[jeffreyH (OP)]

So I have kλ/(2π) = 1. Does this make sense with respect to atomic orbitals. Here k is wave number and lambda is wavelength.

[PmbPhy]

So I have kλ/(2π) = 1. Does this make sense with respect to atomic orbitals. Here k is wave number and lambda is wavelength.

Yes. It's valid.

[Bored chemist]

It might work in the right units, but it's not clear when it would apply.

[jeffreyH (OP)]

It's not clear to me either. I'm still thinking about it.

[jeffreyH (OP)]

If we consider the wavenumber k to be in radians per unit distance we have the following series.

λ = 1, k = 2π
λ = 2, k = π
λ = 3, k = 2π/3
λ = 4, k = π/2

Not sure of any significance.

[jeffreyH (OP)]

I'm looking at the hydrogen spectral lines and the Rydberg formula at the moment.

[Bored chemist]

I'm looking at the hydrogen spectral lines

Pretty colours, aren't they.

[jeffreyH (OP)]

If that's what floats your boat.

[jeffreyH (OP)]

So what if we have the following formula?

Δλ = 2πγ/k

Can we introduce gamma to modify the wavelength due to relative velocity? Can this be a valid way of viewing orbitals?

[Bored chemist]

So what if we have the following formula?

Δλ = 2πγ/k

Can we introduce gamma to modify the wavelength due to relative velocity? Can this be a valid way of viewing orbitals?

No
Orbitals have three dimensional shapes and also odd properties that have to fit with the uncertainty principle.

[jeffreyH (OP)]

For anyone interests here is a video from fermilab. It is not directly related.

[jeffreyH (OP)]

To follow on from what bc said we have the following links describing the electron orbitals.
http://hyperphysics.phy-astr.gsu.edu/hbase/Chemical/eleorb.html
Awful music awful robot voice.

[jeffreyH (OP)]

Now another question. Since the electron has mass it also has inertia and so why are the orbitals considered immune from relativistic effects?

[jeffreyH (OP)]

Within the heavier elements there can be relativistic effects so why would relative motion have no effect?
https://en.m.wikipedia.org/wiki/Relativistic_quantum_chemistry

[Bored chemist]

orbitals considered immune from relativistic effects?

They are not.
You have contradicted yourself.

[jeffreyH (OP)]

I'm just asking questions.

[Bored chemist]

I'm just asking questions.

I will just leave that there...