# Planck-Einstein relation and the Photoelectric Effect

• B
• Abu
In summary, the photoelectric effect explains that photons have energy and can transfer this energy to electrons, causing them to gain kinetic energy. The concept of relativistic mass is not relevant in this explanation.
Abu
Hi everyone, I just have some confusion regarding Planck's and Einstein's equation.
The following is an explanation of the photoelectric effect using Einsteins theory:
Light is composed of photons. Each photon has energy hf and mass hf/c^2. When ultraviolet photons are brought to rest by zinc, the mass of the photon changes to energy. This energy is used to break the binding energy between the outermost electron and the nucleus. The excess energy is carried by the electrons as kinetic energy.

Here is my confusion though:

When we ask for the energy of a photon, we say it is equal to E = hf. When a photon is brought to rest in the explanation of the photoelectric effect, it says the mass of the photon during its motion changes to energy. So shouldn't the energy of the photon be hf/c^2, not hf?

For example, we say that the kinetic energy of the electrons in the photoelectric effect is:
KE = hf - w where w is the work function.
How come it isn't KE = hf/c^2 minus w

Maybe I am misunderstanding the photoelectric effect when I say that the mass of the photon changes to energy? Perhaps the mass does not completely change into energy, and thus hf/c^2 is not applicable, only for E = mc^2?

If my question is unclear, let me know. Thank you very much.

Photons have a mass of zero. Forget the concept of relativistic mass, it is not used any more. Photons cannot be brought to rest (at least not in the way you try to do that here). If the photons hit the metal their energy can be transferred to something else (typically an electron), they stop existing then.
Abu said:
This energy is used to break the binding energy between the outermost electron and the nucleus.
While that is possible, most of the time the electron that absorbs the photon is not bound in a specific atom.
Abu said:
So shouldn't the energy of the photon be hf/c^2, not hf?
That doesn't even have the right units to be an energy.

mfb said:
Photons have a mass of zero. Forget the concept of relativistic mass, it is not used any more. Photons cannot be brought to rest (at least not in the way you try to do that here). If the photons hit the metal their energy can be transferred to something else (typically an electron), they stop existing then.While that is possible, most of the time the electron that absorbs the photon is not bound in a specific atom.That doesn't even have the right units to be an energy.
Thank you so much for your input. Unfortunately, I cannot forget about relativistic mass because it is the way I am being taught currently, so I have to try my best to understand it. But I thought about my question as well as your response:
So from what I know now and what I am currently being taught, the photon has a relativistic mass of hf/c^2 (not used anymore, but I am still being taught it). So we can apply that to E = mc^2 where m is the relativistic mass, correct? So e = hf/c^2(c/^2), and now we have E = hf. So from that, in the explanation provided above that was said by my teacher, we can say that the energy provided by the relativistic mass of the photon is what is allowing the electrons to gain kinetic energy.

I'm sorry I had to disregard the comment on relativistic mass, but its crucial I understand it, I think, even though from what I've read it can run into a whole load of problems.

Thank you very much.

Abu said:
and now we have E = hf.
Right, and the detour via the mass didn't help. The photon has energy, this energy can be transferred to an electron. No masses involved.

## 1. What is the Planck-Einstein relation?

The Planck-Einstein relation, also known as the energy-frequency relation, is a fundamental principle in quantum mechanics that describes the relationship between the energy of a photon and its frequency. It states that the energy of a photon is directly proportional to its frequency, with the proportionality constant being Planck's constant.

## 2. What is the significance of the Planck-Einstein relation?

The Planck-Einstein relation played a crucial role in the development of quantum mechanics, as it provided a way to explain the photoelectric effect, a phenomenon that could not be explained by classical physics. It also helped to lay the foundation for the concept of quantization, where energy is only released or absorbed in discrete units, rather than continuously.

## 3. What is the photoelectric effect?

The photoelectric effect is the phenomenon where electrons are emitted from a material when it is exposed to light of a certain frequency. This effect was first observed by Heinrich Hertz in 1887, but it was not fully understood until Albert Einstein explained it using the concept of photons and the Planck-Einstein relation.

## 4. How does the Planck-Einstein relation relate to the photoelectric effect?

The Planck-Einstein relation explains the relationship between the energy of a photon and its frequency. In the context of the photoelectric effect, it explains why only light of a certain frequency can cause electrons to be emitted from a material. If the frequency of the light is lower than the threshold frequency, no electrons will be emitted, regardless of the intensity of the light.

## 5. What are some real-world applications of the Planck-Einstein relation and the photoelectric effect?

The photoelectric effect and the Planck-Einstein relation have many practical applications in modern technology. They are used in devices such as solar cells, photodiodes, and photomultiplier tubes, which convert light energy into electrical energy. They are also essential in the development of digital cameras and imaging technologies, as well as in the study of atomic and molecular structures.

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