Question

Two radioactive materials X₁ and X₂ have decay constants 10λ and λ respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will belie after a time.

Options

• `1/(10λ)`

• `1/(11λ)`

• `11/(10λ)`

• `1/(9λ)`

Answer 1

`underline(1/(9λ))`

Explanation:

`N_1 = N_0e^{-lambda_1t}`, `N_2 = N_0e^{-lambda_2t}`

∴ `N_1/N_2 = e^{-lambda_1t}/e^{-lambda_2t} = e^{-(lambda_1 - lambda_2)t} = e^{-(10lambda - lambda)t} = e^{-9lambdat}`

Given `N_1/N_2 = e^-1`

∴ -9λt = -1 ⇒ t = `1/(9lambda)`