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physics
college physics a strategic approach 2nd
College Physics Essentials Electricity And Magnetism Optics Modern Physics Volume Two 8th Edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions
13. ••• (a) What is the de Broglie wavelength of the Earth in its orbit about the Sun? (b) Treating the Earth as a de Broglie wave in a large “gravitational” atom, what would be the principal quantum number, n, of its orbit? (c) If the principal quantum number increased by 1, how would
12. ••• According to the Bohr theory of the hydrogen atom, the speed of the electron in the first Bohr orbit is 2.19 × 106 m/s. (a) What is the wavelength of the matter wave associated with the electron? (b) How does this wavelength compare with the circumference of the first Bohr orbit?
11. •• What is the energy of a beam of electrons that exhibits a first-order maximum at an angle of 50°when diffracted by a crystal grating with a lattice plane spacing of 0.215 nm?
10. •• A scientist wants to use an electron microscope to observe details on the order of 0.25 nm. Through what potential difference must the electrons be accelerated from rest so that they have a de Broglie wavelength of this magnitude?
9. •• A charged particle is accelerated through a given potential difference. If the voltage is doubled, what is the ratio of the new de Broglie wavelength to the original value?
8. •• A proton and an electron are accelerated from rest through the same potential difference. What is the ratio of the de Broglie wavelength of the electron to that of the proton?
7. IE •• A proton traveling at a speed 4.5 × 104 m/s is then accelerated through a potential difference of 37 V. (a) Will its de Broglie wavelength (1) increase,(2) remain the same, or (3) decrease, due to the potential difference? Why? (b) By what percentage does the de Broglie wavelength of
6. IE •• Electrons are accelerated from rest through an electric potential difference. (a) If this potential difference increases to four times the original value, the new de Broglie wavelength will be (1) four times,(2) twice, (3) one-fourth, (4) one-half that of the original. Why? (b) If the
5. •• An electron is accelerated from rest through a potential difference so that its de Broglie wavelength is 0.010 nm. What is the potential difference?
4. •• An electron is accelerated from rest through a potential difference of 100 V. What is the de Broglie wavelength of the electron?
3. IE • An electron and a proton are moving with the same speed. (a) Compared with the proton, will the electron have (1) a shorter, (2) an equal, or (3) a longer de Broglie wavelength? Why? (b) If the speed of the electron and proton is 100 m/s, what are their de Broglie wavelengths?
2. • If the de Broglie wavelength associated with an electron is 7.50 × 10−7 m, what is its speed?
1. • What is the de Broglie wavelength associated with a 1000-kg car moving at 25 m/s?
13. Explain why there are always two photons created in pair annihilation. Why can’t the process create just one photon?
12. Can the production of two electrons and two positrons be accomplished using a high-energy photon? Explain.Why can’t two electrons and one positron result?
11. Why is the energy threshold for electron–positron pair production actually higher than the sum of their two masses (1.022 MeV)? [Hint: Linear momentum must be conserved.]
10. A laser requires a metastable state that is a relatively long-lived excited atomic state. What is the uncertainly in the energy of the metastable state compared to non-metastable excited states?
9. A bowling ball has well-defined position and speed, whereas an electron does not. Why?
8. Why is it impossible to simultaneously and accurately measure the position and speed of a particle?
7. What is the basis of the periodic table of elements in terms of quantum theory? What do the elements in a particular group have in common? How about in a particular period?
6. According to the Pauli exclusion principle, can two electrons in an atom have the same spin? Explain.
5. How would the radius for the maximum probability in Figure 28.3a change if the charge on the proton in the hydrogen atom were suddenly decreased? Explain your reasoning.
4. According to modern quantum theory and the Schrödinger equation, there is a probability that if you ran into a wall you could end up on the other side.(Don’t try this!) Explain the idea behind such an event and discuss why it has never been observed to happen.
3. An electron is accelerated from rest through an electric potential difference. Will increasing the potential difference result in a longer or shorter de Broglie wavelength?Explain.
2. If a baseball and a bowling ball were traveling at the same speed, which one would have a shorter de Broglie wavelength? Why?
1. The de Broglie hypothesis predicts that a wave is associated with any object that has momentum. Why isn’t the wave associated with a moving car observed?
16. When a stationary particle and its stationary antiparticle annihilate, a total energy of 25 MeV is released. How do the masses of the particles compare to that of an electron: (a) they are less massive than an electron, (b) they are more massive than an electron,(c) they have the same mass as
15. Due to momentum considerations, pair annihilation could not result in the emission of how many photons:(a) one, (b) two, (c) three, or (d) four?
14. Pair production involves (a) the production of two electrons, (b) the production of two positrons,(c) a hydrogen atom, (d) the production of a particle and its antiparticle.
13. According to the uncertainty principle, if a measurement time interval is done more quickly, the uncertainly in an energy measurement is (a) relatively large, (b) relatively small, (c) exactly the same, or(d) none of the preceding.
12. If the speed of an electron could be exactly measured, that would mean that (a) the particle could be located more exactly, (b) the particle could not be located at all, (c) the uncertainty in its momentum increases,(d) the time to measure the position decreases.
11. If the uncertainty in the position of a moving particle increases, (a) the particle may be located more exactly,(b) the uncertainty in its momentum decreases,(c) the uncertainty in its speed increases, (d) the time to measure the position increases.
