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

Step-by-step solution

The number of counts left after time t array ll & N=N₀ ( 1 2 )^ t / T_ 1 / 2 & 30=240 ( 1 2 )^ 60 / T_ 1 / 2 or & 30 240 = ( 1 2 )^ 60 / T_ 1 / 2 [ t=1 ~h =60 ~min ] or & ( 1 2 )^3= ( 1 2 )^ 60 / T_ 1 / 2 array Comparing the powers, we get array ll & 60 T_ 1 / 2 =3 & T_ 1 / 2 = 60 3 or & T_ 1 / 2 =20 ~min array