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mvr?

Is this an angular momentum thing?

Yeah

^ mvr = angular momentum.

Would you like to do this via photon energy and Coulomb's Law?

(I'm assuming h = Planck's constant. Is this a reasonable assumption?)

yes ...

And you're comfortable with basics like Newton's second law and conservation of energy and all that?

Physic ! ask in right section.

Yes... F=ma and ...energy can neither be created nor be destroyed.

Ok...
Let's start with \[\large f=\frac{c}{\lambda}\]

ok

and
\[\large \Delta E=hf\]

\[\large \rightarrow \frac{1}{hc} \Delta E = \frac{1}{\lambda}\]
Cool so far?

ΔE=0.5m(Δv)2−ke2(r−11−r−12)
I guess sshould be +ke2(...)

Anyway, from here, we can introduce L=mvr -> v=L/mr, and make some substitutions.

so it shows the potential is negative, then delta pot=U2-U1
-ke2/r2-(-ke2/r1)

And most important is how do you want reach to angle momentom!

sorry for my absence here @CliffSedge but I have a small question.

May I ask it? (but it is stupid one, but please allow)

Alright, as long as it isn't *too* stupid. ;-) j/k.
Ask anything.

Right so without assumptions, we have not be able to prove that ?

And postulates can be proven. You are mistaken on that point.

Nothing can be deduced, except tautologies, without assumptions.

I'm sorry you feel that way.
What was your intention for posting this question?

I lost my language and the way I talked was of course have felt bad to you, sorry about that sir.

If you are actually interested in learning the physics, I would be happy to discuss this further.

Should I go for it? sir.