A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?

Question

Philoid · Accepted Answer

Suppose, Initially the amount of radioactive isotope is N₀

After time t if x% of it’s original value remains, and let λ be the decay constant

Then, we can write

∴ λt = ln[100/x]

we know that, ∴

Hence,

Given that

a) If x = 3.125% then t = = ≈ 5T years

b) If x = 1% then, t = = 6.645T years