Bohr's model electron transition paths

[krytek]

Homework Statement

I'm trying to figure out what paths the electrons take when transitioning between stationary orbits.
For example if there are 4 orbits: n1, n2, n3, n4; How do I know if the electron goes from n4 ---> n1 or
n4--->n3 ---->n2 -----> n1 ?
I was asked to calculate the wavelengths of emitted photons. But is there only 1 such wavelength? 4? how many?

 

[SHISHKABOB]

hi, try using the little x₂ button in the post response

basically, an electron can go between any two orbital values

it can go from n₁ to n₂; n₁ to n₃, etc.

but of course, the energy that is required to go from, say, n₃ to n₄ is the same as the energy required to go from n₄ to n₃

Also, photons are only emitted when an electron goes from a higher energy orbital to a lower energy orbital. In other words, only worry about going from some n_x to n_y where y < x

you should have a formula for determining the energy of an electron at some orbital, and an equation for the energy of some photon with a given wavelength. If you take the difference between two orbitals, then that will tell you how much energy was released/absorbed when the electron went between them.

Going from n₃ to n₂ will have some energy difference, use that energy difference to find the wavelength

 

[krytek]

Thank you for the quick reply :)

Just to make sure I understand what you said.
it doesn't matter if it goes straight from n₃ to n₁ OR goes from n₃ to n₂ to n₁, either way there will only be a single photon emitted?
I was thinking the electron could emit 2 photons during the longer transition.

 

[SHISHKABOB]

well, it can go from n₃ to n₂ to n₁, and that will emit two photons. But generally, we just consider one transition at a time. Each transition produces a photon.

Going from n₃ to n₁ will produce a photon with the equivalent energy of the two photons produced when it goes from n₃ to n₂ to n₁.

 

[krytek]

Again, thank you. You're a rock star :)