How do scientists know the half life of a substance when the half life is longer than the time we have known about the substance?
In: Physics
Even if the half-life of Uranium-238 is 4.5 billion years some time will decay now and some in 10 billion years. Every moment U-238 atoms have some chance of decaying it is just very low. It also has no memory so the chances of a single atom decay this minute is the same as for the next minute and so on until it decays. Each atom is independent so neighboring atoms have no effect on it.
Atmos is very small so you can have huge amounts so even if the chances of one atom decay is very small if you have enough som will decay.
If you have one mole of U-238 atoms that have a mass of 238 grams you have 6.02214076×10^23 atoms. That is a 6 with 23 zeros after. If half will decay in 4.5 billion years 3*10^23 atoms will decay during that time.
4.5 billion is 4.5*10^9 so you have 3*10^23 / 4.5*10^9 =6.6*10^13 decays per year. Per second you have 6.6*10^13 /(365*24*60*60)=2*10^6 or 2 million atoms that decay per second.
You can calculate the half-life if you know the number of decays per unit of time today and the number of atoms in the sample.
The math is a simplification with content decay for a half-life, in practice, it will be more at this moment and less over time. It will be an exponential function but assuming a constant decay rate is a lot simple and get the point across.
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