Is it possible to derive E=h f from E=h \nu in the theory of light quanta?

In summary: This equation is the result of the empirical observation of the photoelectric effect combined with the postulate that the energy of a photon is proportional to its frequency, which predated the theory of relativity. However, later on, Bohr proposed that the fundamental quantity to quantize may be the angular momentum instead of energy, which led to the development of the Bohr model for the hydrogen atom. It is worth noting that the equation \Large {E=h f} for the harmonic oscillator does not depend on relativistic formulae. Furthermore, it is interesting to consider that while frequency can be directly measured in terms of space and time, energy is usually measured indirectly.
  • #1
arivero
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If one reads the current version of the wikipedia entry on Photoelectric_effect

The idea of light quanta began with Max Planck's published law of black-body radiation ("On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik 4 (1901)) by assuming that Hertzian oscillators could only exist at energies E proportional to the frequency f of the oscillator by E = hf, where h is Planck's constant.

we see that historically the postulate E=h f predates the relativistic theory. So it is kind of circular to argue in terms of [itex]E=h \nu[/itex] to justify [itex]E=h f[/itex]. The empirical process first postulated E=h f for the black body and then Einstein justifies the cut in the spectrum of the photoelectric effect by postulating a minimal non-zero required energy and that [itex]E = h \nu[/itex], being [itex]\nu[/itex] the frequency of the then-hypothetical quantum of electromagnetic radiation.

Later on, Bohr suspects that the fundamental object to quantize is not the energy but the angular momentum. This rule works both for the 3D harmonic oscillator and for the Coulomb potential, and in this case it allows Bohr to calculate some of the spectrum of the hydrogen atom.

But it is important to reminder that E=h f as it is, for the harmonic oscillator, does not depend of relativistic formulae. Put V(x)= k x^2, solve the non relativistic Schroedinger eq, and you get E(n) = n h f + E(0).

A interesting related point, suggested by Okun, is that f is measurable in terms of space and time, while E seems to be more indirectly measured.
 
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  • #2
where, precisely, does relativity come into play with the photoelectric effect? And [itex]\nu[/itex] is exactly the same quantity as f (two different symbols for exactly the same thing). So what are you trying to say??
 
  • #3
I was trying to set up a framework to clarify (or to obscure, it seems) the initial comments in the thread https://www.physicsforums.com/showthread.php?t=206933 , where relativity was invoked. In that thread, the first answers to the OP were to see the relationship between energy and frequency as a consequence of relativity when applied to massless particles. My hope is that the OP and the people who answered to the OP will read this thread, and your remark, and to discuss on their conceptions.
 
  • #4
But what is *your* point? blechman notes that you have only changed notation from 'f' to 'nu'.

so...
 
  • #5
I see. I didn't realize that this comes in from another post.
 
  • #6
arivero said:
If one reads the current version of the wikipedia entry on Photoelectric_effect



we see that historically the postulate E=h f predates the relativistic theory. So it is kind of circular to argue in terms of [itex]E=h \nu[/itex] to justify [itex]E=h f[/itex]. The empirical process first postulated E=h f for the black body and then Einstein justifies the cut in the spectrum of the photoelectric effect by postulating a minimal non-zero required energy and that [itex]E = h \nu[/itex], being [itex]\nu[/itex] the frequency of the then-hypothetical quantum of electromagnetic radiation.

Later on, Bohr suspects that the fundamental object to quantize is not the energy but the angular momentum. This rule works both for the 3D harmonic oscillator and for the Coulomb potential, and in this case it allows Bohr to calculate some of the spectrum of the hydrogen atom.

But it is important to reminder that E=h f as it is, for the harmonic oscillator, does not depend of relativistic formulae. Put V(x)= k x^2, solve the non relativistic Schroedinger eq, and you get E(n) = n h f + E(0).

A interesting related point, suggested by Okun, is that f is measurable in terms of space and time, while E seems to be more indirectly measured.

If you mean that

[itex]\Large {E=h \nu}[/itex]

cannot be derived, I agree with you.
 

1. What are energies and frequencies?

Energies and frequencies refer to the different forms of energy and the corresponding wavelengths or oscillations at which they vibrate. Energy can take many forms, such as light, sound, heat, and electromagnetic waves, and each form has a specific frequency that determines its properties.

2. How do energies and frequencies affect our daily lives?

Energies and frequencies play a crucial role in our daily lives. They determine the colors we see, the sounds we hear, and the heat we feel. They also have a significant impact on our health, as different frequencies can affect our body's cells and systems in various ways.

3. What is the relationship between energies and frequencies?

The relationship between energies and frequencies is known as the energy-frequency spectrum. It shows the range of energies and frequencies that exist, from low energy and low-frequency radio waves to high-energy and high-frequency gamma rays. The higher the frequency, the more energy is carried by the wave.

4. How do scientists measure energies and frequencies?

Scientists use different tools and instruments to measure energies and frequencies. For example, spectrometers are used to measure the wavelengths of light, while sound waves can be measured using microphones. For more complex measurements, scientists may use specialized equipment like particle accelerators or radio telescopes.

5. Can energies and frequencies be harmful?

Yes, some energies and frequencies can be harmful to living organisms. For example, high-frequency electromagnetic waves, such as X-rays and gamma rays, can damage cells and cause health issues. Similarly, extremely low-frequency electromagnetic fields, such as those produced by power lines, have been linked to potential health risks. However, not all energies and frequencies are harmful, and many are essential for our survival and well-being.

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