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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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SUMMARY
The relationship between energy and frequency is established through experimental results, particularly in the photoelectric effect, where the maximum energy of ejected electrons correlates linearly with light frequency. This linear relationship is defined by Planck's constant (h), leading to the equation E = hν, where E represents energy and ν denotes frequency. The phenomenon is further explained using principles of special relativity, demonstrating that energy divided by frequency remains constant for a given photon. This foundational understanding is critical in fields such as quantum mechanics and electromagnetic theory.
PREREQUISITES- Understanding of the photoelectric effect and its implications.
- Familiarity with Planck's constant (h) and its role in quantum mechanics.
- Basic knowledge of special relativity and energy-momentum concepts.
- Ability to interpret linear equations and graphs in a scientific context.
- Study the photoelectric effect in detail, focusing on experimental setups and results.
- Learn about Planck's constant and its significance in quantum physics.
- Explore the principles of special relativity, particularly energy-momentum relationships.
- Investigate the implications of energy-frequency relationships in various quantum phenomena.
Students of physics, researchers in quantum mechanics, and professionals in fields related to electromagnetic theory will benefit from this discussion on the energy-frequency relationship.
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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?)
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