Question

Two radioactive substances A and B have decay constants 3λ and λ respectively. At t = 0 they have the same number of nuclei. The ratio of the number of nuclei of A to those of B will be `1/"e"` after a time interval:

Options

• `1/λ`

• `2/λ`

• `1/(2λ)`

• `1/(5λ)`

Answer 1

`1/(2λ)`

Explanation:

The decoy constants of radioactive substances A and B are 3λ and λ, respectively.

No of nuclei of A. N₁ = N₀e^−3xt and of B. N₂ = N₀e^−xt 

 ∴ `"N"_1/"N"_2 = ("e"^(-3"xt"))/("e"^"xt") = 1/("e"^(2"xt"))`

Given, `"N"_1/"N"_2 = 1/"e" ∴ 1/("e"^(2"xt")) = 1/"e"`

⇒ 2xt = 1

∴ t = `1/(2λ)`