Question

The mean lives of a radioactive substance are 1620 and 405 years for β-emission and β-emission respectively. The time after which three fourth of a sample will decay if it is decaying both by β-emission and β-emission simultaneously will be ______ years.

(Take ln 2 = 0.693)

Options

• 440

• 449

• 450

• 400

Answer 1

The mean lives of a radioactive substance are 1620 and 405 years for β-emission and β-emission respectively. The time after which three fourth of a sample will decay if it is decaying both by β-emission and β-emission simultaneously will be 449 years.

Explanation:

`1/T = 1/T_alpha + 1/T_beta`

⇒ T = `(T_alphaT_beta)/(T_alpha + T_beta)` = 324 years

`N/N_0 = e^{-lambdat}`

`t = 1/lambda ℓn  N_0/N = T ℓn N_0/N`

t = 324 × 2ℓn2

t = 449.06 years

t ≈ 449 years