Two radioactive sources A and B initially contian equal nno. of radioactive atoms. Source A has t½ of 1 hour and source B has t½ 2 hours. What is the ratio of rate of disintegration of A to B

i)initially

ii)after 2 hours

iii)after 10 hours

What is the method to do these questions?????

Radio active decay follows first order kinetics.

So, rate of decay is given by Rate = k [N₀ (1/2/)ⁿ]  where k is decay constant. k =0.693/ t_1/2 ; n is number of half-lives.

(i) Initially, n=0

So, Rate -1 = (0.693/ 1) N₀  and  Rate-2 = (0.693/ 2) N₀ 

Or (Rate-1 / Rate-2 ) = 2

(ii) After 2 Hours

2 Hours is 2 half lives for for A and 1 Half life for B

Rate -1 = (0.693/ 1) N₀ (1/2)² and  Rate-2 = (0.693/ 2) N₀ (1/2)¹

(Rate-1 / Rate-2 ) = 1

(iii) After 10 Hours

10 Hours is 10 half lives for for A and 5Half life for B

Rate -1 = (0.693/ 1) N₀ (1/2)¹⁰ and  Rate-2 = (0.693/ 2) N₀ (1/2)⁵

(Rate-1 / Rate-2 ) = 0.0625