Modern Physics 3 Question 24
25. 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
Objective Questions II (One or more than one)
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Solution:
- 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 :
$$ t=16.5 \text { days } $$
