As a student and now as a science teacher, I have always thought and taught that electrons orbit in discrete shells and that electrons move to outer shells when energized and then “fall” back to a ground state and release a photon of energy. Standard stuff.
A recent video on quantum mechanics threw me for a loop. It said that Schrodinger’s wave equation explains that electrons orbit in a standing wave of different wavelengths so they have 1, 2, 3 nodes etc. The more nodes they have, the higher the energy.
Electrons, as particles, don’t “jump out”, they act as a wave that change wavelengths to gain energy.
I know that electrons exhibit particle-wave duality but these are two completely different physical ways of viewing electrons in an atom.
Is one more correct that the other?
Is the Bohr model an oversimplification?
Well, the Bohr model is certainly a simplification. But then again, the two sentence description in your second paragraph is also a simplification. Unless you’re covering the chalkboard with super hairy equations, anything you say is going to be a simplification.
So the question is really “What simplification is best for what I’m trying to do?” If you’re trying to get high school students to understand photon emission and basic covalent chemistry, the Bohr model is fine – students should probably be aware that it’s a simplification, especially the geometry (‘inner’ and ‘outer’ shells actually overlap spatially quite a bit, to the extent that spatial overlap makes sense for electron orbitals), but it’s a good, useful simplification for that level and thinking in those terms is fine for just about anyone not becoming a hard-core physical chemist.
The Bohr model is an oversimplificaion, but for Hydrogen is works better than it perhaps should.
What you are missing from the Bohr model is that the circumference of the orbit of the (singular for hydrogen) electron is an integer multiple of its wavelength. When the electron jumps to a new shell, it jumps by an amount that maintains an integer number of wavelengths. You can thus view the electron as a wave phenomenon.
The Bohr model predicts with reasonable accuracy the wavelengths of the emission spectrum of hydrogen. So it is a successful quantum theory as far as it goes. But it fails to work with more than one electron. For that you need the 3D world of Shrodinger’s wave mechanics. That also pulls in stuff that accounts for electron spin, line splitting and so on.
High-school chemistry dissolves in the presence of college-level chemistry.
Also, the inert gasses… aren’t, at least not if fluorine is there to push them around like schoolyard bullies.
Electrons don’t orbit the nucleus in a defined path. They exist in 3D clouds of probability which change shape with varying energy levels. These probability clouds can be visually represented by shaded 3D regions. Here are some examples: Atomic orbital - Wikipedia
This 3D interactive viewer allows you to rotate and inspect the electron orbital cloud, plus manipulate parameters. I don’t know if it works on a tablet.
https://www.falstad.com/qmatom/
It is common to teach high school students that electrons orbit like little satellites around the nucleus. Some reason that teaching even a simplified version of quantum physics to high school students is too hard and that those who go to university will eventually learn the truth and aren’t really handicapped by being taught the wrong thing for several years. This view is typified by the paper “Why we should teach the Bohr model and how to teach it effectively” (McKagan, et al): Phys. Rev. ST Phys. Educ. Res. 4, 010103 (2008) - Why we should teach the Bohr model and how to teach it effectively
However many educators call today’s common secondary school physics curriculum “A deformed vision of science”, Gil, D. P. & Solbes, J., 1993.
At the high school level, it’s not necessary to teach quantum physics or the Schrodinger model with a high degree of mathematical formalism. There are various possible ways this could be taught. Numerous papers have addressed this: Arons, 1990; Aubrecht, 1989; Cuppari, Rinaudo, Robutti, and Violino, 1997; Fischler & Lichtfeldt, 1992; Gil & Solbes, 1993; Jones, 1991, 1992; Lawrence, 1996; M¸ller & Wiesner, 2002; Petri & Niedderer, 1998; Stannard, 1990.
This short 2012 video discusses the negative ramifications of not teaching modern physics: https://www.youtube.com/watch?v=BGL22PTIOAM
Its amusing that the video linked above complains that a high school student sees no physics of the last 150 years. When I was an undergraduate I remember keeping track of when the mathematics we were taught was initially worked out. You could almost manage to get through undergraduate applied mathematics without any mathematics from the last century. Pure maths was a bit better, but not a lot. I remember in physics class how we were taught some new calculus ahead of when the maths course would reach it, so that we had the tools to manage some solid mechanics problems.
That was all a long time ago. Now the maths taught a high school is so dumbed down a large fraction of the first year is remedial mathematics. I don’t regret leaving the university system.
Thank you. I love the 3D viewer.
I was just wondering because the standing wave model does not seem too difficult to understand. If it is a more accurate representation, it could be caught in senior high school classes.
Well said.
As I high school teacher, I try and teach to the top of the class. This is very difficult because most students think they are at the top of the class. There is a lot of outside pressure to keep averages high because it makes student feel valued.
I am perhaps a bit old school and I see myself as a great filter that separates the wheat from the chaff, so to speak. I see so much potential in students wasted because the content is so dumbed down. It’s sad because these kids are hungry to learn and main thing they learn is that school is boring.
I’m not comfortable with the last sentence. One can certainly make the analogy between 1D harmonics and spherical harmonics. You’ll notice the picture in that article has shapes that look an awful lot like s p d and f orbitals. And a standard undergrad chemistry curriculum will have you work out the math that describes those orbitals (which I’ve since forgotten). I think maybe I’m just getting hung up on using “wavelength” here. Maybe I shouldn’t be.
It can be helpful to see a 2D cross section as in the atomic orbital wikipedia article.
My 10th grade chemistry definitely treated the Bohr model as an early-chapter oversimplification, after which we learned about atomic orbitals (complete with all four quantum numbers) and and very briefly touched on molecular orbitals (which I totally didn’t understand until college.) But I don’t recall any 3D wave analogy and I think that would have helped. Not that I could do the math at the time. But I think it would have helped rationalize the otherwise seemingly arbitrary shapes of orbitals.
I like to describe it (for laymen) as the behaviour of free elections being like the waves you see in a large body of water (where the surface of the water is much much larger than the wavelength of the waves). They look like what we usually think of a wave – having a standard wavelength, looking kind of like a sine wave, &c.
The behaviour of electrons in an atom is like the kind of waves you get in a small bucket of water. Just a bunch of sloshing around, but if you shake the bucket just right you get some nice standing patterns that oscillate at discrete frequencies.
Of course, there are lot of ways that electron waves are not like water waves, but analogies can only go so far.
In general, I think that stressing the wave nature of particle mechanics does far more good than harm. No, it won’t enable students to completely understand quantum mechanics (it takes at least an entire semester at the college level, after you’ve already mastered multivariate calculus, to do that, and probably a lot more when you account for dismantling classical misconceptions and intuition), but it does give at least a partial view that’s mostly accurate, and serves to demystify a great deal of quantum weirdness (for instance, the Uncertainty Relation also applies to classical waves).
I fully agree with this, and I’ll expand on it: The most famous Uncertainty Relation falls right out of the fact position and momentum are conjugate to each other, which means they’re related to each other by a Fourier transform. As far as I’m concerned, that alone is enough to put the wave mechanic view front and center in teaching quantum mechanics: The fact the Uncertainty Relation is the same in the quantum world as it is in the classical “guitar string” world isn’t a random neat fact, it’s hooked right into other fundamental facts, and is something which should drive intuition.
First day of genchem in college. I’m all ready to learn about moles n stuff. Instead:
She was so damn chipper about it, too.
In hindsight it was good, but at the time I was questioning my choices.