Question

At a certain time, a radioactive sample contains 2 × 10²⁰ atoms and disintegration rate is 3 × 10¹⁰ atom Per sec. when 2 × 10¹⁵ atoms are Left to decay its disintegration rate will be 

(A) 3 × 10⁵ atom/s 

(B) 3 × 10¹⁰ atom/s 

(C) 6.6 × 10¹ atom/s 

(D) 2.0 × 10² atom/s

Answer 1

The correct option is (A) 3 × 10⁵ atom/s.

Explanation:

Disintegration rate = (dN / dt) = – λN  i.e. R = – λN

Given : R = 3 × 10¹⁰ when N = 2 × 10²⁰

∴ λ = [(– R) / N] = – [(3 × 10¹⁰) / (2 ×10²⁰)] = – 1.5 × 10^–10

∴ when N = 2 × 10¹⁵

then    R = – λN = – (– 1.5 × 10^–10) × 2 × 10¹⁵

R = 3 × 10⁵ atom/sec