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

Options

A. 80 min
B. 120 min
C. 20 min
D. 30 min

Answer

C

Explanation

After time(=nT), the fraction of radioactive atom left behind is given by
`((N)/(N_(0)))=((1)/(2))^(n)=((1)/(2))^(i//T)`
where T is half-life time.
`rArr`   `((30)/(240))=((1)/(2))^(t//T)`    `rArr((1)/(2))^(3)=((1)/(2))^(i//T)`
`rArr`    3=`(60)/(T)rArr` T=20min.