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The half-life of Au-198 is 2.7 days. When there are 800 atoms of Au-198 in a sample, a scientist starts a stopwatch. The scientist stops the stopwatch at 8.1 days. How many atoms of Au-198 remain?

Answer :

Final answer:

Using the concept of half-life, which is 2.7 days for Au-198, and knowing that 8.1 days have passed (which equals 3 half-lives), we can calculate that from the initial 800 atoms, only 100 atoms would remain after 8.1 days.

Explanation:

Calculating the Remaining Atoms

The question involves the half-life of a radioactive isotope, specifically Au-198. The half-life is the time required for half of the radioactive atoms in a sample to decay. In this case, the half-life of Au-198 is 2.7 days.

If a scientist starts with 800 atoms and measures them again after 8.1 days, we need to calculate how many atoms remain.

To determine how many atoms are left after 8.1 days, we need to calculate the number of half-lives that have passed. 8.1 days divided by the half-life of 2.7 days is 3 half-lives (8.1 / 2.7 = 3).

Each half-life reduces the number of atoms by one half. Therefore, after the first half-life, there would be 400 atoms remaining, after the second half-life 200 atoms, and after the third half-life 100 atoms.

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