The isotope 38Sr 90 is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500-g sample diminishes to 0.393 g in 10.0 yrs. Calculate the half-life.

Half-life = 28.8 years

Explanation:

The radioactive decay of an atom follows the equation:

Ln[A] = -kt + ln[A]₀

Where [A] is actual amount of isotope after time t; k is decay constant and [A]₀ initial amount of isotope

Solving for k:

Ln[0.393g] = -k*10yrs + ln[0.500]

-0.2408 = -k*10yrs

0.02408yrs⁻¹ = k

Half-life, is:

Half-life = ln 2 / k

Half-life = ln 2 / 0.02408yrs⁻¹

Half-life = 28.8 years