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## Q. 12.9

A radioactive sample of mass 1.0 mg has a half-life of 1.0 h, which means that about 50% of the 1-mg sample will decay in 1.0 h. What fraction decays in 2.0 h?

## Verified Solution

At first thought, we might think that another 0.5-mg sample might decay in the next hour, leaving none of the original sample, but that is incorrect. During the second-hour period the probability is still 50% for each remaining nucleus to decay. Therefore during the second hour, the amount that decays is 50% of 0.5 mg, or 0.25 mg. The total amount decayed in the first two hours is then 0.50 mg + 0.25 mg = 0.75 mg, or 75% of the original sample. This result is consistent with the data point shown at time $2 t_{1 / 2}$ in Figure 12.10.