# What exactly is the shape of an atom as per modern physics?

I am currently a student of grade $$11$$. I am pretty confused about how exactly the atom looks like? In books I have read till now used the electron orbiting model of atom. Some say there is "electron cloud" inside the atom. So can someone clarify my doubt?

• See this amazing visual by minutephysics Jul 1, 2023 at 14:30
• Actually, I think it's a very good question and you're getting some good answers. The bottom line is that it's very difficult to even define the concept of "shape" for something which comprises components defined statistically. Jul 2, 2023 at 6:51
• @khaxan For those who like to skip sponsoring parts, note that there is also a bit of information in the last 15 seconds of the video. Jul 3, 2023 at 10:04

The confusion arises because you have not yet learned much about quantum physics. Quantum physics is the most accurate and wide-ranging set of concepts and mathematical methods in physics, and it describes atoms very well. But quantum physics tells us that there is no single simple way to picture an electron.

An electron is not like a tiny particle moving from one place to another like a tiny planet on an orbit. But it is hard to say what it is like. This is why people bring in the word 'cloud'. This is because an electron is a bit like a charged cloud, smoothly filling a region of space around the atomic nucleus. The more precise statement is that the location and motion of the electron is fully described by a mathematical function called wavefunction. The modulus square of this function gives information about where the electron is. The way the function oscillates from place to place gives information about other properties such as energy and momentum.

If you take the squared wavefunction and multiply by the mass of an electron, you get the mass density. If instead you multiply by the charge of an electron, you get the charge density. It is usually this density which is plotted when you see pictures of what are called 'atomic orbitals'.

These orbitals are also like standing waves. But they are 3-dimensional ones. They oscillate with time and they typically have spatial oscillation in the radial direction and angular direction too. These 3-dimensional wavelike functions are, then, your best aid to visualizing the motion of an electron in an atom. But you should not entirely forget the orbit-like picture, because it reminds you that the electron is moving in and out and round and round, relative to the nucleus, by different amounts depending on which state of motion it is in.

• @Aqua - I know as much as you do about these things, but one thing I've come to realize about just about any subject is - the truth is almost always complicated and difficult to understand. And when you start to learn something (like in school), you start with a simplified approximation of that thing. Sometimes even a completely wrong approximation. And then, as you keep studying, you replace that approximation with a different (but more complicated) one, sometimes even multiple times. This is especially true of things involving quantum mechanics. Jul 1, 2023 at 21:53
• @Aqua Not exactly. The example of an ionic bond can be explained using this model as changes in those wavefunctions that describe the electrons of the sodium and chlorine atoms, and the changes do involve that ‘extra’ electron being more likely to be near the chlorine atom. And even though the textbook description is not ‘correct’, it’s a useful abstraction because it explains most macro-scale (that is, larger than subatomic-scale) behavior accurately in a way that people can easily conceptualize without diverging too much from what we believe to be the ‘correct’ model. Jul 1, 2023 at 22:27
• Dont look for a straight answer here, or by any physics professor, or any physics textbook. These people simply dont know. They will not admit it, no, not as long as the sun shines. They will talk about maths and quantum this and superposition that but you will get no answer.
– Atif
Jul 1, 2023 at 22:42
• @Aqua: All models are wrong. Some models are useful. To be more precise, some models are useful in some contexts. Jul 2, 2023 at 8:57
• Re textbook and chemistry. For ionic bonds the notion of an electron leaving one atom and going to another is a reasonable way to say what happens. The wavefunctions are indeed redistributed like that. And for covalent bonds you absolutely need quantum theory to make any sense of them. Now the wavefunction of one (or more) electrons extends between the atoms. More generally, the classical orbit picture cannot account for the stability of the situation. This is to do with emission of electromagnetic waves so beyond the entry-level discussion. Jul 2, 2023 at 10:55

The electrons in an atom do, in a sense, orbit its nucleus. However, if you imagine this as being like planets orbiting a star then this picture is misleading.

One difference is that the shapes of the electrons orbits (called "orbitals") are more complicated than the elliptical shapes of planets' orbits. The shape of an electron's orbital depends on how many other electrons are in the atom and which layers or "shells" they occupy.

Another difference is that because of quantum mechanics we cannot say exactly where an electron is at any point in time. Instead, its orbital is a "cloud" or distribution of probabilities - we can say where the electron is most likely to be, but there is always a chance it could be in a different place.

This Wikipedia article illustrates the shapes of some electron orbitals.

• IMO this is a better explanation for a high school student than the top answer. Jul 2, 2023 at 12:31
• "We can say where the electron is most likely to be, but there is always a chance it could be in a different place" If we can only talk in terms of probabilities then instead of making the claim that reality is probabilistic we should admit that our maths is incomplete and do not really explain what goes on. In other words, the maths is right some of the times, with some probability of being right. Whenever we look for an electron we do find it at one place, right? (contd.)
– Atif
Jul 4, 2023 at 8:11
• ...Did we ever observe same electron at two places? Do it even make sense? Obviously our maths do not match with our observation. So the fault is in maths. That should be said upfront and repeatedly, so one shouldn't question their observations, only their maths. Whenever we observe, in whatever way, we find a particle at only one place, any particle that be. Not just that but also in only one state. There is no superposition in reality. Superposition is a product of our maths, specifically our fourier transform, it has no resemblance with reality.
– Atif
Jul 4, 2023 at 8:14
• Mathematicians - which includes physicists - dont produce anything other than equations. Its engineers that design products. Engineers use maths when it makes sense, not when it tell fairy tales such as quantum this and string that. Maths make sense when its process, the step by step working of it, matches with reality, not when only inputs and outputs match with reality. Its because stepwise matching tells mechanism and engineers need that, they have to you know actually produce something.
– Atif
Jul 4, 2023 at 17:08
• You haven't read him, right? You are parroting what others said. If you have read him you would know that pi = 4 thing is for kinematics only, not geometry. Geometry is static, not changing, no time dimension. Also, do science, experiment, find the value yourself (see his experiment). There are no favourites in science, only in politics, dont do politics.
– Atif
Jul 4, 2023 at 17:14

It's a hard question to answer, as we really only have mathematical formulas, and can only create illustrations that emulate some aspects of the math (but not all).

Personally, I like to visualize electrons in an atom as standing waves around the nucleus, like this experiment.

When they are interacting with photons or otherwise participating in collisions, I picture it as a localized point particle (billiard ball).

I'm not claiming this is the most rigorously accurate approach possible, but it helps me and I think tracks reasonably well with the math.

Visuals are important to aid our understanding and calculation, and will never encompass the full reality.

Additional Note: although the various orbitals take a variety of mode shapes, the outermost orbital in any free atom is the s orbital, which is spherical. So the "shape" determining its collisions and interactions with other atoms (e.g. in a noble gas like Helium or Argon, or a gas of atomic hydrogen) is spherical. Molecules on the other hand like $$\mathrm{H}_2$$ or benzene in gaseous form can take on elliptical or more complex shapes. And condensed matter like liquid or solid is another topic entirely.

• Personally, I put my trust in the Wigner representation of QM. When you apply it to the Hydrogen ground syate, you get a simple expression for e.g. the kinetic energy in the $x$ direction. It shows you that along the $x$ axis there is no contribution. Momentum and position are orthogonal. In other words: the electron rotates around the nucleus. Trivial? No, not at all. Jul 2, 2023 at 17:59