A piece of radioactive material contains 10²° atoms. If the half life of the material is 20 seconds; the number of disintegration in the first second is?

A. 3.47 x 10¹⁸
B. 6.93 x 10²⁰
C. 3.47 x 10²⁰
D. 6.93 x 10¹⁸

Correct Answer:

Option A – 3.47 x 10¹⁸

Explanation

The number of disintegration,∆N in time interval At, is given by
– ∆N = N∆t
Where N is the number of atoms present at the time t
But ^ = (0.693)/T
∴ ∆N = (0.693)/1(1)/2 N∆t = (0.693 x 10)^{20 x 10}/20 = 3.47 x 10¹⁸