 3\Rightarrow \frac{t_{1 / 3}}{3}= \frac{1}{\lambda} \ln (3)^{1 / 3}=\frac{1}{\lambda} \ln \left[\frac{N_{0}}{N_{0} /(3)^{1 / 3}}\right] }

Posted by

Ritika Kankaria

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