Radioactivity and Half-life

Question

A rock containing 1mg of plutonium-239 is found in a glacier. The half-life of plutonium-239 is 25,000 years. If the rock was deposited 100,000 years ago during an Ice Age, how much plutonium-239 was in the rock at that time?

Answer 1

How many half lives have elapsed?

100,000 yrs x 1 half life/25,000 years = 4 half lives have elapsed.

After 1 half life...0.5 remains

After 2 half lives...0.25 remains

After 3 half lives...0.125 remains

After 4 half lives...0.0625 remains

Original mass of rock: 0.0625 x = 1 mg

x = 16 mg

Done another way, in case you don't have an exact number of half lives elapsed:

fraction remaining = 0.5ⁿ where n = number of half lives elapsed

fraction remaining = 0.5⁴

fraction remaining = 0.0625