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Compton wavelength
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Everything about Compton Length totally explained

The Compton wavelength lambda of a particle is given by » lambda = frac = alpha^2 a_0

The Planck mass is special because ignoring factors of 2 pi and the like, the Compton wavelength for this mass is equal to its Schwarzschild radius. This special distance is called the Planck length. This is a simple case of dimensional analysis: the Schwarzschild radius is proportional to the mass, whereas the Compton wavelength is proportional to the inverse of the mass.

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