The Earth

To find how old the Earth is, try measuring the ages of rocks. Just find the oldest.

But how do you measure the age of a rock?

You need a clock.
That can be any physical process in which some kind of change happens at a known rate.

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Simplicio: Well, you are lost there. Rocks don't change.

Sagredo: Sure they do. Rock formations get bent. Rock surfaces get weathered.

Simplicio: But you don't know the rate for that.

Sagredo: For once, you are right.

Salviati: Why not use radioactive decay.

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There are several possible methods.
One is K⁴⁰ --> Ar⁴⁰. (K is potassium, Ar is argon.)

• Assumption: When the rock solidified, there may have been some potassium, but there was no argon.
  • Potassium is highly reactive, so it likes to make chemical compounds.
  • argon is an inert gas, does not combine with chemicals in the rock.
• Half life for the this decay is 1.3 x 10⁹ years.
• 12% if the K⁴⁰ atoms decay to Ar⁴⁰.
• Measure amount of Ar gas trapped in the rock crystal.
• Measure the amount of K⁴⁰ that is still there decaying.
• Thus get number of K⁴⁰ atoms that must have been there to start with.
• Compute time since rock solidified.

Notes:

• There are several possibilities for the decay to be used.
• Sometimes the method is more elaborate.
• Use decays with long half lives for old things...
• Some assumptions are needed.

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Result: oldest rocks on Earth are about 4.0 x 10⁹ years old.

The Earth must be older than that.

Ages of oldest meteorites is about 4.6 x 10⁹ years.

So a good guess is that the age of the Earth is about
4.6 x 10⁹ years.

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