[opportunity (OP)]

I used this idea in two other threads (https://www.thenakedscientists.com/forum/index.php?topic=72350.msg533201#msg533201, https://www.thenakedscientists.com/forum/index.php?topic=71484.72) and thought I should post a new thread about the subject, as I'd like some feedback, someone to point out where I may have erred.

I mentioned the following: I think Planck was wrong about frequency and energy as a direct relationship, on the atomic level, as electrodynamics with shells of electrons and the proton, and the electromagnetic field, it doesn't add up. Anyone who knows the energy levels of the atom knows the frequency of photon release increases with each photoelectric effect the higher-out the energy shell...and not as the Planck equation suggests; the further out the energy shell (higher as we call it) the lower the energy release though, and thus the lower the energy release for the higher the frequency for the photo-electric effect. I'm not sure how Planck didn't notice that.

I'm wondering if I am wrong in thinking that. Are there greater energy releases from higher-out energy shells? For instance, a photon jump from shell 4 to 3 is a higher frequency than a photon jump from shell 3 to 2. I'm suggesting that the energy of the photon jump from 4 to 3 is less than 3 to 2. Is there data to suggest otherwise?


We know the electrical potential (energy) of a charged object decreases the further two electrically charged objects move apart. The same would exist with the electron shells and their relation to the proton in an atom.

Consider this post by jeffreyH: https://www.thenakedscientists.com/forum/index.php?topic=72344.24

If a field requires a source, the source here for quanta being the photoelectric effect, then Planck is wrong with his equation proposing energy and frequency are directly proportional. The implications of this on physics theory regarding singularities, gravity, and so on, are huge.

[Colin2B]

“Are there greater energy releases from higher-out energy shells? For instance, a photon jump from shell 4 to 3 is a higher frequency than a photon jump from shell 3 to 2. I'm suggesting that the energy of the photon jump from 4 to 3 is less than 3 to 2. Is there data to suggest otherwise?”

Lots of data, the greater the number of levels an electron (not a photon) jumps the greater the amount of energy absorbed or released. Most secondary school text will explain this.
You’ll have a hard time breaking planck, but do try in new theories if you want.

PS i think you may be confusing the energy of each level with the energy required to transition levels.

[opportunity (OP)]

I understand  energy is put into the process of electron shell building. Yet focussing on the actual electron shell jumps as energy release is something else.

I'll post a new thread in "new theories"? I was actually thinking this was a mainstream physics question and not a new theory?

Think of a building with 5 levels. The higher up we go, the more energy we need to build those higher levels, yet the energy jump between the floors closer together is less than the floors further apart in factoring in the floors closer together are the furthest from the proton.

[Colin2B]

It is mainstream physics, but to suggest “ that the energy of the photon jump from 4 to 3 is less than 3 to 2” is definitely a new theory and would require evidence.

EDIT whoops misread post, see my post here https://www.thenakedscientists.com/forum/index.php?topic=72373.msg533353#msg533353

[opportunity (OP)]

Planck of course had a reason to directly proportionalise the energy of a photon with its frequency though?

[Colin2B]

@opportunity sorry, trying to do too many things at a time here - spammers around.

Misread what you were saying:

“For instance, a photon jump from shell 4 to 3 is a higher frequency than a photon jump from shell 3 to 2. “ - this is wrong bigger gap between 3 to 2 for electron to jump hence higher energy.

“I'm suggesting that the energy of the photon jump from 4 to 3 is less than 3 to 2.” - correct if you speak of electron jump and energy of emitted photon.

[opportunity (OP)]

The less distance of the jump, the higher the frequency. The outer shells are closer together according to Rydberg.  There's less "energy" in terms of electrostatic interaction between the proton and electron on those outer "lower wavelength, higher frequency" jumps. Correct me if I am wrong. I'm questioning Planck. A new theory is something else. There would be too many theories available in changing the Planck scale. I'm questioning the Planck equation as per how the photo-electric effect actually works.

Jumps can be up or down. Here I am referring to "down" jumps releasing quanta.

[Colin2B]

The less distance of the jump, the higher the frequency. 

...Jumps can be up or down. Here I am referring to "down" jumps releasing quanta.

How are you defining distance of jumps?
Take hydrogen. Energy difference between levels n=1 and n=2 is 13.6-3.39=9.7eV ignoring sign
Between n=2 and n=3 it is 3.9-1.51=2.39eV

So bigger energy jump between 1&2 than between 2&3. So higher energy (higher frequenency) photon emitted when electron moves between 1&2 than between 2&3.
Yes, upper shells are closer together so less energy for each photon for transitions between adjacent levels.

[opportunity (OP)]

Correct me if I am wrong, the distance of the energy jump is indicative of the wavelength of jump, and thus inversely proportional to the frequency?

