Question

If the number of nuclei of a radioactive substance becomes `1/e` times the initial number in 10 days, what is the decay constant of the substance?

Answer 1

N(t) = N0e−λt

∴ `(N(t))/N_0 = e^(−λt) 1/(e^(−λt))`

∴ In this case `1/e = 1/(e^(−λt))`    ∴ λt = 1

∴ The decay constant, λ = `1/t = 1/10 day^(-1)`

= 0.1 day⁻¹