# de Broglie waves and the connection between particles

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have:

proton mass 1.67*10-27 kg and speed 10 000 km/c = de Broglie wave - A

electron mass 9.1*10-31 kg and speed 10 000 km/c= de Broglie wave - B

and atom of hydrogen consisting of proton and electron. mass atom of hydrogen 1.67*10-27 kg + 9.1*10-31 kg , speed 10 000 km/c

question what will be de Broglie wave atom of hydrogen?
alleged options:
1:
the electron of the hydrogen atom = de Broglie wave - A
the proton of the hydrogen atom = de Broglie wave - B
this seems logical
2:
de Broglie wave atom of hydrogen= С ( С<B and C<<A )
this option seems not logical,because the electron in the atom has a mass of free electron and the electron has a speed 10 000 km/c
What happens in reality and why?

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have:

proton mass 1.67*10-27 kg and speed 10 000 km/c = de Broglie wave - A

electron mass 9.1*10-31 kg and speed 10 000 km/c= de Broglie wave - B

and atom of hydrogen consisting of proton and electron. mass atom of hydrogen 1.67*10-27 kg + 9.1*10-31 kg , speed 10 000 km/c

Why four times you wrote km/c?

Edited by Sensei

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1.67*10-27 kg + 9.1*10-31 kg

At this level of accuracy (2 significant digits) the mass of the electron is 0.

Also, the mass of a hydrogen is not just the sum of the proton and electron mass. You need to take into account the binding energy

Mass of proton = 1.67262178 × 10-27 kg

Mass of hydrogen atom = 1.6735326 × 10-27 kg

Beyond that, I don't know what you are trying to ask.

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Beyond that, I don't know what you are trying to ask.

sorry I do not speak English

I use translator

I wanted to ask about how to calculate the wave for the hydrogen atom, should we assume that the hydrogen atom is indivisible or that his electron will have its own wave and proton own wave?

Edited by alkis3

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There is no physically "real" correct answer to what the de Broglie wave (-length) of a composition of particles is. But there is an mainstream accepted community-wide agreement on how to treat that particular case:

When you start developing the quantum mechanical wave-function of the hydrogen atom, the very first step is a change in coordinated: The coordinates of the proton's and electron's center of mass (which effectively is just the location of the proton) and the deviation of the two particles from their common center of mass. The solution for the full system then separates into a wave function of the center of mass and the relative positions of proton and electron. The former is what you could call "the full atom". That's the thing you are after, and its de Broglie wave should behave as if the particle had a mass equal to the sum of the individual masses (although I am not 100% sure of that at the moment). The other part, the one you are not after, is what is treated in QM texts about the hydrogen atom.

In short: You treat the hydrogen atom as a single object in its own right.

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That's the thing you are after, and its de Broglie wave should behave as if the particle had a mass equal to the sum of the individual masses

if we consider the bound particles as a whole , this means that the relationship affects wave

but the problem is that the connections have different energy.

Then how energy affects the wave?

Can I be considered for waves as the whole molecule?

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The total wavefunction of the system has two parts: The center-of-mass part and the relative-distance part. Both contribute to the energy of the system. The former behaves as a free particle (-> de Broglie wave), the other is what is commonly meant by "energy levels of the hydrogen atom". The two parts add up to yield the total energy of the hydrogen atom.

Also note that the scenario is a bit more complicated than you seem to imagine it, but the proper way to understand that would require a bit of math. The following page may be a bit too advanced, but it describes what I mean by the "two parts" and demonstrates how their energies "add up": http://farside.ph.utexas.edu/teaching/qmech/lectures/node58.html#stwo . The relevant equation is (424), which explicitly shows that energy is a sum of center-of-mass motion, relative motion, and potential energy due to relative position.

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okay,this is difficult,and when you consider that I do not know English ,it is not possible

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Exactly. That is why I recommend accepting these "take home" messages, even if they are incomplete:

- The hydrogen atom is usually described in terms of the center-of-mass of electron and proton and their relative position (and not in terms of the two particles' positions individually, which would technically be possible).

- In this picture, the center of mass behaves as a single particle with a mass equal to the sum of electron and proton mass.

- This implies a corresponding de Broglie wave for the center of mass.

- The relative position is associated with a more complicated wave function, which is not described by a de Broglie wave.

- The relative position part adds to the total energy. But it does not influence the center-of-mass part.

- It is not automatically true that the whole hydrogen atom is well-described by its center-of-mass alone. But if you ask for a de Brogile wave (-length) of a hydrogen atom, the de Broglie wave (-length) of the center-of-mass part is what most people would mean by this (because the relative part would usually not be called a de Broglie wave).

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- The hydrogen atom is usually described in terms of the center-of-mass of electron and proton and their relative position (and not in terms of the two particles' positions individually, which would technically be possible).

- In this picture, the center of mass behaves as a single particle with a mass equal to the sum of electron and proton mass.

- This implies a corresponding de Broglie wave for the center of mass.

I can understand it.

BUT I don't understand how it works in the real world.

In an atom the electron is far from the nucleus

Then why the electron and the nucleus behave as a whole...Yes,they interact ,but they are not a monolith,but behave as a monolith.....

Edited by alkis3

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"far away" is quite a relative statement. The distance is roughly 0.1 nanometers, i.e. 0.2% of the wavelength of visible light. I believe in many cases that would count as "the electron and the nucleus are practically at the same position". That is also the cases you might expect that often it is the center-of-mass that interests you. You are of course right that this is not always the case. Sometimes, the relative location of proton and electron is important.

So please do not misunderstand my comments as saying that you always treat the electron-proton bound state as a single point-sized Hydrogen. That is not the case. What I tried to argue is that in the context of asking for de Broglie waves, plane matter waves, the concept can only be applied to the center-of-mass part of the total wave function. The relative positions of electron and proton are still relevant in other scenarios. For example, the spectral line structure of hydrogen (the light frequencies absorbed and emitted by it) have their origin in the relative-position part of the hydrogen. The center-of-mass part merely adds some blue- or redshift to it.

Also, the common separation into a center-of-mass and a relative position has no physical significance. It is merely chosen for practical reasons (to make the math clearer and to be able to attribute phenomena to different parts of the wave function). Purely physically, you could treat the system as an electron and a proton with an interaction between them. You just would not be able to make much sense out of the mathematical notation of the wave function you get.

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is it possible to consider the person as a whole particle with the mass?

I mean whether it is right in the expression - Planck's constant / (mass man * speed man)=wave ?

if it is not correctly,then where is the line?

I mean electron mass+proton mass = mass A

Planck's constant / (mass A * speed A)=wave correctly

Planck's constant / (mass man * speed man)=wave not correctly

what condition communications between particles should be ,so that the particles in such relationships were with a common center of mass?

but if it correctly - (Planck's constant / (mass man * speed man)=wave)

then the question: - can we consider two people holding hands particles with a common center of mass?

Edited by alkis3

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You can even consider the center of mass of two people not holding hands. It's just that in the case of hydrogen atoms doing so can make sense for, e.g. scattering experiments or separating the full solution into parts that one can associate physical effects to. In the case of two persons you are not very likely to find a scenario where the concept of their common de Brogile wavelength helps with anything, partly because it is going to be much smaller than the relative positions.

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