# Why Thomson scattering calls for a size-changing electron?

1. ### Gibby_Canes

21
Why Thomson scattering calls for a "size-changing" electron?

From my limited understanding of Thomson scattering, it only works for wavelengths comparable to the size of the electron. Because scattering was observed at a variety of wavelengths, it was assumed that the size of the electron must change when rays of different wavelengths were scattered off of it. One of the merits of the Compton Effect was that it described this phenomenon without imposing unlikely constraints on the electron.

But I don't understand why? Why does the scattering only work for certain wavelengths? And how exactly does this transfer into the idea of an electron of variable size?

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3. ### Simon Bridge

14,660
Re: Why Thomson scattering calls for a "size-changing" electron?

In classical optics, the scattering of a wave off a barrier depends on the size of the barrier and the incoming wavelength.
Knowing the wavelength, you should be able to work out the size of the barrier - it is a common teaching lab experiment.
The equation should work for any wavelength - it's just that the ones that are comparable to the size of the barrier give easy to measure patterns.

When you use the same model to find the "size" of an electron, you get different values depending on the wavelength of the incoming light. So it appears that different kinds of light see different sizes for the electron ... or: the classical model has a flaw in it ;)

4. ### Jano L.

1,217
Re: Why Thomson scattering calls for a "size-changing" electron?

Gibby_Canes,

what you describe does not seem correct. Can you post a reference where you read it?

Thomson scattering is a term referring to scattering of X-ray radiation by (almost) free electrons; the X-rays are supposed to be comparable or lower than the size of the atoms, not electrons.

In practice, Thomson let X-rays scatter off the air molecules and calculated effective scattering cross-section for such scattering (for Poynting energy).

However, this cross-section is not connected directly with the size of the charge distribution of the electron. Point-like electron of zero radius still has non-zero Thomson cross-section

$$\frac{8\pi}{3}r_e^2,$$

where

$$r_e = \frac{e^2}{4\pi\epsilon_0mc^2}.$$

In fact, the Thomson derivation is for situation where the wavelength is much greater than the electron.

The Compton effect is related, but was about something different - it shows the relation between the change in wavelength of the gamma radiation and the angle of scattering.

Neither Thomson or Compton's calculations use the idea that electron has definite non-zero size.