Question

Suppose the amount of a certain radioactive substance in a sample decays from 8.00mg to 3.30mg over a period of 20.9 years. calculate the half life of the substance. round your answer

Answer 1

N = N0 e^-λ t basic equation for radioactive decay

N / N0 = e^-λ t

ln N / N0 = ln 3.3 / 8.0 = - 20.9 λ

λ = .886 / 20.9 = .0424

T(1/2) = .693 / .0424 = 16.4 yrs half life

Check 20.9 / 16.4 = 1.27 half lives

2^1.27 = 2.41 will decay to 1 / 2.41 in 20.9 yrs

3.3 * 2.41 = 7.95