In how many half-lives will 10.0 g of a radioactive nuclide decay to less than 10% of its original value?
Question 18.2: In how many half-lives will 10.0 g of a radioactive nuclide ...
We know that 10% of the original amount is 1.0 g. After the first halflife, half the original material remains and half has decayed (5.00 g). After the second half-life, one-fourth of the original material remains (i.e., one-half of 5.00 g). This progression continues, reducing the quantity remaining by half for each half-life that passes.
| 4 | 3 | 2 | 1 | 0 | Half-lives |
| 6.25% | 12.50% | 25% | 50% | 100% | Percent remaining |
| 0.625 g | 1.25 g | 2.50 g | 5.00 g | 10.0 g | Amount remaining |
Therefore the amount remaining will be less than 10% sometime between
the third and the fourth half-lives.
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