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Physics for Scientists and Engineers, 6e Chapter 40 - Introduction to Quantum Physics

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This figure shows two stars in the constellation Orion. Betelgeuse appears to glow red, while Rigel looks blue in color. Which star has a higher surface temperature? Betelgeuse 2.Rigel 3.They both have the same surface temperature. 4.Impossible to determine.

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A very hot star will have its peak in the blackbody intensity distribution curve at wavelengths shorter than the visible. As a result, more blue light is emitted than red light.

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While standing outdoors one evening, you are exposed to the following four types of electromagnetic radiation: yellow light from a sodium street lamp, radio waves from an AM radio station, radio waves from an FM radio station, and microwaves from an antenna of a communications system. Rank these types of waves in terms of increasing photon energy, lowest first sodium light, AM, FM, microwave 2.AM, FM, sodium light, microwave 3.AM, FM, microwave, sodium light 4.microwave, sodium light, AM, FM

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The order of photon energy will be the same as the order of frequency. See Figure for a pictorial representation of electromagnetic radiation in order of frequency.

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Consider one of the curves shown in this figure. Suppose the intensity of the incident light is held fixed but its frequency is increased. The stopping potential in the figure: remains fixed 2.moves to the right 3.moves to the left

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When the frequency is increased, the photons each carry more energy, so a stopping potential larger in magnitude is required for the current to fall to zero.

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Note that for any given scattering angle θ, Equation (seen below) gives the same value for the Compton shift for any wavelength. Keeping this in mind, for which of the following types of radiation is the fractional shift in wavelength at a given scattering angle the largest? radio waves 2.microwaves 3.visible light 4.x-rays

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The shift Δλ is independent of λ. Thus, the largest fractional shift will correspond to the smallest wavelength.

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We have discussed two wavelengths associated with the electron—the Compton wavelength and the de Broglie wavelength. Which is an actual physical wavelength associated with the electron? the Compton wavelength 2.the de Broglie wavelength 3.both wavelengths 4.neither wavelength

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The Compton wavelength (Section 40.3) is a combination of constants and has no relation to the motion of the electron. The de Broglie wavelength (Eq ) is associated with the motion of the electron through its momentum.

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As an analogy to wave packets, consider an “automobile packet” that occurs near the scene of an accident on a freeway. The phase speed is analogous to the speed of individual automobiles as they move through the backup caused by the accident. The group speed can be identified as the speed of the leading edge of the packet of cars. For the automobile packet, the group speed is the same as the phase speed. 2.the group speed is less than the phase speed. 3.the group speed is greater than the phase speed.

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The group speed is zero because the leading edge of the packet remains fixed at the location of the accident.

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As another analogy to wave packets, consider a “runner packet” that occurs at the start of a footrace of length L. As the runners begin the race, the packet of runners spreads in size as the faster runners outpace the slower runners. The phase speed is the speed of a single runner, while we can identify the group speed v g as the speed with which the average position of the entire packet of runners moves. The time interval for the winning runner to run the race is greater than L/v g. 2.equal to L/v g. 3.less than L/v g.

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The phase speed of the winning runner is larger than the average speed of all the runners, so the time interval for the winning runner is less than L/v g.

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The location of a particle is measured and specified as being exactly at x = 0, with zero uncertainty in the x direction. How does this affect the uncertainty of its velocity component in the y direction? It does not affect it. 2.It makes it infinite. 3.It makes it zero.

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The uncertainty principle relates uncertainty in position and velocity along the same axis. The zero uncertainty in position along the x axis results in infinite uncertainty in its velocity component in the x direction, but it is unrelated to the y direction.

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A quantum argument for the phenomenon of diffraction of light claims that photons passing through a narrow slit have been localized to the width of the slit. Because we have gained information about their position, they must have a larger uncertainty in momentum along the plane of the screen in which the slit is cut. Thus, the photons gain momentum perpendicular to their original direction of propagation and spread out, forming on a screen a bright area that is wider than the slit. Suppose we are observing diffraction of light and suddenly Planck’s constant drops to half its previous value. This quantum argument for diffraction would claim that the bright area on the screen is unchanged. 2.the bright area on the screen becomes wider. 3.the bright area on the screen becomes narrower.

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According to the uncertainty principle, if Planck’s constant is smaller, the uncertainty in momentum can be smaller and the momentum perpendicular to the original direction of propagation would be smaller. Note that classical wave theory does not include Planck’s constant, so it would predict no effect.

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