A sample of a radioactive nuclide has a mass of 10 g. How many half lives must transpire until less than 21% of the original sample is present?

3 half-lives.

Explanation:

The decay of radioactive elements obeys first-order kinetics. Half-life time is the time required for the initial concentration be decreased to its half value.

Half-life time is constant for first-order reaction.

21% of the sample (10 g) represents (10.0 x 0.21 = 2.1 g).

10 g (first half-life) → 5 g (second half-life) → 2.5 g (third half-life) → 1.25 g.

∴ 3 half-lives are needed for the sample to reach less than 21% (<2.1 g) of its initial value.