The Compton wavelength, λc, of a particle of mass m is defined as follows: λc = h/mc. (a) Calculate the Compton wavelength of a proton. (b) Calculate the energy of a photon that has the same wavelength as found in part (a). (c) Show, in general, that a photon with a wavelength equal to the Compton wavelength of a particle has an energy that is equal to the rest energy of the particle.

The Compton wavelength, λc, of a particle of mass m is defined as follows: λc = h/mc. (a) Calculate the Compton wavelength of a proton. (b) Calculate the energy of a photon that has the same wavelength as found in part (a). (c) Show, in general, that a photon with a wavelength equal to the Compton wavelength of a particle has an energy that is equal to the rest energy of the particle.

Similar questions

Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic field strength of 0.25 T. The typical temperature of a sunspot is 3500 K the equipartition equation for velocity v, temperature T and mass m of a particle, is, 3kgT V = m kB is Boltzmann's constant (1.38×10–23 J/K). a) The mass of the Sun is approximately 2 × 1030 kg. Use this information and the infor- mation given above to compute the acceleration g due to gravity at the surface of the Sun. b) Compute the drift velocity Ūg due to gravity for a proton and an electron located within a sunspot. c) Assuming a typical mass density of the Sun's photosphere of 10-3 kg/m³, compute the number density of protons and electrons in the photosphere (where sunspots reside) assuming that the Sun is comprised of pure ionized hydrogen. d) Calculate the total current density J (accounting for the contributions of both electrons and tons) within sunspots. You may assume that you can treat the ensemble of…
An electron and a positron, with a mass of 9.1 x 10-31 kilograms, annihilate each other, producing two photons. What is the approximate energy of each emerging photon? It is 0.51 Mev 2.0 MeV 4.0 MeV 1.02 MeV It cannot be determined unless the frequency of the photon is known.
As noted in the chapter, the cosmic microwave background radiation fits the Planck equation for a blackbody at 2.7 K. (a) What is the wavelength at the maximum intensity of the spectrum of the background radiation? (b) What is the frequency of the radiation at the maximum? (c) What is the total power incident on Earth from the background radiation
Determine the distance between the electron and proton in an atom if the potential energy UU of the electron is 11 eV (electronvolt, 1 eV =1.6×10−19=1.6×10−19 J). Give your answer in Angstrom (1 A = 10-10 m).
When you shine a certain source of EM radiation on a sheet of gold (work function W1 = 5.1 eV), the stopping voltage required to bring all the ejected electrons to a halt is V = 3.5 V. If you were to use this same source of EM radiation on a sheet of potassium (work function W2 = 2.3 eV), what would be the maximum speed of ejected electrons?
An electron and an antielectron (each has mass 9.11 x 10-31 kg), each traveling at 0.6c relative to the lab frame, collide head on and annihilate, resulting in the creation of two identical photons which travel away in opposite directions. What is the frequency of each photon?