Why can’t electron just reside between two energy shells? What would happen if we grab an electron and forcefully keep it in between two shells?
In: Physics
The best answer has to do with the Schrodinger wave function which I’m not qualified to talk about. (More about that below.)
The more attainable version has to do with the deBroglie wavelength of the electron. If an electron is a standing wave, then it has a wavelength and it can only occupy a space that’s either 1, or 2, or 3… wavelengths long.
“What if we grab an electron and forcefully keep it between two shells” is analogous to “what if we take a spring (or an old-school phone cord) and try to set up a standing wave that’s 0.8, or 0.9, or 1.1, or 1.2 times the length of the spring/cord?”. The answer is you can’t get a standing wave that way; you’ll get a chaotic mess of interference because your wave doesn’t match the cord length. In other words, the electron will refuse to settle down there, and because it’s a probability function you can’t force it; it can literally teleport (tunnel) out of your grasp to get to a spot where it’s stable.
Example: hydrogen electron in ground state; mass is 9.11×10^-31 kg, energy is 13.6eV (2.176×10^-18 J). Velocity is sqrt(2E/m) = 2.19×10^6 m/s. deBroglie wavelength is h/mv = 3.32×10^-10 m. If you wrap that wavelength around a circle, the circle has a radius of 5.29×10^-11 meters and…oh, wow, that’s exactly the Bohr radius. 🙂
If you want to watch, Angela Collier on YouTube has a video that I think is called “how big is a hydrogen atom” where she hacks through the in-depth explanation. Even she shortcuts some of the math because it’s a tedious pain in the ass, but she shows more detail than I’ve ever seen anywhere else.
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