Question

A radioactive sample remains undecayed 916 after time t. how much sample remains undecayed after time T/2​

Answer 1

It has given that, a radioactive sample remains undecayed 916 after time T.

To find : amount of sample remains undecayed after time T/2.

solution : you know as well, A radioactive decay is a first order reaction and it can be calculated by using equation, N = N₀e¯(λt)

where N is amount of substance remains undecayed after time t, N₀ is initial amount of substance and λ is radioactive constant.

here N = 916 at time T

so, 916 = N₀e¯(λT) .......(1)

let after time T/2 , N' will remain undecayed.

so, N' = N₀e¯(λT/2) = N₀e¯(λT)e½

⇒N' = 916 × e½ = 1510.2288 ≈ 1510

Therefore the amount of sample remains undecayed after time T/2 is 1510