Number of Photons and wavelength?

In summary, the number of photons emitted by a charged particle in Cerenkov radiation is inversely proportional to the wavelength, with shorter wavelengths having a higher relative intensity per unit frequency. Further explanation and mathematical reasoning can be found in the Wikipedia article and in Jackson's work.
  • #1
vhbelvadi
67
1
I read recently that the "number of photons emitted by a charged particle is inversely proportional to wavelength" with regard to Cerenkov radiations. (The wavelength refers to the radiation which is of comparatively shorter wavelength, towards the blue-end.)

I was looking for a more detailed explanation for this. A little (or a lot of) maths would help too!

Thank you.
 
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  • #3
@jedishrfu - I did that already! Wikipedia states,

"Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter wavelengths) are more intense in Cherenkov radiation."

I was looking for an explanation on how (mathematically) 'relative intensity per unit frequency' and frequency are related. I know they're proportional, but I'd like a mathematical explanation/reasoning for it.
 
  • #4
There's a (rather mathematical) derivation of the Cherenkov frequency spectrum in Jackson.
 

FAQ: Number of Photons and wavelength?

What is the relationship between the number of photons and wavelength?

The number of photons and wavelength are inversely proportional to each other. This means that as the wavelength decreases, the number of photons increases, and vice versa. This relationship is described by the equation E = hc/λ, where E is the energy of a photon, h is Planck's constant, c is the speed of light, and λ is the wavelength.

How does the number of photons affect the intensity of light?

The number of photons is directly related to the intensity of light. Intensity is defined as the amount of energy per unit area per unit time. This means that as the number of photons increases, the intensity of light also increases. In other words, the more photons there are, the brighter the light will appear.

Can the number of photons be measured?

Yes, the number of photons can be measured using a device called a photometer. This device measures the intensity of light and can calculate the number of photons based on the energy of each individual photon and the total energy of the light source.

How does the number of photons affect the color of light?

The number of photons does not directly affect the color of light. Color is determined by the wavelength of light, not the number of photons. However, as mentioned earlier, the number of photons and wavelength are inversely proportional, so a change in the number of photons can result in a change in the color of light.

How is the number of photons related to the photoelectric effect?

The photoelectric effect is the emission of electrons from a material when light of a certain frequency or higher is shone on it. The number of photons is directly related to the energy of the light, and the energy of the light is what causes the electrons to be emitted. Therefore, the number of photons is indirectly related to the photoelectric effect.

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