please help me with this equation- astronomy!! im so confused.?

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

One small correction to the answers you've recieved. Using the mathematical model, you'd have to wait infinitely long for all of the K-40 to decay, but that model applies only as long as you have a "large" number of atoms in the sample. It's a statistical model. As an extreme example, suppose you had only one atom of K-40. After one half-life, does that mean you have half an atom left? Clearly not. As the number of atoms declines, you reach a state where the half-life stops being adequately represented by saying "half of the sample decays" and move into the region where you have to say it represents a 50% probability that any given atom will decay. This is much more difficult to model mathematically.

If you give the "infinitely long" answer, I'm sure it'll be accepted. If you're studying this stuff for real, though, you need to be aware what the models are that you're using and where they start to break down.

Answer 2

u need the half life of the radioactive potassium. lets say the half life is x years. now after x yrs u will have 0.40kg since half has decayed. similarly after 2 x yrs u will have 0.20kg.

so for every k.x years u will have 1 / (2^k) of 0.80kg

hence calculate k using half life and 1.3 billion like k.x = 1.3 billion and then use k to get mass.

Answer 3

The half life of K40 is 1.26 billion years, so after 1.3 billion years, about half of it is left (400 grams); after 2.6 billion years, half of that, or 200 grams, and after 3.9 billion years, half of that, or 100 grams. You would have to wait infinitely long to be certain that none was left.