## standing circular wave model

$\lambda=\frac{h}{p}$

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905290504
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### standing circular wave model

in today's lecture, Lavelle's explanation of the standing wave model kind of flew over my head. How does this model explain how electrons have quantized energy states in atoms?

Samantha Pedersen 2K
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### Re: standing circular wave model

When waves interact while they are out-of-phase, they do not form a complete circle and they create an unstable state. In-between energy levels (such as 1.4 or 2.6) are represented by these incomplete circles and thus are unstable states. Whole number energy levels (such as 1, 2, 3, etc.) are represented by waves that interact in-phase to form a complete, smooth circle which is a stable state. Electrons want to be in the stable states, so they exist in quantized (whole number) energy levels represented by the waves that form complete, smooth circles.

Charlotte Adams 1A
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### Re: standing circular wave model

Is the standing circular wave model that shows waves out of phase (picture in lecture slides) inaccurate?

Jagveer 1I
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### Re: standing circular wave model

Charlotte Adams 2D wrote:Is the standing circular wave model that shows waves out of phase (picture in lecture slides) inaccurate?

Yes, it is inaccurate because that model shows what it would look like if you tried to model the electron in between energy levels, so you will get a circular standing wave that is not stationary, so the ends will not be in phase

Nadya Higgins 3F
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### Re: standing circular wave model

So I'm not super clear on it either, but to my understanding, it shows that electrons can only exist in certain quantized energy levels or orbits (n=1,2,3...).

First I think it's important to define a standing wave. From what I know, a standing wave is a wave pattern where two waves with the same frequency and amplitude are moving in opposite directions. They interfere with each other, producing an oscillating wave that appears fixed in the space.

A good example of a standing wave, is the strings on a guitar. If you imagine it, its ends are trapped, allowing it to vibrate only between its fixed points and at certain frequencies, wavelengths, or amplitudes depending on how hard it is plucked (how much energy is put into the system) and a variety of other factors like the length of the string or the tension in the string. However, for any string on a guitar, the waves appear fixed in spaced when the string is plucked.

The electron is similar to the strings of a guitar. Electrons are confined to certain orbitals and can not stably be somewhere in tandem between two energy levels (either it received enough energy to move up a level, or it didn't). So, instead of being a string trapped across a guitar, they can be imagined as a wave forming circular standing waves around the nucleus instead. However, in order for it to properly do this, only a whole or integral number of wavelengths can fit in the circumference (no partial wavelengths). This shows how electrons can only exist in certain quantized energies in an atom.

If anyone understands this more, please feel free to correct me because I am in no way an expert. I really only learned this today and I'm taking what I learned in high school physics (so it may be rusty).

Also here are some resources that may help more than my explanation; I encourage you to do more research if needed:

https://spark.iop.org/episode-507-elect ... waves#gref
https://demos.smu.ca/index.php/demos/mo ... ctronwaves
https://www.physicsclassroom.com/class/ ... ar-Strings

Eileen Quach Dis 2A
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### Re: standing circular wave model

When the peak of one wave meets the peak of another wave, or in other words, the waves are in phase, then that means that the energy absorbed/ emitted equals the energy difference between the specific energy levels. However, if the peak of one wave meets the trough of another, like in the diagram on the right in the lecture, the waves can't join together. This represents how the energy absorbed/emitted was not the exact amount of the energy difference between the energy levels.

DMaya_2G
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### Re: standing circular wave model

What exactly does it mean when an atom is "not a stable mathematical model/system?"

Massimo_Capozza_1G
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### Re: standing circular wave model

When talking about the standing circular wave model, does this model show the general "path" of the electron as it circles the atom's nucleus? I understand that electrons have wave-like properties, but it is also a physical particle, so does the circular wave model describe its orbit?

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