Question

Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time `1/("a"lambda)` The value of a ______.

पर्याय

• 5

• 6

• 9

• 10

Answer 1

Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time `1/("a"lambda)` The value of a 9.

Explanation:

Radioactive material N_A have decay constant, λ₁ = 25λ 

Radioactive material N_B have decay constant, λ₂ = 16λ

N = N₀e^-λt

⇒ `"N"_"B"/"N"_"A" = "e"^(-lambda_(2)"t")/"e"^(-lambda_(1)"t") = "e"^(-lambda_(2)"t")."e"^(lambda_(1)"t")`

`"e"^1 = "e"^((lambda_1lambda_2)"t")` ⇒ ( λ₂ - λ₁)t = 1

⇒ t = `1/(lambda_1-lambda_2)=1/(25lambda-16lambda)=1/(9lambda)`

Compair with `1/("a"lambda)`, so a = 9