Most probable radius of an atom Exactly WHAT is the most probable radius of a hydrogen atom? On what factors does it depend, if at all? Does it perhaps decrease/increase with an decrease/increase in the principal quantum number, n? There are some other answers on this website concerning the same but none explain what exactly it is. 
I have just passed out of high school and it would be great if someone could explain it to me in simple terms. 
Thanks very much! :) 
 A: The radius of an atom is determined entirely by quantum mechanics. There is no classical explanation. Explaining why electrons didn't just stick to the nucleus was one of the problems that drove the discovery of quantum mechanics. 
The problem with quantum mechanics is that it makes a lot less intuitive sense than classical mechanics. It starts with postulates that have no obvious connection with reality, and draws conclusions that seem wrong or even contradictory. But the conclusions match experimental results even when classical mechanics does not. 
In quantum mechanics, an electron doesn't have a definite position or momentum. It has a wave function from which the probability of finding it at a particular position or momentum can be calculated. An electron bound to a proton will probably be very near the proton.
One of the foundations of quantum mechanics is the Uncertainty Principal. The Uncertainty Principle says that if the uncertainty of an electron's position is reduced by confining it near a nucleus, then the uncertainty in its momentum increases. 
In very loose terms, an electron that may have a high momentum isn't likely to stay near a nucleus very long. On the other hand, an electron that is confined to a large radius is can have a small momentum. The nucleus can pull it closer. 
There is a size where these two opposing uncertainties balance. This determines the size of atoms. 
This is enough to give the idea, but it is not very quantitative. To really answer the question, you need to calculate the wave function of the electron. This is done with the Schrodinger equation, which is another not-all-that-intuitive foundation of quantum mechanics. 
The calculation is reasonably straightforward for hydrogen. But when you have more than one electron, it turns out that no two electrons can use the same wave function. So it gets more complicated. It is more than can be answered from scratch in one question. 
I will add one result. All atoms are about the same size as hydrogen. A hydrogen nucleus has a charge of +1. 
One electron bound to a larger nucleus of charge +n would have a smaller radius. But there are n electrons. To the last electron, a +n nucleus and n-1 electrons does not look extremely different from a proton. 
