Question

If radioactive elements start their half-life after the atoms are made through nuclear fusion in other stars, aren't scientists calculating the birth year of the atom instead of the birth year of Earth?

Scientists use radiometric dating of meteorites that fell into the earth to calculate age of the earth using the half life of radioactive substances.
Who said radioactive atoms start decaying when they come to Earth?

Answer 1

Good point - see below

Explanation:

Nuclear fusion inside a star doesn't make elements with half-lives that are long lived enough to be considered. It is my understanding that solar nuclear fusion stops at Iron, and Iron's radioactive isotope has a very short halflife (compared to Uruanium, etc).

Most long lived radioactive isotopes (usually very heavy elements) like Uranium are not made through fusion in the star's core, but rather during the supernova event when the star "explodes".

I'm a biochemist and this is outside my realm of expertise, but the "vomit" of a supernova starts to gather into centers of mass, and you make a new solar system (simplistic). I think an excepted time-frame for this condensation of matter can be calculated. The uranium that ends up in Earth's crust was created before Earth was created, but if you take a sample of this Uranium, you can determine the number of half-lives it has undergone. Along with the solar system condensation timeline, you can get a rough estimate for the age of the Earth.