Question

How do you determine the total mass of an original 28.0-milligram sample of Po-210 that remains unchanged after 414 days?

Answer 1

Polonium (Po), a radioactive, silvery-gray or dark metallic component of the oxygen gathering ($Group{\text{ }}16{\text{ }}\left[ {VIa} \right]$ in the periodic table). The first component to be discovered by radiochemical analysis, polonium was discovered in 1898 by Pierre and Marie Curie, who was investigating the radioactivity of a specific pitchblende, a uranium ore. The extremely intense radioactivity not owing to uranium was ascribed to another component, named by them after Marie Curie's country, Poland. Its abundance in the Earth's crust is around one section in ${10^{15}}$ . It occurs in nature as a radioactive decay result of uranium, thorium, and actinium. The half-life of its isotopes range from a small amount of a second as long as $103$ years; the most common natural isotope of polonium, polonium-210, has a half-life of $138.4$ days.

Complete step by step answer: Given the boundary conditions of the problem, it was specified that the mass of
$^{210}Po$ stayed unaltered. I recognize, notwithstanding, that this is a radioactive decay problem, and $^{210}Po$ is a shouting hot isotope and α−emitter with a half-existence of $138.4$ days; this information should have been provided with the problem.
Thus your polonium isotope has encountered 3 half-lives.........And there is in this way
${(1/2)^3} = 1/8$ of the original mass i.e.$.{\text{ }}3.5{\text{ }}m.g$

Note:
Polonium usually is isolated from by-products of the extraction of radium from uranium minerals. In the chemical isolation, pitchblende ore is treated with hydrochloric Acid, and the resulting solution is warmed with hydrogen sulfide to hasten polonium monosulfide, PoS, alongside other metal sulfides, such as that of bismuth, $B{i_2}{S_3}$ , which resembles polonium monosulfide closely in chemical behavior, however, it is less soluble. Because of the difference in solubility, repeated partial precipitation of the combination of sulfides concentrates the polonium in the more soluble fraction, while the bismuth accumulates in the less soluble portions. The solubility in solubility is small, be that as it may, and the process must be rehashed ordinarily to achieve a total separation.