Cesium-137 undergoes beta decay and has a half-life of 30.0 years.How many beta particles are emitted by a 14.0-g sample of cesium-137 in three minutes?

Question

Quizplus · Accepted Answer

The number of beta particles emitted is proportional to the number of atoms of cesium-137 present and the time elapsed. The number of atoms of cesium-137 present is proportional to the mass of the sample. The time elapsed is 3 minutes, which is 0.05 hours. The half-life of cesium-137 is 30.0 years, which is 26280 hours. The fraction of atoms remaining after 0.05 hours is 2^(-0.05/26280) = 0.9999999999999999. The number of beta particles emitted is therefore proportional to 0.9999999999999999 * 14.0 g * 0.05 hours / 30.0 years * 26280 hours/year * 6.022 * 10^23 atoms/mol * 1 mol/137 g = 8.1 * 10^15 beta particles.

Cesium-137 Undergoes Beta Decay and Has a Half-Life of 30