Question

For radioactive substances, the fraction of its initial quantity (N₀) which will disintegrate in its average lifetime is about ______.

(e = 2.71)

Options

• `(2/3)N_0`

• `(1/3)N_0`

• `(1/2)N_0`

• `(0.9)N_0`

Answer 1

For radioactive substances, the fraction of its initial quantity (N₀) which will disintegrate in its average lifetime is about `underlinebb((2/3)N_0)`.

Explanation:

The initial amount of substance = N₀

and remaining amount = N

According to first-order decay,

N = `N_0e^{-lambdat}`

Fraction of substance remaining = `N/N_0 = e^{-lambdat}`

Here, `t = tau = 1/lambda`

∴ `N/N_0 = e^{-lambda. 1/lambda} = e^-1 = 1/e ⇒ N/N_0 = 1/2.71`

∴ Fraction of substance disintegrate = `1 - N/N_0`

= `1 - 1/2.71 = 1.71/2.71 ≈ 2/3`

∴ The fraction of the disintegrated initial quantity will be `(2/3)N_0`.