Question

Deduce the expression, N = N₀e^-λt for the law of radioactive decay.

Answer 1

Let the number of atoms present at any given time t is N and at the time t + Δt this number decreases N – ΔN to its value then, the rate of decay of atoms is – ΔN/Δt Therefore, according to the law of Rutherford and Soddy.

If at the time Δt the nucleus ΔN will be disintegrated then the rate of disintegration,

or dN = -λNdt ……. (i)

Now, arranging equation (1) again,

Integrating both the sides, we have

Taking the exponential on both the sides, we get

N/N₀ = e^−λt
or

N = N₀e^−λt …… (2)