(a) Show that the frequency f and wavelength λ of a freely moving quantum particle with mass are related by the expression (F/c)2 = 1/λ2 + 1/λC2where λC = h/mc is the Compton wavelength of the particle. (b) Is it ever possible for a particle having nonzero mass to have the same wavelength and frequency as a photon? Explain.

(a) Show that the frequency f and wavelength λ of a freely moving quantum particle with mass are related by the expression (F/c)2 = 1/λ2 + 1/λC2where λC = h/mc is the Compton wavelength of the particle. (b) Is it ever possible for a particle having nonzero mass to have the same wavelength and frequency as a photon? Explain.

Similar questions

2. A free particle (a particle that has zero potential energy) has mass 8 eV/c² and total energy 10 eV and is traveling to the right. At x = 0, the potential jumps from zero to Vo = 5 eV and remains at this value for all positive x. (a) In classical mechanics, what happens to the particle when it reaches x = 0? (b) What is the wavenumber of the quantum particle in the region x > 0? (c) Find the reflection coefficient R and the transmission coefficient T for the quantum particle. (d) If one million particles with this same momentum and energy are incident on this poten- tial step, how many particles are expected to continue along in the positive x direction? How does this compare with the classical prediction?
(a) If the wavelength of an electron is 4.77 ✕ 10−7 m, how fast is it moving? ______ km/s (b) If the electron has a speed equal to 3.50 ✕ 106 m/s, what is its wavelength? ______m.
The distance between atoms in a crystal of NaCl is 418.5 nm. The crystal is being studied in a neutron diffraction experiment. At what speed (in m/s) must the neutrons be moving so that their de Broglie wavelength is the same length as the spacing between the atoms? (Assume the neutrons are non-relativistic.)
The allowed energies of a quantum system are 0.0 eV, 5.5 eV , and 9.0 eV. What wavelengths appear in the system's emission spectrum? (Express your answers in nanometers in ascending order separated by commas).
Question 1. An electron beam of a TEM leaves the gun with an energy of 300 keV. a) Determine the classical (non-relativistic) and relativistic wavelengths for the electron. (4) b) Determine the classical (non-relativistic) and relativistic momentum, frequencies and energies. (3)
A proton moving freely has a wavelength of 0.600 pm (a) what is its momentum? (b) what is its speed (c) Through what potential difference might it have been accelerated through, from rest, to this speed?
What is the velocity (in m/s) of a 0.430 kg billiard ball if its wavelength is 7.70 cm (large enough for it to interfere with other billiard balls)?
= 1. Photoelectric effect. In a photoelectric experiment in which monochromatic light of wave- length \ falls on a potassium surface, it is found that the stopping potential Vstop is 1.9 V for > 300 nm and 0.88 V for \ = 400 nm. Imagine we know neither Planck's constant, nor the workfunction for potassium, nor the threshold frequency fo. But assume we do know the elementary charge e 1.60 × 10-19 C and want to test the theoretical prediction of Eintsein's theory. = (a) From the given data, calculate a value for Planck's constant, h. (b) From the same data, find the workfunction Eo and the threshold frequency fo for potas- sium. (c) Then compare your results for h and Eo to their known values (see Knight, Table 38.1 for the work function). (d) Plot eVstop as a linear function of frequency f. Include the information you have found in parts (a) and (b) as well as the experimental data.
During a certain experiment, the de Broglie wavelength of an electron is 610 nm = 6.1 x 10- m, which is the same as the wavelength of orange light. How fast (in m/s) is the electron moving? m/s