Modern Physics Ques 123
- The half-life of the radioactive radon is $3.8$ days. The time, at the end of which $1 / 20$ th of the radon sample will remain undecayed, is (given $\log _{10} e=0.4343$ )
$(1981,2 M)$
(a) $3.8$ days
(b) $16.5$ days
(c) $33$ days
(d) $76$ days
Show Answer
Answer:
Correct Answer: 123.(b)
Solution:
Formula:
- Using $N=N _0 e^{-\lambda t}$
where $\quad \lambda=\frac{\ln 2}{t _{1 / 2}}=\frac{\ln (2)}{3.8}$
$\therefore \quad \frac{N _0}{20}=N _0 e^{-\frac{\ln (2)}{3.8} t}$
Solving this equation with the help of given data we find :
$ t=16.5 \text { days } $
BETA
