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Chapter 3: Q19E (page 93)
What wavelength of light is necessary to produce photoelectron of speed with a magnesium target?
The wavelength of light necessary to produce photoelectron of speed with a magnesium target is .
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A gamma-ray photon changes into a proton-antiproton pair. Ignoring momentum conservation, what must have been the wavelength of the photon (a) if the pair is stationary after creation, and (b) if each moves off at , perpendicular to the motion of the photon? (c) Assume that these interactions occur as the photon encounters a lead plate and that a lead nucleus participates in momentum conservation. In each case, what fraction of the photon's energy must be absorbed by a lead nucleus?
A bedrock topic in quantum mechanics is the uncertainty principle. It is discussed mostly for massive objects in Chapter 4, but the idea also applies to light: Increasing certainty in knowledge of photon position implies increasing uncertainty in knowledge of its momentum, and vice versa. A single-slit pattern that is developed (like the double-slit pattern of Section 3.6) one photon at a time provides a good example. Depicted in the accompanying figure, the pattern shows that pho tons emerging from a narrow slit are spreadall-over; a photon's -component of momentum can be any value over a broad range and is thus uncertain. On the other hand, the -coordinate of position of an emerging photon covers a fairly small range, for is small. Using the single-slit diffractionformula , show that the range of likely values of , which is roughly , is inversely proportional to the range of likely position values. Thus, an inherent wave nature implies that the precisions with which the particle properties of position and momentum can be known are inversely proportional.
A beam of light strikes a barrier in which there is a narrow single slit. At the very center of a screen beyond the single slit, photons are detected per square millimeter per second.
(a) What is the intensity of the light at the center of the screen?
(b) A secood slit is now added very close to the first. How many photons will be detected per square millineter per sec and at the center of the screen now?
Radiant energy from the sum arrives at Earth with an intensity of. Making the rough approximation that all photons are absorbed, find (a) the radiation pressure and (b) the total force experienced by Earth due to this “solar wind”.
According to Wien's Law, the wavelength of maximum thermal emission of electromagnetic energy from a body of temperature Tobeys
localid="1660036169367"
Show that this law follows from the spectral energy density obtained in Exercise 13. Obtain an expression that, when solved, would yield the wavelength at which this function is maximum. The transcendental equation cannot be solved exactly, so it is enough to show thatlocalid="1660036173306" solves it to a reasonable degree of precision.
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