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jd12345
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Why is energy proportional to frequency? Does this question have an answer or is it a fundamental thing that just happens?
Understanding the Relationship Between Energy and Frequency
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In summary, the energy of a photon is directly proportional to its frequency, which is an experimental result from the photoelectric effect experiment. This is described by the equation E=h√, where h is Planck's constant. Additionally, in special relativity, the energy divided by frequency is constant for a photon, regardless of the observer's frame of reference.
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Fewmet
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jd12345 said:
It is an experimental result. When you measure the maximum energy of ejected electrons in the photoelectric effect experiment and plot it against the frequency of the light that caused the emission (see example here), you get a straight line with a slope that is Planck's constant h. Applying the formula for a straight line and taking the binding energy of the electron into account, the equation of the line is E=h√.
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tiny-tim
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hi jd12345! 
for light, it's a straightforward result from special relativity …
(i'll use unit with h = c = 1)
a photon moving in the x-direction with frequency eα and energy E is a wave, with phase 2πeα(t-x) and energy-momentum 4-vector (E,E,0,0)
a second observer moving in the x-direction with rapidity eβ will see the light red-shifted, with phase 2πeα-β(t-x) and energy-momentum 4-vector (Eeα-β,Eeα-β,0,0)
so energy divided by frequency is a constant for that particular photon
(there's probably a similar proof for electrons etc … would anyone else like to have a go at that?)
jd12345 said:
for light, it's a straightforward result from special relativity …
(i'll use unit with h = c = 1)
a photon moving in the x-direction with frequency eα and energy E is a wave, with phase 2πeα(t-x) and energy-momentum 4-vector (E,E,0,0)
a second observer moving in the x-direction with rapidity eβ will see the light red-shifted, with phase 2πeα-β(t-x) and energy-momentum 4-vector (Eeα-β,Eeα-β,0,0)
so energy divided by frequency is a constant for that particular photon
(there's probably a similar proof for electrons etc … would anyone else like to have a go at that?)
FAQ: Understanding the Relationship Between Energy and Frequency
1. What is the relationship between energy and frequency?
The relationship between energy and frequency is known as the Planck-Einstein relation, which states that the energy of a photon (a particle of light) is directly proportional to its frequency. This means that as the frequency of a photon increases, its energy also increases.
2. How does energy affect frequency?
Energy can affect frequency in several ways. Firstly, as mentioned in the Planck-Einstein relation, the energy of a photon is directly proportional to its frequency. This means that a higher energy photon will have a higher frequency. Secondly, energy can also cause changes in the frequency of waves. For example, in a medium such as water or air, an increase in energy can result in an increase in the frequency of the wave.
3. What is the unit of measurement for energy and frequency?
The unit of measurement for energy is the joule (J), while the unit of measurement for frequency is hertz (Hz). However, in certain cases, other units such as electron volts (eV) or megahertz (MHz) may be used.
4. How do energy and frequency relate to electromagnetic radiation?
Electromagnetic radiation, such as light, is a form of energy that travels in waves. The energy of electromagnetic radiation is directly proportional to its frequency, meaning that higher frequency radiation (such as X-rays or gamma rays) has more energy than lower frequency radiation (such as radio waves).
5. Why is understanding the relationship between energy and frequency important?
Understanding the relationship between energy and frequency is crucial in many areas of science and technology. It is used in fields such as astronomy, where the energy and frequency of light can provide information about distant objects. It is also important in fields such as telecommunications, where the frequency of electromagnetic waves determines the speed and quality of communication. Additionally, understanding this relationship can help in the development of new technologies and advancements in various industries.