Chapter 3: 6CQ (page 92)
An isolated atom can emit a photon and the atom's internal energy drops. In fact, the process has a name:spontaneous emission. Can an isolated electron emit a photon? Why or why not?
An isolated electron cannot emit a photon on its own as this process would violate energy and momentum conservation.
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A stationary muon annihilates with a stationary antimuon (same mass, role="math" localid="1657587173645" . but opposite charge). The two disappear, replaced by electromagnetic radiation. (a) Why is it not possible for a single photon to result? (b) Suppose two photons result. Describe their possible directions of motion and wavelengths.
The charge on a piece of metal can be "watched" fairly easily by connecting it to an electroscope, a device with thin leaves that repel when a net charge is present You place a large excess negative charge on a piece of metal, then separately shine light source of two pure but different colors at it. The first source is extremely bright, but the electroscope shows no change in the net change. The second source is feeble, but the charge disappears. Appealing to as few fundamental claims as possible, explain to your friend what evidence this provides for the particle nature of light.
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?
An object moving to the right at 0.8c is struck head-on by a photon of wavelength moving to the left. The object absorbs the photon (i.e., the photon disappears) and is afterward moving to the right at 0.6c. (a) Determine the ratio of the objectโs mass after the collision to its mass before the collision. (Note: The object is not a โfundamental particleโ, and its mass is, therefore, subject to change.) (b) Does Kinetic energy increase or decrease?
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.
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