Prove that : mvr = \(\frac{nh}{2\pi}\)

- anonymous

Prove that : mvr = \(\frac{nh}{2\pi}\)

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- ParthKohli

mvr?

- anonymous

Is this an angular momentum thing?

- anonymous

Yeah

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- anonymous

^ mvr = angular momentum.

- anonymous

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

- anonymous

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

- anonymous

yes ...

- anonymous

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

- anonymous

Physic ! ask in right section.

- anonymous

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

- anonymous

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

- anonymous

ok

- anonymous

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

- anonymous

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

- anonymous

So we'll now express Delta-E in terms of kinetic and potential energy differences.
\[\large \Delta E =0.5m(\Delta v)^2-ke^2(r_1^{-1}-r_2^{-1})\]
Where m, v, e, and r are the mass, velocity, charge, and orbital radius of the electron.
Let me know when you're ready to continue.

- anonymous

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

- anonymous

@mahmit2012 , this is assuming an electron moving from an upper level to a lower level, so potential energy is decreasing. I should have been more clear that r_1 is the upper and r_2 is the lower. That is confusing now that I look at it like that.

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Where I was going to go with this, but I don't think @SheldonEinstein is still interested, was:
\[\large \Delta E =\frac{L^2}{2m}(r_1^{-2}-r_2^{-2})-ke^2(r_1^{-1}-r_2^{-1})\]
Putting together F=ke^2/r^2 and a=v^2/r with F=ma,
\[\large \frac{ke^2}{r^2}=\frac{mv^2}{r}\]
\[\large \rightarrow r=\frac{L^2}{kme^2}\]

- anonymous

Now the energy equation can be written as
\[\large \Delta E = \frac{k^2e^4m}{2}(L_1^{-2}-L_2^{-2})\]
Now this can be put into
\[\large \frac{\Delta E}{hc}=\frac{1}{\lambda}\]
and then set equal to
\[\large \frac{1}{\lambda} =R(2^{-2}-n^{-2})\]
This is the Balmer Series, where R = Rydberg constant.
(This part might take more explanation . . .)
Anyway, to make a long story shorter, L=mvr=nh/2π is the only solution for L that works.

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

have you proved that : mvr = nh/2 pi
the above you wrote is to be read by me but after getting your response to my above short question...

- anonymous

Let me check . . .
Yes.
I can show some of the intermediate steps. I assumed you could do a lot of the algebra yourself.

- anonymous

Yes, but let me tell you that this is "bohrs second postulate" and postulates can't be proved.
Majesty, you proved it! Any comments by you on this?

- anonymous

I assume that you might have taken anything unproven... that makes your work as not exactly a proof.
I hope you're getting my point.

- anonymous

No, I'm not.
Postulates are assumed to true for the purpose of proving a statement given certain assumptions.

- anonymous

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

- anonymous

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

- anonymous

Nothing can be deduced, except tautologies, without assumptions.

- anonymous

If you're just wasting my time by trying to be cute playing with semantics, then be warned that I have plenty of time to waste.

- anonymous

I am controlling myself at present, be nice to others (at least to the one who has not done any thing offensive ..)
The people interested to leave have an exit door also ...

- anonymous

http://mathworld.wolfram.com/Postulate.html
http://answers.yahoo.com/question/index?qid=20101027183239AAcXeJa
http://en.wikipedia.org/wiki/Axiom
http://openstudy.com/study#/updates/4fea1f19e4b0bbec5cfa34ae
Hope it justifies my answer as no to "postulates can be proven" ...

- anonymous

Not really . . .
Ah, so you are just being cute playing with semantics. That's nice, dear.
Regarding link 1: I understand that modern mathemeticians use the words "axiom" and "postulate" interchangeably, but they are not exactly the same thing in all contexts.
Regarding link 2: Some level-7 neckbeard on Yahoo! Answers doesn't qualify as a reliable source to me.
Regarding link 3: That is a wikipedia page on "Axiom" not "Postulate," though I assume you are using it as reference to define 'postulate' as non-logical axiom. This is all irrelevant, because -
Regarding link 4: Even if we do accept the narrow definition of postulate to be synonymous with axiom, this statement is important, "Postulate is the starting point of any argument, the basis of any reasoning and proof. "
Proofs follow from axioms and postulates (and other intermediate theorems).
If you are trying to assert that nothing based on an assumption can be proven, then you are stuck in a Cartesian 'the-only-thing-that-cannot-be-doubted-is-the-fact-that-I-am-doubting' / 'cogito ergo sum' bit of philosphical nonsense.
With that out of the way, I suppose we can come to this point, viz.
Bohr's second postulate is "Each emission or absorption of radiation energy represents the electron transition from one stationery orbit to another. The radiation emitted during such transition is homogeneous."
So your remark that I was proving Bohr's second postulate is false.
Lastly, if mvr=nh/2π is a postulate then why was I able to derive it from basic principles?
Your claims are without merit or basis.
Your reply @SheldonEinstein ?

- anonymous

So it seems that you are merely trying to play a little logic games that goes like
Premise one: Postulates can't be proven.
Premise two: Here' a postulate, try to prove it.
Premise three: Haha, you tried to prove it; but, by premise one, postulates can't be proven, nany-nany-boo-boo!
Conclusion: You're a dummy. Look at how smart I must be in comparison.
That is very childish, and all the more embarrassing for you because your premises were false.
I hope you are more successful at playing your childish games elsewhere.
I'm sure you derive much pleasure from them.

- anonymous

@CliffSedge I respect your knowledge and opinion but the way you talked here is quite bad to me at least, I respect your work done here but I didn't do the way of your talking here. The way you lost your temper itself shows that you are a "child" not me, your this behavior proved a lot. Thanks!

- anonymous

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

- anonymous

It happened like this sir:
I was watching a lecture, of Atomic Structure and the teacher said "It is still a mystery for me that how did Bohr came to this formula --> mvr = nh/2 pi and how can we prove it? "
This produced just a willingness to see that can experts here on OS help to prove? I posted it first in chemistry section, they said 'postulates can't be proven" and my stupidness I agreed them some how , I came to the maths section then , asked here and got the solution from you but unfortunately I was not able to understand anything, I studied the lecture of the teacher more and came to know something about Rydberg's constant and other constants, variables used by you here.

- anonymous

Then you would have been better served by asking more questions instead of boldly claiming that I had attempted to prove a postulate that could not be proved.

- anonymous

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

- anonymous

Yes sir, I agree with you that I must have asked quest. rather than claiming with overconfidence, I am guilty for that :( , sorry , forgive me sir....

- anonymous

You asked me to do a certain task and then I did it, then you claimed that I had not without even understanding what I had done. You jumped to a conclusion.
I forgive you for that, but take that as a lesson to be more patient in the future; because please know: that when it comes to arguing points of logic, I am *very* patient, and very ruthless at attacking and destroying bad arguments.
It may seem sometimes that I am attacking the person, but that is not so, I only brutally attack and dismantle bad ideas, not people.

- anonymous

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

- anonymous

Agreed sir, thanks for forgiving, the lesson saved permanently in my mind. Yes sir, why not? Can I post this as a new question here in maths section but my first question will be :
"CCan postulates be proved?"

- anonymous

Should I go for it? sir.

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