Gold-198 is a radioactive isotope, and it has a half-life of about 2.5 days. You have 100 grams of Gold-198. How many grams remain after 20 days?

3.125 grams
1.5625 grams
0.78125 grams
0.390625 grams

0.390625 grams

Explanation:

A half-life of an element is the amount of time that it takes for half the mass of the element to decay.

Gold-198 having a half-life of 2.5 days therefore means that every 2.5 days, the mass is cut in half.

If there are 20 days, find out how many half-life periods there are:

= 20 / 2.5

= 8 periods

The half life is:

= Original mass * 0.5^number of half-life periods

= 100 * 0.5⁸

= 0.390625 grams

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