Jackeline Crist
Feb 19, 2025
physics – In the Bohr model, how many electron wavelengths fit around this orbit?
A hydrogen atom is in the n = 2 state. In the context of the Bohr model, how many wavelengths of the electron fit around this orbit?
2 Answers
Jan 12, 2025
You have mutually exclusive concepts here. In the Bohr model, the electron is a particle with no wavelength.
At the quantum scale, the electron’s wave function spreads out over the larger volume of space it occupies at higher energies. It will become in essence a standing wave at the orbit, or if unable to stabilize, the excess energy is released as photons with well-known wavelength and the electron "drops" down into the ground state, and stabilizes as a "standing wave" in orbit.
I like Bekki’s analysis, but it assumes things that cannot be bourne out by experiment, just as the Bohr model does. The electron is a ½ integer spin fermion, and as a direct result, the wave functions will be standing half-waves.
Thus, the wavelength orbit will be ½n where n is the principal quantum number.
At n = 2, you will have one wavelength as the circumference.
Of course, all of the above ignores relativistic effects.
Bohr’s hypothesis was that for principal quantum number n, the angular momentum is n hbar.
From that, you can calculate that the orbital radius is n^2 times the bohr radius. Therefore the circumference also goes up like n^2.
So if the angular momentum goes up by a factor of n, and the radius goes up by n^2, the momentum must go down like 1/n.
The deBroglie wavelength goes like 1/p, so it is proportional to n.
So the number of wavelengths per circumference goes like n^2/n = n.
So if the ground state orbital is one wavelength, the answer for any other orbital would be n.
–And yes, what X says is correct. ANY attempt to analyze the Bohr model in detail means building upon assumptions that we now know are incorrect.
Related Questions
"If this same quantity of energy were transferred to 2.5 kg of water at its boiling point, what fraction of the water wo...
Have you ever noticed how the rear wheel of a bike seems to follow the front wheel closely? Why does this happen, and is...
Please identify each of the following as measurements: Length Area Volume Mass Density Time Temperature...
A rescue pilot needs to drop a survival kit while flying at an altitude of 2,000.0 meters with a forward velocity of 100...
Today's CPUs operate at speeds measured in gigahertz rather than kilohertz. Is this statement true or false?
I have a question regarding torque in a magnetism context. I understand that the equation τ = IABsin(θ) will be relevant...
A 4.5 kg box slides down a 4.4 m high frictionless hill, starting from rest. It then travels across a 2.4 m wide horizon...
How does friction play a role in sledding and skiing? Specifically, what are the effects of friction on speed, control,...
What is the speed of light in kilometers per hour?
A radio telescope features a parabolic surface, as illustrated below. Given that the telescope is 1 meter deep and 12 me...