Question

The half-life of ²³¹₉₁Pa is 3.25 × 10⁴ y. How much of an initial 10.40 microgram sample remains after 3.25 × 10⁵ y?

Answer is 0.0102

Answer 1

Given that the half life of ²³¹Pa₉₁ is 3.25 x 10⁴ year

Initial amount is 10.4 x 10^-6 grams, t = 3.25 x 10⁵ year

we can use the integrated rate law for a first-order nuclear reaction

That is ln(N/No) = -kt and k = 0.693/t_1/2

ln(N/10.4*10^-6) = - (0.693/3.25*10⁴)*(3.25*10⁵) -------------------------------(1)

The above equation (1) gives N = 1.02 x 10^-8 grams of ²³¹Pa₉₁

Therefore, the sample remaining after 3.25 x 10⁵ years is 0.0102 Micrograms