Question

Two radioactive sources A and B of half lives of 1 hour and 2 hours, respectively, initially contain the same number of radioactive atoms. At the end of two hours, their rates of disintegration are in the ratio of ______.

विकल्प

• 1 : 4

• 1 : 3

• 1 : 2

• 1 : 1

Answer 1

Two radioactive sources A and B of half lives of 1 hour and 2 hours, respectively, initially contain the same number of radioactive atoms. At the end of two hours, their rates of disintegration are in the ratio of 1 : 2.

Explanation:

Given, T_A = 1 hr, T_B = 2 hr

t = 2 hr, R₀ = same for A and B

`R_A = R_0e^{-lambdat}`

= `R_0e^{-0.693/(1h) xx 2h} = R_0e^{-1.386}`

`R_B = R_0e^{-0.693/(2h) xx 2h} = R_0e^{-0.693}`

∴ `R_B/R_A = e^0.693 = 2  "or"  R_A/R_B = 1/2`

R_A : R_B :: 1 : 2