In this case, we are looking at a certain radioactive element with a half-life of 5 hours. With this information, we can determine how much of the original mass will be left after 2 days (48 hours). To do so, we need to calculate how many half-lives have passed during that time period: 48 hours / 5 hours = 9.5 half-lives.
Since each successive half-life reduces the mass by one half, after nine and a half such reductions our initial 6,470 grams would be reduced to 1/2^9 x 6 470 grams = 0.098 grams = 98 milligrams. Therefore after two days there would be 98 milligrams (0.098 grams) left from the initial 6,470 grams of radioisotope present when it was first measured.
Understanding and being able to utilize this concept can prove useful in many different situations and industries – medical professionals may use it when diagnosing diseases or creating treatments involving radioactive materials; scientists researching new substances may use it when attempting understand what happens during complex processes involving isotopes; engineers may find applications while designing equipment that could house or interact with such materials too; and so on
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