Use the following information to answer the question. In an experiment, a researcher studied the decay of (}^210_{84)PO , which decays by alpha emission and releases a stable (}^206_(82)Pb atom. The half-life of ()^210_{84)Po is 138.4 days.The mass of the sample of (}^210_{84) Po at the start of the experiment was 34.0 g. Numerical Response 6. The amount of {}^21084 Po remaining after 415.2 days was __ g.

Here's how to calculate the amount of Polonium-210 remaining after 415.2 days:<br /><br />1. **Determine the number of half-lives:**<br /> * Time elapsed: 415.2 days<br /> * Half-life of Po-210: 138.4 days<br /> * Number of half-lives = Time elapsed / Half-life = 415.2 days / 138.4 days = 3<br /><br />2. **Calculate the remaining amount:**<br /> * Initial mass: 34.0 g<br /> * After 1 half-life: 34.0 g * (1/2) = 17.0 g<br /> * After 2 half-lives: 17.0 g * (1/2) = 8.5 g<br /> * After 3 half-lives: 8.5 g * (1/2) = 4.25 g<br /><br />Therefore, the amount of ${}^{210}_{84}$Po remaining after 415.2 days is $\boxed{4.25}$ g.<br />