Determine the de Broglie wavelength of a particle of mass m and kinetic energy K. Do this for both (a) a relativistic and (b) a nonrelativistic particle.
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Determine the de Broglie wavelength of a particle of mass m and kinetic energy K. Do this for both (a) a relativistic and (b) a nonrelativistic particle.
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- Louis de Broglie proposed that a particle of mass m and moving at the speedv will have a wavelength related to its momentum. Air molecules of mass 30 amu travel at speeds which you can take to be 500 ms−1. Calculate their de Broglie wavelength.De Broglie postulated that the relationship ? = h/p is valid for relativistic particles. What is the de Broglie wavelength for a (relativistic) electron having a kinetic energy of 3.18 MeV?In quantum interpretation of the electromagnetic waves in vacuum the photon has the energy E = hw/2n and the momentump= hk/2n. So the ratio E of the energy to the momentum is = c, the speed of light in k vacuum. Similar relation can be obtained in classical electrodynamics as follows. Consider the time-averaged energy density of the electromagnetic field ɛ = B² /2µ0 + €0 E² /2 for a plane wave propagating in vacuum along the z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a wave S = E × H and confirm that its ratio to the time-averaged energy density ratio is equal to the speed of light in vacuum, S/e = c.
- . Find the momentum of a photon in eV/c and in kg·m/s if the wavelength is (a) 400 nm, (b) 1 Å = 0.1 nm, (c) 3 cm, and (d) 2 nm.Louis de Broglie proposed that a particle of mass m and moving at the speed v will have a wavelength related to its momentum. Air molecules of mass 30 amu travel at speeds which you can take to be 500 ms-1. Calculate their de Broglie wavelength.Assuming that the smallest measurable wavelength in an experiment is 0.650 fm , what is the maximum mass of an object traveling at 815 m⋅s−1 for which the de Broglie wavelength is observable?
- A light source is emitting radiation at 7.63•1014 Hz is incapable of ejecting photoelectrons from a certain metal. However, if the source is given a velocity of 0.28 c towards the metal, photoelectrons just begin to be ejected. A) What is the work function of the metal ? B) Determine the stopping voltage if the source is instead moved at 0.57 c towards the metal ?The minimum uncertainty Ay in the position y of a particle is equal to its de Broglie wavelength. Determine the minimum uncertainty in the speed of the particle, where this minimum uncertainty Avy is expressed as a Avy percentage of the particle's speed vy Percentage = × 100 % Vy ignored. Number Units 6). . Assume that relativistic effects can be