Well, we know that it is impossible to say exactly when a radioactive atom will go on decay. It is a random process. My question is why then a collection of them decays in a predictable nature (exponential decay)? Does the randomness disappear when they get together? What is the cause of this drastic change of their behaviour?
[Physics] Why does a collection of radioactive atoms show predictable behaviour while a single one is highly random
radioactivityrandomnessstatisticsstochastic-processes
Best Answer
Law of large numbers
This law simply states that if you repeat a trial many times, the result tends to be the expected value. For example if you roll a 6-sided die, you could get any of the six results 1, 2, 3, 4, 5, 6. But the average of the six results is 3.5, and if you roll the 6-sided die a million times and take the average of all of them, you are extremely likely to get an average of about 3.5.
But you 1) might not get a number close to 3.5, in fact there's a non-zero chance you get an average of, for example, 2 or 1, and 2) still can't predict which result you will get when you roll a single die.
In the same way, you might not be able to predict when a single atom will decay (i.e. when you roll a single die), but you can make very good predictions when you have lots of atoms (i.e. equivalent to rolling the die millions of times).