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Chapter 6: Q32E (page 1249)
If a muon is traveling at 0.999c, what are its momentum and kinetic energy? (The mass of such a muon at rest in the laboratory is 207 times the electron mass.)
The momentum and kinetic energy
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A pulsed dye laser emits light of wavelength 585 nm in 450@ms pulses. Because this wavelength is strongly absorbed by the hemoglobin in the blood, the method is especially effective for removing various types of blemishes due to blood, such as port-wine鈥揷olored birthmarks. To get a reasonable estimate of the power required for such laser surgery, we can model the blood as having the same specific heat and heat of vaporization as water 14190 J > kg . K, 2.256 * 106 J > kg2. Suppose that each pulse must remove 2.0 mg of blood by evaporating it, starting at 33_C.
(a) How much energy must each pulse deliver to the blemish?
(b) What must be the power output of this laser?
(c) How many photons does each pulse deliver to the blemish?
A hydrogen atom undergoes a transition from a 2p state to the 1s ground state. In the absence of a magnetic field, the energy of the photon emitted is 122 nm. The atom is then placed in a strong magnetic field in the z-direction. Ignore spin effects; consider only the interaction of the magnetic field with the atom鈥檚 orbital magnetic moment. (a) How many different photon wavelengths are observed for the 2p1s transition? What are the values for the initial and final states for the transition that leads to each photon wavelength? (b) One observed wavelength is exactly the same with the magnetic field as without. What are the initial and final values for the transition that produces a photon of this wavelength? (c) One observed wavelength with the field is longer than the wavelength without the field. What are the initial and final ml values for the transition that produces a photon of this wavelength? (d) Repeat part (c) for the wavelength that is shorter than the wavelength in the absence of the field.
When ultraviolet light with a wavelength of 4.00nm falls on a certain metal surface, the maximum kinetic energy of the emitted photoelectrons is measured to be 1.10eV. What is the maximum kinetic energy of the photoelectrons when light of wavelength 300.0nm falls on the same surface?
A particle is in the ground level of a box that extends from x= 0 to x= L. (a) What is the probability of finding the particle in the region between 0 and L/4? Calculate this by integrating , where c is normalized, from x= 0 to x= L/4. (b) What is the probability of finding the particle in the region x= L/4 to x= L/2 ? (c) How do the results of parts (a) and (b) compare? Explain. (d) Add the probabilities calculated in parts (a) and (b). (e) Are your results in parts (a), (b), and (d) consistent with Fig. 40.12b? Explain.
A proton (rest mass ) has total energy that is 4.00 times its rest energy. What are (a) the kinetic energy of the proton; (b) the magnitude of the momentum of the proton; (c) the speed of the proton?
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