When an X-ray photon with wavelength λ collides with a stationary free electron of mass m, the X-ray photon is scattered at an angle θ relative to its original direction of propagation, and its wavelength changes to λ′. This phenomenon is called the Compton effect.
The wavelength λ′ of the scattered X-ray photon satisfies the following relationship, using Planck's constant h and the speed of light in a vacuum c:
λ′−λ=mch(1−cosθ)During the collision, the electron receives energy and momentum from the X-ray photon and is ejected as a recoil electron. By considering the conservation of momentum for the entire system before and after a collision, if we know the wavelength of the scattered X-ray photon λ′, the wavelength of the X-ray photon before the collision λ, and the scattering angle θ, we can directly determine the magnitude of the momentum of the ejected recoil electron pe.
Now, when an X-ray photon with wavelength λ collides with a stationary electron, the wavelength of the X-ray photon scattered in the direction of scattering angle θ=90° is 100101 times the original wavelength. In this collision, express the magnitude of the momentum of the ejected recoil electron pe using the magnitude of the momentum of the X-ray photon before the collision p.
When the dimensionless ratio ppe of the momentum of the recoiling electron pe and the momentum of the X-ray photon before collision p is found, this value can be expressed as 101N. Enter the value of the natural number N inside the square root.