[evan_au]

I think Planck was wrong about frequency and energy as a direct relationship

I think you are talking about the Planck-Einstein equation:
E = h f
Where:
- E is the Energy of a photon
- h is the Plank constant
- f is the frequency of the photon
- This is a linear relationship (photon energy is directly proportional to photon frequency).

This equation is well-proven over many orders of magnitude. So you would need some much better evidence to suggest that it is wrong.

https://en.wikipedia.org/wiki/Photon_energy

the photo-electric effect

The equivalent equation for the photoelectric effect can be written as:

E_max = h f - φ
Where:
- E_max is the maximum Energy of an electron, which has been kicked out of a metal by a photon
- h is the Plank constant
- f is the frequency of the incoming photon
- h f is the energy of the incoming photon
- φ is the work function of the metal
- This is a linear relationship (electron energy is proportional to photon frequency)
- But it is not a direct proportionality, because it takes energy to extract an electron from the conduction band of a metal. Thus the ejected electron has less energy than the incoming photon

This does not invalidate the linearity of the Plank-Einstein equation; in fact, it provides strong evidence that the energy of a photon is directly proportional to its frequency.
Einstein received the Nobel Prize for deducing that light was quantized (E=h f) from the photoelectric experiment.

See: https://en.wikipedia.org/wiki/Photoelectric_effect

Anyone who knows the energy levels of the atom knows the frequency of photon release increases with each photoelectric effect the higher-out the energy shell...and not as the Planck equation suggests; the further out the energy shell (higher as we call it) the lower the energy release though, and thus the lower the energy release for the higher the frequency for the photo-electric effect

I think that mentioning the photoelectric effect is just confusing this statement?

The equation for the energy levels of a Hydrogen atom is called the Rydberg equation:
E  α R (1/n² - 1/m²)
Where:
- E is the energy of the photon which is emitted or absorbed by this atom
- α means "proportional to"
- R is the Rydberg constant
- n is the lower shell number that the electron resided in
- m is the higher shell number that the electron resided in

What this says is that:
- A transition from shell 3 to 1 releases more energy (a higher-frequency photon) than a transition from shell 3 to 2
- A transition from shell 3 to 2 releases more energy (a higher-frequency photon) than a transition from shell 4 to 3
- This can be understood in terms of the inverse-square law, where the electrostatic attraction between electron and nucleus is much stronger for small n, and so electrons jumping between low-numbered shells release more energy than electrons jumping between high-numbered shells.
- The inverse square law and the Rydberg equation are both non-linear equations.
 
This non-linear relationship for the energy levels of an electron in an atom does not in any way invalidate the linear relationships for the energy of a photon in "E = h f" and implied by  "E_max = h f - φ".

See: https://en.wikipedia.org/wiki/Rydberg_formula

[opportunity (OP)]

What is this saying:

What this says is that:
- A transition from shell 3 to 1 releases more energy (a higher-frequency photon) than a transition from shell 3 to 2
- A transition from shell 3 to 2 releases more energy (a higher-frequency photon) than a transition from shell 4 to 3
- This can be understood in terms of the inverse-square law, where the electrostatic attraction between electron and nucleus is much stronger for small n, and so electrons jumping between low-numbered shells release more energy than electrons jumping between high-numbered shells.
- The inverse square law and the Rydberg equation are both non-linear equations.


I know exactly what you're saying. Do you know what you've posted?

Practically speaking therefore.......energy jumps through shorter distances represent lower wavelength and thus higher frequency. Am I wrong with that?

[Colin2B]

I know exactly what you're saying. Do you know what you've posted?

Of course he knows. @evan_au  is one of our most reliable posters.

Practically speaking therefore.......energy jumps through shorter distances represent lower wavelength and thus higher frequency. Am I wrong with that?

Yes, you are wrong with that.
The outer shells (if you want to think of them that way) are closer together (less distance) and release less energy than the ones closer to the centre which are wider (more distance) more energy.
Less energy released = photons which have lower frequency and shorter wavelengths.

[jeffreyH]

I wouldn't want to bet against Evan.

[chiralSPO]

Correct me if I am wrong, the distance of the energy jump is indicative of the wavelength of jump, and thus inversely proportional to the frequency?

This is wrong, you stand corrected

I think you may be confusing the "distance" between energy levels with an actual spatial distance. An electron doesn't have to to move physically through space to change energy levels. The Bohr model of the atom shows electrons as distinct particles moving in circular orbits around the nucleus like a mini solar system, but this model is a dramatic oversimplification which is in many ways misleading. If instead we think about orbitals (not orbits), in which electrons are behaving as waves in a spherical distribution about the nucleus, it can be seen that there is no strict relationship between where the electron is in the atom and how much energy it has (you can think of electrons in high energy levels as either having more potential energy than their lower-energy counterparts, which would place them farther from the nucleus, or having more kinetic energy, but actually being as close or closer.

