MCQ
A count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later the meter shows a count rate of $30$ per minute. The half-life of the source is ..........$min$
- A$120$
- B$80$
- C$30 $
- ✓$20$
✓
Answer
Correct option: D.
$20$
d
(d) $A = {A_0}{\left( {\frac{1}{2}} \right)^n}$
(d) $A = {A_0}{\left( {\frac{1}{2}} \right)^n}$
$ \Rightarrow 30 = 240{\left( {\frac{1}{2}} \right)^n}$
$ \Rightarrow {\left( {\frac{1}{2}} \right)^3} = {\left( {\frac{1}{2}} \right)^n}$
==> $n=3$
$\therefore$ $\frac{t}{{{T_{1/2}}}} = 3$
$ \Rightarrow\frac{{{v^2}}}{r} = \frac{{{n^2}{r^2}}}{{4{\pi ^2}{m^2}{r^2}}}= 20\, min$
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