A count rate meter shows a count of 240 per min from a given radioactive source. One hour later the meter shows a count rate of 30 per min. The half-life of the source is

Step-by-step solution

Let N be the amount of substance left, N₀ be the total amount of substance. The amount of substance left after N half-life is given by N N₀ = 1 2^ n Hence, 30 240 = 1 2^ n (Since, decay rate proportional to amount of substance) 2^ n =8 n=3 Number of half-life passed =3 Time taken for the substance to decay from 240 count rate to 30 count rate =1 ~h =60 ~min aligned Half-life &= Total time Number of half - life t_ 1 / 2 &= 60 3 =20 ~min aligned