In a Compton experiment, the frequency of an incident photon is 5 * 1016 Hz. Calculate the de Broglie wavelength of the scattered electron when the scattering angle of the photon is (a) 90° and (b) 180°. Please give a detailed answer
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- 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/sX-ray photons of wavelength 0.0248 nm are incident on a target and the Compton-scattered photons are observed at 80.0° above the photons' incident line of travel. [Use relativistic units for this problem!] (a) What is the wavelength of the scattered photons? nm (b) What is the momentum of the incident photons? eV/c What is the momentum of the scattered photons? eV/c (c) What is the kinetic energy of the scattered electrons? eV (d) What is the momentum (magnitude and angle) of the scattered electrons? eV/cTo study crystal diffraction we need wavelengths of about 0.5 x 10-10 m. What would be the corresponding kinetic energies in eV of (a) a photon, (b) an electron, and (c) a neutron?
- A photon moving in the +x-direction, scatters off a free stationary electron. The wavelength of the incident photon is 0.0310 nm. After the collision, the electron moves at an angle a below the +x- axis, while the photon moves at an angle = 81.3° 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)? 47.21 What is the shift in wavelength of the photon due to the scattering? How can you use momentum conservation in the horizontal and vertical directions to determine the angle? ° counterclockwise from the +x-axis (b) Determine the speed of the electron (in m/s). m/sA photon has an energy E and wavelength l before scattering from a free electron. After scattering through a 135° angle, the photon’s wavelength has increased by 10.0%. Find the initial wavelength and energy of the photon.The velocity of an electron is known to be 1.000×105 m/s, with an uncertainty of Av = 1.00×102 m/s. (a) What is the minimum uncertainty in the electron's position, Av, in meters? (b) How does this compare to the de Broglie wavelength of the electron? (c) One of your professors (m = 75.0 kg) is pacing at the front of the classroom, and you measure their velocity to an uncertainty of Av = 0.100 m/s. What is the minimum uncertainty in a measurement of their position? (d) How does this compare to the height of your professor?
- In the 1920s Clinton Davisson and Lester Germer accidentally observed diffraction when electrons with 54 eV of energy were scattered off crystalline nickel. The diffraction peak occurred when the angle between the incident beam and the scattered beam was 50°. (a) What is the corresponding angle u relevant for Eq.? (b) The planes in crystalline nickel are separated by 0.091 nm, as determined by x-ray scattering experiments. According to the Bragg condition, what wavelength do the electrons in these experiments have? (c) Given the mass of an electron as 9.11 x 10-31 kg, what is the corresponding classical speed vcl of the diffracted electrons? (d) Assuming the electrons correspond to a wave with speed vcl and wavelength λ, what is the frequency f of the diffracted waves? (e) Quantum mechanics postulates that the energy E and the frequency f of a particle are related by E = hf, where h is known as Planck’s constant. Estimate h from these observations. (f) Our analysis has a small flaw:…A 0.00220-nm photon scatters from a free electron. For what (photon) scattering angle does the recoiling electron have kinetic energy equal to the energy of the scattered photon?answer in degrees °