# Mathematical relationship between frequency wavelength and energy

### Light - Hydrogen Energy Levels - NAAP An inverse relationship exists; electromagnetic radiation with shorter wavelengths is more energetic. The relation- ship between energy and frequency is given. The relationship between frequency and wavelength is covered in The speed ( of sound) – hence also the speed with which (sound) energy. Light can be thought of as “particles” of electromagnetic energy called photons. Photons For light, the relationship between wavelength (λ) and frequency (ƒ) is .

The variation in speed of light with vacuum wavelength is known as dispersionand is also responsible for the familiar phenomenon in which light is separated into component colors by a prism.

Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength is known as a dispersion relation.

## What is the mathematical relationship between wavelength and frequency?

Nonuniform media[ edit ] Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore  Wavelength can be a useful concept even if the wave is not periodic in space.

For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth. The figure at right shows an example. The result is how the energy depends upon the wavelength of light. If you increase the frequency of a light source by a factor of 30, how much does the energy of the photons change?

### HubbleSite - Reference Desk - FAQs

If a light sources wavelength is 25 times smaller than before how does that change the energy of the photons? You could also figure this out by looking at how the frequency changes when you change the wavelength. If the wavelength is 25 times smaller than the frequency is 25 times larger.

Wien's Law - This law is used for black bodies, perfect radiation light emitters and absorbers and indicates at which wavelength they tend to give off most of their light. This law is used to explain why the colors of objects change as you change their temperatures. Basically as the temperature goes up, max goes up and vice versa. If you increase the temperature of a black body by a factor of 5, how does its value of max change?

The value of max is 5 times smaller than what it was before. An object has a temperature of 10, K. What is its value of max? Stefan-Boltzmann Law - This law is used for black bodies, perfect radiation light emitters and absorbers and indicates how much total energy they give off. Interesting thing to note - the energy they give off depends only on their temperatures, nothing else about the object matters like what it is made of.

Also this measure the total energy given off, so all energy at all wavelengths is what this indicates. But you have to be careful, T is taken to the fourth power, so a small change in it results in a very large change in the total amount of energy given off.

### Mathematical Applications

If you increase the temperature of a black body by a factor of 5, how does that change the amount of total energy given off? These frequencies are very high by everyday standards. Have a look around the room and find something that's the colour red.

How many times are the tiny crests of the light waves coming from that red object passing through the front of your eyes every second? In other words, what is the frequency of red light? Well, we know the speed of light and can take an average figure for the wavelength of red light. Let's say it's nm, that is: We now have everything we need to work out the frequency: So when we look at something that is medium red about ,, tiny little wave crests pass through our eyes every second!

How To Calculate The Energy of a Photon Given Frequency & Wavelength in nm Chemistry

This is certainly a very large number but still measurable using modern equipment. Indeed, the screen you are using had to have this number taken into account when it was being designed. If it hadn't you wouldn't be able to see this: