My prof said that if the ratio of mass (in a rock) for 40K and 40Ar was 1:3 then the age of the rock would be 2.5 billion years. I don't understand how he concluded that to be the age. The only thing he knew was that the half-life of K40 = 1.25 billion year. This is my thinking.


1/3 = 1/2 ^ (t/(1.25x10^9))
log(1/3)/log(1/2) = t/(1.25*10^9)
1.58=t/(1.25*10^9)
t= 1.58 *(1.25*10^9)
t= 1.98*10^9

I don't understand where he came up with 2.5 billion years as the age of the rock.

I noticed that it's the same question you asked earlier...

I was right that it's 4:1...that way it would be 2.5 billion years. lol

Ugh...

So the prof is wrong to say 1:3 would be 2.5 billion?

Yeah. Try the calculations for 4:1.

^^Nope, your prof is right...it's 1:3. Yes, there is 1/4 of the original amount (which is why your computation should have 1/4, ginaj), but the ratio of K40 to Ar40 is 1:3. Let's see why:

-After one halflife period, half of the K40 has decayed into Ar40, so it's 50% K40, 50% Ar40...namely, the ratio is 50:50, or 1:1

-After two halflife periods, there is now 25% of the original amount of K40, and 75% of it has decayed into Ar40...25:75, or 1:3.

Hope that helps!

Lol. My bad. I wasn't thinking straight...