Radioactive decay: elapsed time

Worked example

A radioisotope (half-life 576 yr) decays from 74.4 mg to 27.6 mg. How much time has passed?

1. 1. Radioactive decay: solve for t

   $t = t_{1/2}\,\dfrac{\ln(N_0/N)}{\ln 2}$

   = 824.0 yr

Answer: t = 824 yr

Method

t = t½ · ln(N₀/N) / ln 2.

Formulas used

• Radioactive decay

  $N = N_0\left(\tfrac{1}{2}\right)^{t/t_{1/2}}$

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