In a Compton scattering experiment, an x - ray photon scatters through an angle of 17.4° from a free electron that is initially at rest. The electron recoils with a speed of 2 180 km/s. Calculate (a) the wavelength of the incident photon and (b) the angle through which the electron scatters

A free electron moving along the x-direction (one for which V(x) = 0) would have a wave function of the form f(x) = A eikx + B e−ikx where A and B are constants. (a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm¯¹)? Express your answer in scientific notation with three significant figures. (b) The Hamiltonian operator for a free electron is given by p² ħ² d² Ĥ 2me 2me dx² The wave function provided at the top is an eigenstate of Â. If one measures the energy for an electron in this state using Â, what would be the result, and how does it compare to the classical kinetic energy of a free electron with this velocity?

A photon moving in the +x-direction, scatters off a free stationary electron. The wavelength of the incident photon is 0.0390 nm. After the collision, the electron moves at an angle a below the +x-axis, while the photon moves at an angle e = 84.3° above the +x-axis. (For the purpose of this exercise, assume that the electron is traveling slow enough that the non-relativistic relationship between momentum and velocity can be used.) (a) What is the angle a (in degrees)? |• counterclockwise from the +x-axis (b) Determine the speed of the electron (in m/s). m/s

You use 0.124 nm x-ray photons in a Compton-scattering experiment. At what angle is the wavelength of the scattered x rays 1.0% longer than that of the incident x rays? 70.6° 67.0° 60.7° 56.5°