So, I was told that, while radioactive elements have half lives that have been estimated (i.e. the time it takes for a material to decay to half it’s mass), kt’s not entirely predictable how often particles will decay in a given moment. If all that is true (which it might not be, feel free to correct in replies), is there a chance, if microscopically small, that a uranium rod could just fizzle out of existence in a matter of nanoseconds?
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> have half lives that have been estimated
Well, in many cases this has been measured very precisely. There is nothing particularly special about the “half” life, by the way – it’s just a convenient unit of measurement. It’s straightforward to convert it to/from the amount of time needed for any other given fraction to decay.
> that a uranium rod could just fizzle out of existence in a matter of nanoseconds
It’s difficult to get your head around just how many particles are in everyday quantities of stuff. There are about 10,000,000,000,000,000,000,000,000 water molecules in a glass of water, for example. I don’t know how big nuclear fuel rods are, but we’re talking that kind of quantity. Imagine rolling 10,000,000,000,000,000,000,000,000 dice and every single one lands on a 1. It’s technically possible, but you’re never going to see it happen.
This consideration comes up very often in physics and chemistry. You might have some kind of model of how a system made up of N particles behaves, but you might only be interested in cases where N is extremely, extremely large. In such cases, you can treat N as if it’s essentially infinite. This often allows you to turn a complicated model with random elements into a much simpler one that is purely deterministic. It’s called the “thermodynamic limit”. It’s technically just an approximation, but in many cases it’s essentially perfect. And that’s the case with reasonably large samples of radioactive isotopes. There is a random process underlying it, but if you wait 1 half-life, half of the sample *will* have decayed.
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