Question

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?

; 13.5 mg

Answer 1

General half‑life formula: A(t) = m(1/2)^{t/h}.

For m = 50 mg, h = 5.3 yr and t = 10 yr:
A(10) = 50(1/2)^{10/5.3} ≈ 50 · 2^{-1.8868} ≈ 13.5 mg.

(Equivalently A(t) = 50 e^{-(ln 2 / 5.3) t}.)