Relationship Between Energy and Wavelength

In summary, the conversation discusses the equations E=h\nu and \lambda=h/p and their relationship. The individual is trying to determine the connection between E and \lambda and comes up with E=\lambda\nup, which simplifies to E=cp. However, they are unsure if there is a mistake or if they should look into the units of each variable. They later realize that by setting cp=mc^2 and finding c=v, they can simplify the equation.
  • #1
pzona
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I'm looking at the equations E=h[tex]\nu[/tex] and [tex]\lambda[/tex]=h/p and trying to determine the relationship between E and [tex]\lambda[/tex]. What I'm coming up with is E=[tex]\lambda[/tex][tex]\nu[/tex]p, which simplifies to E=cp. This doesn't quite make sense to me though, is there a mistake, or should I just look more into the units of each variable?

EDIT: Not sure why, but nu looks like a superscript when I posted this. I assume everyone here is familiar the equations, but I just want to clarify that I'm not trying to say "lambda to the nu power."
 
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  • #2
Nevermind. I just took it a little further by setting cp=mc^2 and found c=v. Mods, feel free to lock/delete this thread.
 
  • #3


The relationship between energy and wavelength is a fundamental concept in physics and is described by the equations you mentioned. These equations are known as the Planck-Einstein relation and the de Broglie relation, respectively.

The equation E=h\nu relates the energy of a photon (E) to its frequency (nu) and the Planck constant (h). This equation shows that as the frequency of a photon increases, its energy also increases. This makes sense intuitively, as higher frequency photons have more energy and are therefore more energetic.

On the other hand, the equation \lambda=h/p relates the wavelength (\lambda) of a particle to its momentum (p) and the Planck constant (h). This equation is derived from the de Broglie hypothesis, which states that all particles, including photons, have a wave-like nature. This equation shows that as the wavelength of a particle decreases, its momentum increases. This also makes sense intuitively, as shorter wavelengths correspond to higher frequencies and therefore more energetic particles.

Combining these two equations, we can derive the relationship E=\lambda\nu, which is the energy of a photon or particle in terms of its wavelength and frequency. This equation shows that the energy of a photon or particle is directly proportional to its frequency and inversely proportional to its wavelength. In other words, as the frequency increases, the energy increases, and as the wavelength increases, the energy decreases.

The equation E=cp that you came up with is not correct. This equation would imply that the energy of a photon or particle is directly proportional to its momentum, which is not the case. Momentum and energy are related, but they are not the same thing. The correct equation is E=\lambda\nu, which takes into account both the frequency and wavelength of a photon or particle.

In conclusion, the relationship between energy and wavelength is a fundamental aspect of the wave-particle duality of matter and is described by the equations E=h\nu and \lambda=h/p. These equations show that as the frequency of a photon or particle increases, its energy also increases, while a decrease in wavelength corresponds to an increase in energy.
 

What is the relationship between energy and wavelength?

The relationship between energy and wavelength is known as the wave-particle duality of light. This means that light can behave as both a wave and a particle. In terms of energy, the shorter the wavelength of light, the higher the energy it carries. This is because shorter wavelengths have a higher frequency, which is directly proportional to energy.

How does the energy of light affect its wavelength?

The energy of light directly affects its wavelength. This is because different wavelengths of light have different amounts of energy. For example, visible light has a range of wavelengths, with red having the longest wavelength and violet having the shortest. Red light has less energy compared to violet light, which has more energy.

Is there a mathematical relationship between energy and wavelength?

Yes, there is a mathematical relationship between energy and wavelength. This relationship is described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This equation shows that energy and wavelength are inversely proportional - as one increases, the other decreases.

How is the energy and wavelength of light related to its color?

The color of light is determined by its wavelength. As mentioned earlier, longer wavelengths correspond to lower energy and appear as red light, while shorter wavelengths correspond to higher energy and appear as violet light. The other colors of the visible spectrum fall in between these two extremes, with yellow having a longer wavelength and lower energy than green, for example.

Can the energy and wavelength of light be measured?

Yes, the energy and wavelength of light can be measured using various instruments such as spectrometers and photometers. These instruments use different techniques to measure the energy and wavelength of light, allowing scientists to study the properties of light and its relationship to energy in detail.

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