I got this question in school:
Explain, based on the properties of an ideal gas, why the ideal gas law only gives good results for hydrogen.
We know that the ideal gas law is $$P\cdot V=n\cdot R\cdot T$$ with $P$ being the pressure, $V$ the volume, $n$ the amount of substance, $R$ the gas constant and $T$ the temperature (Source: Wikipedia - "Ideal gas").
An ideal gas must fulfill the following:
The particles do have an infinitely small volume (or no volume),
The particles do not interact with each other through attraction or repulsion,
The particles can interact through elastic collisions.
Now, why does only hydrogen sufficiently fulfill these conditions? I initially assumed that the reason is that it has the smallest volume possible as its nucleus only consists of a single proton. However, two things confuse me:
(Let's first assume that my first idea was correct and the reason is the nucleus' scale/volume) helium's nucleus consists of two protons and two neutrons. It is therefore four times as large than hydrogen's nucleus. However, hydrogen's nucleus is infinitely times larger than an ideal gas molecule (which would have no volume), so why does the difference of $4$ significantly affect the accuracy of the ideal gas law, while the difference of an infinitely times larger hydrogen (nucleus) doesn't?
My first idea is not even true, as atoms do not only consist of their nucleus. In fact, most of their volume comes from their electrons. In both hydrogen and helium, the electrons are in the same atomic orbital, so the volume of the atoms is identical.
Other possibilities to explain that the ideal gas law only work for hydrogen and therefore only leave the collisions or interactions. For both of these, I do not see why they should be any different for hydrogen and helium (or at least not in such a rate that it would significantly affect the validity of the ideal gas law).
So where am I wrong here?
Note: I do not consider this a homework question. The question is not directly related to the actual problem, but I rather question whether the initial statement of the task is correct (as I tested every possible explanation and found none to be sufficient).
I asked my teacher and told them my doubts. They agreed with my (and yours from the answers, of course!) points but still were of the opinion that Hydrogen is the closest to an ideal gas (apparently, they were taught so in university). They also claimed that the mass of the gas is relevant (which would be the lowest for hydrogen; but I doubt that since there is no $m$ in the ideal gas equation) and that apparently, when measuring, hydrogen is closest to an ideal gas.
As I cannot do any such measurements by myself, I would need some reliable sources (some research paper would be best: Wikipedia and some Q&A site including SE - although I do not doubt that you know what you are talking about - are not considered serious or reliable sources). While I believe that asking for specific sources is outside the scope of Stack Exchange, I still would be grateful if you could provide some soruces. I believe it is in this case okay to ask for reference material since it is not the main point of my question.
I asked a new question regarding the role of mass for the elasticity of two objects. Also, I'd like to mention that I do not want to talk bad about my teacher since I like their lessons a lot and they would never tell us something wrong on purpose. This is probably just a misconception.