Imagine you have 1 person sitting in a concert hall. You want to know when they’ll cough. Issue is that there us no reason why they should ever cough. They could sit there for all eternity and not cough once.
Right so… you do this with two people. Still hard to say. However if you get enough people, someone will cough and when they do you ask them to leave. Someone will statistically cough up almost instantly if you got enough people. However the less people you have less likely they are to, since there is no reason why they should ever cough.
Half life is just the definition we have for statistical probability of half of the audience having coughed and left the concert hall.
Since atoms are not actually “real solid” things. They are made of particles of which we can only say that they are probably in a certain position at a certain time. Electrons for example can be wherever they want to be in their probability space; there is no reason why they should be in a specific place at a specific time, so we can only say that they are probably there. Issue we face as our microchips are getting smaller is that electrons can pass (tunnel) through insolators. Since they just decrese the possibility of electron being at the other side of it.
It is the same thing with light. You don’t know where it is until you have interacted with it. Until that it can be anywhere it isn’t probability area. There us no reason why light released from decay of an atom has to go to certain direction; it is just a burst of energy, it goes where ever it wants and you can only say that it probably is somewhere.
So in short, once your mass of atoms has decayd to on last atom. There is no reason why it should ever decay. Halflife just says that in this time period there is 50% chance that it has.
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