# Half life and the age of a planet

1. Jan 29, 2008

### stunner5000pt

1. The problem statement, all variables and given/known data
An extra solar planet is discovered that is 500 light-years away. It is found through spectroscopic analysis that the abundance of potassium - 40 to potassium - 39 on the planet is 99.9%. Assuming that the planet was created with equal amounts of the two potassium isotopes, how old is the planet?

2. The attempt at a solution
K-39 is stable with 20 neutrons

K-40 half life is 1.277 x 10^7 years

K-40 decays to Ar-40 but that is stable.
Since K-39 and K-40 were in equal proportion to begin with
$A_{0} = 0.5$
$A(t) = 0.01$

we can use the half life equation
$$A(t) = A_{0} \left(\frac{1}{2}\right)^{t/h}$$
And solving for t=8.48 x 10^7 s [/tex]

But the light from this planet took some time to reach us - 500 light years. But that doesnt make much of a difference

So the answer is 8.48 x 10^7 years or 6.6 half lives.

2. Jan 30, 2008

### Shooting Star

.

What does the ratio mean in terms of percentage? Please check your data. Do you mean that K40 is 99.9% of the total K?

3. Jan 30, 2008

### stunner5000pt

A(t) = .999 not 0.001

because the ratio is K-40/K-39 so there is 999 K-40 for every 1000 K-39

is that correct??

4. Jan 30, 2008

### Shooting Star

That sounds a bit reasonable. Then you have to find t from:

0.999 = 1*(1/2)^(t/h).

5. Jan 30, 2008

### stunner5000pt

Thanks for the help

This question is solved :)