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Question

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 210 grams of a radioactive isotope, how much will be left after half-lives?Use the calculator provided and round your answer to the nearest gram.

Answer 1

Since there is no specified number of half-lives, is the question designed to produce a table? In any event, the formula for determining how much is left after X half lives is:

Mf = Mi*(HF^n),

where Mf = final mass, Mi = initial mass, H is the value 0.5 for the half-life, and t = n is the number of half-lives.

Thus, starting with 210 g, you can produce a table:

The amounts are rounded to the nearest gram. After the first half-life, 105 grams remain. Half of that is gone by the second half-life, to leave 53 grams, and so on.