A count rate metre shows a count of 240 per minute from a given radioactive source later the metre shows a count rate 0f $30\min^{- 1}\ $. The half-life of the source is

Question

Dr. Abubacker · Accepted Answer

(c) The number of counts left after time t
$N = N_{0}\left( \frac{1}{2} ight)^{\frac{t}{T_{1/2}}}$
$	herefore$ $\ \ \ \ 30 = \ 240\left( \frac{1}{2} ight)^{\frac{60}{T_{1/2}}}$
or $(\because t\  = 1h\  = \ 60\ \min)$
$\frac{30}{240} = \left( \frac{1}{2} ight)^{\frac{60}{T_{1/2}}}$
or$\ \left( \frac{1}{2} ight)^{3} = \left( \frac{1}{3} ight)^{\frac{60}{T_{1/2}}}$
Comparing the powers, we get
$	herefore\ \ \frac{60}{T_{1/2}} = \ 3$
$\ \ \ \ T_{1/2} = \frac{60}{3}$
$\ \ \ \ \ \ T_{1/2}$= 20 min

Q. A count rate metre shows a count of 240 per minute from a given radioactive source later the metre shows a count rate 0f $30\min^{- 1}\ $. The half-life of the source is

Explanation

Reviewed by Dr. Abubacker

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