It is fairly easy to prove that red light has longer wavelength than green light, which is still longer than the wavelengths for blue light. All you need is a diffraction grating and some monochromatic lasers, or just white light (and the equation which relates diffraction patterns to wavelength, found here: https://en.wikipedia.org/wiki/Diffraction_grating#Theory_of_operation )

That the energy of shorter (bluer) light is higher than for others can be demonstrated through the photoelectric effect or by looking up (or testing) the voltages required for monochromatic LEDs to emit light. I can easily power a red LED with 2 V, but need at least 3 to get my blue LED to function.

[Colin2B]

@chiralSPO is another of our reliable posters and should be taken note of. You will notice he has also raised the question I asked “what do you mean by distance”.
I hope the combination of answers will help you understand the relationship between electron energy transitions and photon energy/frequency.

[opportunity (OP)]

Thanks Colin. I wasn't sure about how frequency was being defined with the electron jumps. On consulting the Rydberg formula it clearly states the frequency gets lower the further out the jumps, and thus longer wavelength.

I'm clear now about the energy "level". Higher energy levels are recorded with shorter wavelength (lower electron shell) transitions. Thus the higher the frequency, the higher the higher the energy.

Good discussion. I knew it wasn't a new theory, hence kept it here. I just needed to have the idea as clear as crystal.

I can see how the energy on the Planck scale seems off the charts now. But I'm still wonderign if the Planck scale is valid if the whole idea of quanta requires an atomic platform and not something on the Planck scale itself? That made me think initially that somehow below the atomic electron-shell level there could be a type of reversal between wavelength an energy, an inverse proportionality (like a golden ratio thing). That's a theory I'm working on, but its vastly complicated, hoping to have it done later this year.

[evan_au]

Oops - crossover with @opportunity.

The Bohr model of the atom shows electrons as distinct particles moving in circular orbits around the nucleus like a mini solar system, but this model is a dramatic oversimplification which is in many ways misleading.

If you are a professional chemist like @chiralSPO, you can't use the Bohr model.

But if you are struggling to understand an atom, like @opportunity, I think we can get away with a simplification of the Bohr atom.

Imagine a number line extending from 0 to the right, with equal-spaced numbers: 0, 1, 2, 3, 4.
- At 0 we place a positive proton.
- We have one negative electron, which we can place at 1, 2, 3, 4, etc. (ie electron energy is quantised)
- The electron can't appear at points in between these numbers, or at 0.
- Let's call the potential energy of the electron at position 1 as E₁
- Due to the inverse-square law, the amount of force on the electron at position 2 is E₂ = E₁/4.
- Similarly, the force on the electron at position 3 = E₃ = E₁/9 (Force is not Energy, but let's ignore that... ).
- And in general, E_n = E₁/n²
- When an electron jumps between shells n & m, it releases a photon with energy E₁(1/n² - 1/m²), ie photon energy is quantised, too.

We have recreated something like Rydberg's equation in this very compromised model.
...and the shells do correspond to physical distances, as imagined by @opportunity (which they don't in real atoms!)

So an electron jumping from position 3 to 1 will release an amount of energy E₁(1-1/9) = 0.889E₁
and jumping from position 3 to 2 will release E₁(1/4-1/9) = 0.138E₁
This proves my assertion that "A transition from shell 3 to 1 releases more energy than a transition from shell 3 to 2."

And it doesn't disprove the observation from multiple sources that the energy of a photon is proportional to frequency.
For example, Planck solved a long-standing problem in Physics with understanding the spectrum of glowing objects by assuming that light is quantised (photons), and the energy of the photon is proportional to frequency.
See: https://en.wikipedia.org/wiki/Black-body_radiation 

Edit: Simplification: Force is not Energy

[opportunity (OP)]

Thanks Evan.

It's true that I'm struggling with the atom, only though with the idea Planck proposed as the vastly small scale he introduced. Energy and frequency are indeed in direct proportion, yet the basis for light requires electron shell jumping. How does that work on the scale he proposes, many magnitudes smaller than the atom itself?

The title of the post here is: Is the Planck scale accurate according to the photo-electric effect? So my intention has been about questioning the Planck scale itself. I threw a spanner in re. why frequency and energy are in direct proportion with electron shells and the photo-electric effect, but we're clear on how that works. But below that, diving to the level of the Planck scale, that's what I don't comprehend, as the whole idea of quanta as packages of light required even back then when the theory was presented electron-shell jumps.

[Colin2B]

@opportunity
“Good discussion. I knew it wasn't a new theory, hence kept it here.”
Anything becomes a new theory if it suggests an alternative to an established, current theory. We allow limited discussion here for clarification but if objections persist it is best to continue the discussion in new theories where it can be wider ranging.

[opportunity (OP)]

Understood, and thanks again.