The ratio of the Compton wavelength (λc) to the de Broglie wavelength (λdB) depends on the mass and velocity of the particle in question.
The Compton wavelength is given by the formula:
λc = h / (mc)
where h is the Planck constant, m is the mass of the particle, and c is the speed of light.
The de Broglie wavelength, on the other hand, is given by:
λdB = h / p
where p is the momentum of the particle.
To find the ratio λc / λdB, we can substitute the expressions for λc and λdB into the ratio:
(λc / λdB) = (h / (mc)) / (h / p)
Simplifying, we get:
(λc / λdB) = p / (mc)
So, the ratio of the Compton wavelength to the de Broglie wavelength is equal to the momentum of the particle divided by its mass times the speed of light.