Modern Physics Help: K-40/Ar-40 Atom Ratio Analysis, Age Calculation

[rock.freak667]

Homework Statement

Analysis of potassium and argon atoms in a moon rock sample shows that the ratio of the number of stable Ar-40 atoms to the number of radioactive K-40 atoms is 10.3.
Assume that all the Ar atoms were produces by the decay of K atoms, with a half-life of 1.25x10^ years.
(i)Calculate:
a) the fraction of the original K-40 atoms remaining in the rock
b) the number of half-lives that has elapsed
c) the age of the rock.

(ii) From the answers above, deduce the age of the solar system.

Homework Equations

$$N=N_0e^{-\lambda t}$$

The Attempt at a Solution

Can someone guide me on how to start this?

"the number of stable Ar-40 atoms to the number of radioactive K-40 atoms is 10.3."

Now in the formula N=N_0exp(-$\lambda t$) N is the no. of radioactive atoms at time t, So I am a bit lost.

 

[rl.bhat]

If N is the no. of radioactive atoms at time t and N_o is the no. of radioactive atoms at time t = 0, then what is N_o - N? And what is (N_o - N)/N ?

 

[rock.freak667]

Well $N_0-N$ would be the number of radioactive atoms left at time t.

But how do I find N_0 or N since I don't have the value of N at t=0 or at any value for t?

 

[rl.bhat]

(N_0 - N) is the number of stable atoms.
In the problem (N_0 - N)/N is given. And that is equal to [e^(lambda t)] -1.