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| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 19.3 | The Compton Effect and Pressure of Light |
In these revision notes for The Compton Effect and Pressure of Light, we cover the following key points:
When X-radiation falls on crystals, it interacts with the electrons of crystal atoms or molecules. As a result, the incident radiation scatters in different directions from the original. This scattered radiation is also known as "diffuse radiation". It is made up by two components: one has the same wavelength as the incident radiation and it is called the "coherent component" while the other has a greater wavelength than the incident radiation and is called "non-coherent component" of the diffused radiation. This is known as the Compton Effect.
Compton found experimentally that the change in wavelength Δλ between the scattered radiation λ' and incident radiation λ depend only by the scattering angle θ. Mathematically, this dependence is written as
The quantity λC (which obviously has the unit of wavelength) is known as the "Compton wavelength". It is a constant and its value is found experimentally (λC = 0.00243 nm = 2.43 × 10-12 m).
Compton observed the interaction of photons produced by the X-radiation and the weakly bonded electrons. This interaction is a perfectly elastic collision in which both energy and momentum of the photon-electron system are conserved. Compton found theoretically that
where m is the mass of electron (m = 9.1 × 10-31 kg), h is the Planck's constant (h = 6.626 × 10-34 J · s) and c is the speed of light in vacuum (c = 3 × 108 m/s).
The Compton wavelength λC therefore is
Pyotr Lebedev found experimentally that light pressure depends on the following factors:
Combining these factors, Lebedev found the following formula for light pressure P:
It is a known fact that 0 ≤ r ≤ 1 where r = 0 for black bodies and r = 1 for perfect mirrors. Therefore, light pressure in perfect mirrors is twice the pressure produced by the same light beam on black bodies for the same incident angle.
If ΔE is the light energy incident on the area A0 during a very short time interval Δτ, we obtain
where I is the intensity of light.
The number ΔN of photons incident on the given surface A0 during the time interval Δτ is
where n is the concentration of photons (the number of photons per unit volume).
The relationship between the intensity of light beam and energy of incident photons is
The quantity (h ∙ f) ∙ n represents the volume density of photons energy and it is denoted by w. Hence, we obtain for the pressure of light:
The wave interpretation of light is based on the action exerted by the electric and magnetic components E⃗ and B⃗ of light waves on matter electrons. Electronic currents are induced under the effect of electric field and the magnetic Lorentz Force acts on them. This action determines the pressure effect of light. According to this theory, even if the existence of photons is not considered, the light pressure is calculated by the two equations
and
where the quantity w bears the meaning of volume density of light wave.
Nowadays, the idea of dual nature (wave-particle) of light is widely accepted in the scientific circles. We call "photons" the particles of light. However, we use the wave approach to describe the way in which photons propagate in space.
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