help with calculating years?

Question

if you start with 0.80kg of radioactive potassium (small40)K (or k to 40th power), how much wil remain after 1.3 billion years? After 2.6 billion years? After 3.9 billion years? How long would you have to wait until there was no (small40)K remaining?

Answer 1

The half life of potassium-40 is 1.28 billion years, which we shall estimate at 1.3 billion years.

Then in 1.3 billion years 0.5 * 0.80 kg = 0.40 kg will remain.

In 2.6 billion years 0.5 * 0.5 * 0.80 kg = 0.20 kg remains.

and at 3.9 billion years 0.5 * 0.5 * 0.5 * 0.80 kg = 0.10 kg is left.

The time you would have to wait until none remained is indeterminate, since the predictable 50% decrease is only applicable to large numbers of atoms and cannot be applied when the number of remaining atoms approaches zero.

Answer 2

The half life of Potassium 40 is 1277.000 Million years, so after that time, you will have only half of it left. And after another 1277.000 Million years, only half of the remaining will be left. You can do the math. And since you loose only half of it each half life, you will always have a bit left over. Even if you are really, really patient.