63Ni decays by a first-order process via the emission of a beta particle. The 63Ni isotope has a half-life of 100. years. How long will it take for 65% of the nickel to undergo decay?

151.4863 years

Explanation:

Half life, t1/2 = 100 years

Initial concentration,[A]o = 100%

Final concentration, [A] = 35% (after 65% have been decayed)

Time = ?

Half life for a first Order reaction is given as;

t1/2 = ln (2) / k

k = ln (2) / 100

k = 0.00693y-1

The integral rate law for first order reactions is given as;

ln[A] = ln[A]o - kt

kt = ln[A]o - ln[A]

t = (ln[A]o - ln[A]) / k

t = [ln (100) - ln (35) ] / 0.00693

t = 1.0498 / 0.00693

t = 151.4863 years