Radioactive Dating: Age of Ancient Rock Determined by Half-Life

[reree17]

A sample of an ancient rock contains one atom of lead for every atom of uranium. the uranium in the rock has a half - life of 4500 million years. It decays to form lead which is not radioactive. Explain why the age of the rock is 4500 million years.

I assumed that 1 x 4500 million years = 0.5 atom (half) / 2
2 x 4500 million years = 1 atom / 2. I have no idea what I was doing, ignore my terrible attempt. What I don't understand is WHY the age of the rock is 4500 million years, can someone please explain?

 

[ehild]

Half life means the time needed that the amount of the material decrease half of its initial amount. Uranium 238 undergoes a long decay chain till it becomes lead, but the half lives of all the intermediate steps are much shorter than the first one when the uranium atom decays to thorium, by emitting an alpha particle. So one can consider that half of the original uranium atoms in the rock converts to lead atoms in 4500 million years. The rock contains eual number of uranium atoms and lead atoms. All the lead atoms were uranium atoms at the beginning, when the rock was formed. What is the ratio between the number of the present uranium atoms to the initial number of uranium?

ehild