Nuclear decay occurs according to first-order kinetics. What is the half-life of europium-152 if a sample decays from 10.0 g to 0.768 g in 50.0 years

13.5 years

Explanation:

Initial Concentration [Ao] = 10g

Final Concentration [A] = 0.768g

Time t= 50 years

Half life t1/2 = ?

These quantities are related by the following equations;

ln[A] = ln[Ao] - kt (i)

t1/2 = ln(2) / k (ii)

where k = rate constant

Inserting the values in eqn (i) and solving for k, we have;

ln(0.768) = ln(10) - k (50)

-0.2640 = 2.3026 - 50k

50k = 2.3026 + 0.2640

k = 2.5666 / 50 = 0.051332

Insert the value of k in eqn (ii);

t1/2 = ln(2) / k

t1/2 = 0.693 / 0.051332 = 13.5 years