# Which atom is the smallest atom?

Is hydrogen or helium the smallest atom? My teacher said that the smallest atom is the helium atom, but I think that the smallest atom is the hydrogen atom. It has a single electron and a single proton, whereas the helium atom has a pair of electrons, a pair of neutrons, and a pair of protons, which obviously occupy more space than the hydrogen atom.

My question is, which atom is the smallest atom of all?

• There is generally applicable and mostly successful way called searching, usually providing bigger number of more comprehensive answers in shorter time than interactive asking. The latter way is recommended only if the former one failed, as it spends resources of others by answering, instead of your own by searching. Oct 3 at 0:32
• @Poutnik I have searched my question in Chem.SE and other Q&A sites and I don't find any satisfactory answers. Most of the questions I search ask "how small is an atom?", rather than "the smallest atom". Resources of others by answering a question never gets wasted. The answer may be helpful to some ot the other future visitor. Why do you discourage asking a question? What is the purpose of Q&A sites then? Oct 3 at 5:11
• SE and Q/A sites are very small part of internet. I do not discourage asking, I discourage asking without proper searching. // When you ask, it is expected you have thoroughly searched and thought about the topic, providing explicit summary of partial answers/ideas/thoughts you have got until then. It is quite common requirement across all StackExchange sites. // Resources are wasted, when answering what is already written on multiple places. // Atomic radius + Data page Oct 3 at 6:07
• Be aware the proper terms to search do not always match your question, see e.g. google: atomic radius data page Oct 3 at 6:42
• @Poutnik The data page has two answers depending whether you look at the empirical radius or the theoretical radius. I was surprised that hydrogen is not even the second smallest accourding to theory. Oct 3 at 14:52

1. The volumes of the nuclei are negligible compared to the atomic radii (like a "pea in a soccer/football/cricket stadium").
2. The higher the nuclear charge, the closer the electrons to the nucleus in a given shell.
1. Helium has the smallest atomic radius.
• @huzaifaabedeen No, electrons are considered to be point particles, with no internal structure we know of. Protons are made of quarks, etc., and are extremely tiny, but not point particles.
– Ed V
Oct 2 at 16:58
• Maybe I should edit to say space visited by the electrons. @EdV Oct 3 at 0:22
• Just the fact that a small bird is flying in larger area than an elegant is walking does not mean a bird is bigger than an elefant. Oct 3 at 6:11
• @KarstenTheis I've initially upvoted your comment but "space visited by the electrons" is too orbit-oriented. Actually we shall speak of orbitals etc although it can go to far for OP. I would stick to the idea that the key is in the atomic radius. I also note that the question is someone surprising from a logical point of view. Oct 3 at 8:32

The behaviour of electrons in atoms is not well describes by the classical points and orbits model of the atom. a more accurate modle for electrons is using quantum physics, in the is system the electron aren't at a specific spot, instead they are described by a quantity called the wave function which gives the probability of the electron being in a specific position.

from statistics you can then work out the average position (the expectation value), this is the product of the position and how likely it is to be there (the probability)

if you do this for hydrogen and helium you get the figure below, where the solid lines are the probability distribution and the dashed lines are the average radius, which show that on average the electrons in helium are closer to the nucleus than in hydrogen.

hopefully that helps

Also if you want to break from the periodic table, there are atoms where the electrons are replaced by their subatomic cousins, muons. muons are heavier so are a lot closer to the nucleus so the atoms are a lot smaller, they are called Muonic atoms

• I think something went wrong with the integration: the (average) theoretical radius of Helium should be larger than that of He+ (0.500). Oct 22 at 15:03

Rutherford's gold foil experiment taught us that the protons and neutrons fill only a tiny portion of the atom, which we call the nucleus. The size of the atom is therefore only defined by the electron shells (orbitals), which in turn depend on the nuclear charge.

Your intuition about more electrons leading to a larger atom is correct, but more protons actually lead to a smaller atom. Which effect dominates depends on whether or not an additional electron finds a place in an existing electron shell. To gain some intuition as to how this works, it may be helpful to do a Gedankenexperiment wherein we build atoms by adding protons and electrons one at a time, neglecting the neutrons which are not important here.

1. Imagine you start with one proton and one electron; this is the $$\ce{H}$$ atom. Let's say its radius is 1 (the Bohr radius).

2. Add one proton to the nucleus to obtain the $$\ce{He+}$$ ion. Because the central charge of the nucleus has increased by a factor of two, but the number of electrons hasn't changed, the radius of this ion is halved compared to $$\ce{H}$$, i.e. 0.500.

3. Now add an electron to this system to obtain neutral $$\ce{He}$$. This second electron joins the first one in the 1s shell, expanding the atom only a bit to a radius of 0.567. This is just a sliver larger than $$\ce{He+}$$ and considerably smaller than $$\ce{H}$$.

4. If you were to move on to $$\ce{Li+}$$, the additional proton would contract the radius to about 2/3 of $$\ce{He}$$, but when you add a third electron to obtain $$\ce{Li}$$, it spawns a new 2s shell at a radius of 2.556, making the $$\ce{Li}$$ atom much larger than $$\ce{H}.$$

You can in principle continue this procedure, whereby each additional proton contracts the radius, and each additional electron expands it slightly. Whenever an electron shell is filled, adding another electron will cause a step-change in the atomic radius as can be seen in the jagged graph in one of the answers above.

Helium turns out to be the smallest atom on that graph, which is one of the reasons it was discovered in the sun before it was discovered on earth.