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 210_(84) Po at the start of the experiment was 34 .og. releases a stable (}^206_(82)Pb atom. The half-life of ()^210_{84)PO is 138.4 days.The mass of the sample of Numerical Response 6. The amount of 210_(84) Po remaining after 4152 days was __ g. (Record your three-digit answer in the numerical-response section on the answer sheet.)

Here's how to calculate the amount of Polonium-210 remaining after 4152 days:<br /><br />1. **Determine the number of half-lives:**<br /> Divide the total time (4152 days) by the half-life (138.4 days):<br /><br /> 4152 days / 138.4 days/half-life = 30 half-lives<br /><br />2. **Calculate the remaining amount:**<br /> Start with the initial mass (34.0 g) and divide it by 2 for each half-life. Since there are 30 half-lives:<br /><br /> 34.0 g * (1/2)^30 = 0.0000310 g<br /><br />3. **Round to three significant figures:**<br /> The question asks for a three-digit answer. Rounding 0.0000310 g gives us 0.0000310 g, which to three significant figures is 0.0000310 g or 3.10 x 10^-5 g. Since we need a three-digit answer, we express this in standard notation and fill in leading zeros: 000.031. We take the first three digits.<br /><br />Therefore, the answer is $\boxed{031}$<br />