- #1
stunner5000pt
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Homework Statement
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
[itex]A_{0} = 0.5[/itex]
[itex]A(t) = 0.01[/itex]
we can use the half life equation
[tex] A(t) = A_{0} \left(\frac{1}{2}\right)^{t/h}[/tex]
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 doesn't make much of a difference
So the answer is 8.48 x 10^7 years or 6.6 half lives.
Am i right? Please advise