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  • The half life of the radioactive radon is 3.8 days. The time, at the ends of which <img alt="\frac{1}{20 ^{th}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7B1%7D%7B20%20%5E%

The half life of the radioactive radon is 3.8 days. The time, at the ends of which \frac{1}{20 ^{th}}  of the radon sample will remain undecayed, is (Give \mathrm{ \log _{10} e=0.4343} )
 

Option: 1

3.8 days
 


Option: 2

16.5 days
 


Option: 3

33 days
 


Option: 4

76 days.


Answers (1)

best_answer

\begin{aligned} &\mathrm{Using ~N=N_0 e^{-\lambda t}}\\ &\mathrm{where, ~\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{0.693}{3.8}}\\ \mathrm{\therefore \frac{N_2}{20}} &\mathrm{ =N_0 e^{-\frac{\ln (2)}{3.8} t} }\\ \mathrm{\frac{1}{20} }&\mathrm{ =e^{-\frac{\ln (2)}{3.8}} }\\ \mathrm{\log \frac{1}{20} }&\mathrm{ =\log e^{-\frac{\ln (2)}{3.8} t}}=\mathrm{\log e^{-\frac{0.693}{3.8} t} }\\ \mathrm{ t} &=16.5 \text { days. } \end{aligned}

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