A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later m

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13.Nuclei

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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 $

D

$20$

Solution

(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$

Standard 12

Physics

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