An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 W. An infrared lamp emits light of wavelength 700 nm, also at the rate of 400 W. (a) Which lamp emits photons at the greater rate and (b) what is that greater rate?
The infrared lamp emits photons at greater rate.
(b) The rate of emitted protons is
The expression of emission rate is given by,
Here, P is power.
The energy of a photon of wavelength is given by,
Here, h is Planck’s constant and c is the speed of light.
The wavelength of the photon and energy of the photon has an indirect relationship, so; the wavelength of the photon will be larger when the energy is smaller. Here, the wavelength of infrared light is more than ultraviolet light.
Therefore, the energy of the infrared photon is less than the ultraviolet photon. But the power emitted by both lamps is the same.
Here, the energy emitted per second is constant and equal to 400 W.
From the above relation, it can be observed that if the energy of the infrared photon is less than the ultraviolet photon, then the number of photons emitted by the infrared light will be more.
Therefore, the infrared lamp emits photons at a greater rate.
The expression to calculate the emission rate is given by,
Substitute the below values in eq 1.
Therefore, the rate of emitted protons is
(a) the Compton shift ,
(b) the fractional Compton shift , and
(c) the change in photon energy for light of wavelength scattering from a free, initially stationary electron if the scattering is at to the direction of the incident beam? What are
(e) , and
(f) for scattering for photon energy 50.0 keV (x-ray range)?
For the thermal radiation from an ideal blackbody radiator with a surface temperature of , let represent the intensity per unit wavelength according to the classical expression for the spectral radiancy and represent the corresponding intensity per unit wavelength according to the Planck expression. What is the ratio for a wavelength of
(a) (at the blue end of the visible spectrum) and
(b) (in the far infrared)?
(c) Does the classical expression agree with the Planck expression in the shorter wavelength range or the longer wavelength range?
Question: The function displayed in Eq. 38-27 can describe a free particle, for which the potential energy is in Schrodinger’s equation (Eq. 38-19). Assume now that constant in that equation. Show that Eq. 38-27 is a solution of Schrodinger’s equation, with giving the angular wave number k of the particle.
An orbiting satellite can charge by the photoelectric effect when sunlight ejects electrons from its outer surface. Satellites must be designed to minimize such charging because it can ruin the sensitive microelectronics. Suppose a satellite is coated with platinum, a metal with a very large function . Find the longest wavelength of incident sunlight that can eject an electron from the platinum.
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