10. For an electron, the number of values the spin quantum number ms can have is (a) one, (b) two, (c) three, (d) four.
9. The magnetic quantum number mℓ tells (a) the z- component of an orbit’s angular momentum,(b) an orbit’s angular momentum, (c) the total energy of a state, (d) the electron’s spin angular momentum.
8. The orbital quantum number ℓ determines (a) the total energy of a state, (b) the z-component of the orbital angular momentum, (c) the orbital angular momentum of an orbit, (d) the electron’s spin angular momentum.
7. The principle quantum number n is associated with(a) the total energy of a state, (b) the orbital angular momentum of an orbit, (c) the z-component of the orbital angular momentum, (d) the electron’s spin angular momentum.
6. An electron can tunnel through a “potential energy barrier.” Classically if it were in the barrier region, its kinetic energy would be (a) negative, (b) zero,(c) positive, or (d) zero.
5. The square of a particle’s wave function is related to(a) the energy of the particle, (b) the radius of the particle, (c) the probability of locating the particle,(d) the quantum number of its state.
4. Schrödinger’s wave equation involves a particle’s(a) kinetic energy, (b) potential energy, (c) total energy,(d) all of the preceding.
3. An electron can travel at different speeds. Which of the following speeds (all in m/s) would be associated with the shortest de Broglie wavelength: (a) 103, (b) 104,(c) 102, or (d) the wavelength is the same at all speeds?The SchrÖdinger Wave Equation
2. If the following were traveling at the same speed, which would have the longest de Broglie wavelength:(a) an electron, (b) a proton, (c) a carbon atom, or(d) a hockey puck?
1. Which color light consists of photons with the least momentum: (a) red, (b) green, (c) violet, or (d) yellow?
54. • To achieve population inversion between two atomic states separated by an energy of 3.5 eV, what wavelength of pumping light should be used?
53. • Suppose a hypothetical atom had two metastable excited states, one 2.0 eV above the ground state and one 4.0 eV above the ground state. If used in a laser with transitions only to the ground state, (a) what would be the wavelength emitted from each excited state? (b) Which transition is in
52. ••• For an electron in the ground state of a hydrogen atom, calculate its (a) potential energy, (b) kinetic energy, and (c) total energy. [Hint: You will need to use the orbital radius.]
51. ••• Show that the orbital speeds of an electron in the Bohr orbits are given (to two significant figures) by vn = (2.2 × 106 m/s)/n.
50. •• What is the binding energy for an electron in the ground state in the following hydrogen-like ions:(a) He + (Z = 2) and (b) Li2+ (Z = 3)?
49. IE •• (a) How many transitions in a hydrogen atom result in the absorption of red light: (1) one, (2) two,(3) three, or (4) four? (b) What are the principal quantum numbers of the initial and final states for this process? (c) What is the energy of the required photon and the wavelength of
48. •• If the electron in a hydrogen atom is to make a transition from the first excited state to the fourth excited state, what frequency of light is needed? What type of light is this?
47. •• A hydrogen atom absorbs light of wavelength 486 nm. (a) How much energy did the atom absorb?(b) What are the values of the principal quantum numbers of the initial and final states of this transition?
46. •• The hydrogen spectrum has a series of lines called the Lyman series, which results from transitions to the ground state. What is the longest wavelength in this series, and in what region of the EM spectrum does it lie?
45. IE •• (a) For which of the following transitions in a hydrogen atom is the light of the longest wavelength emitted: (1) n = 5 to n = 3, (2) n = 6 to n = 2, or (3) n = 2 to n = 1? (b) Justify your answer mathematically.
44. •• A hydrogen atom in its ground state is excited to the n = 5 level. It then makes a transition directly to the n = 2 level before finally returning to the ground state.(a) What are the wavelengths of the emitted light?(b) Is any of the emitted light in the visible?
43. IE •• A hydrogen atom has an ionization energy of 13.6 eV. When it absorbs a photon with an energy greater than this energy, the electron will be emitted with some kinetic energy. (a) If the energy of such a photon is doubled, the kinetic energy of the emitted electron will(1) more than
42. •• What is the frequency of light that would excite the electron of a hydrogen atom (a) from a state with a principal quantum number of n = 2 to that with a principal quantum number of n = 5? (b) What about from n = 2 to n = ∞?
41. •• Find the energy required to excite a hydrogen electron from (a) the ground state to the first excited state and (b) the first excited state to the second excited state. (c) Classify the type of light needed to create each of the transitions.
40. • Find the binding energy of the hydrogen electron for states with the following principal quantum numbers:(a) n = 3, (b) n = 5, (c) n = 7.
39. • Some scientists study “large” atoms; that is, atoms with orbits that are almost large enough to be measured in our everyday units of measurement. For what excited state (give an approximate principal quantum number) of a hydrogen atom would the diameter of the orbit be on the order of
38. • Find the radius of the electron orbit in a hydrogen atom for states with the following principal quantum numbers: (a) n = 2, (b) n = 4, (c) n = 5.
37. • Find the energy of a hydrogen atom whose electron is in the (a) n = 2 state and (b) n = 3 state.
36. IE ••• The Compton effect can occur for scattering from any particle – for example, from a proton.(a) Compared with the Compton wavelength for an electron, the Compton wavelength for a proton is(1) longer, (2) the same, (3) shorter. Why? (b) What is the value of the Compton wavelength
35. •• X-rays of frequency 1.210 × 1018 Hz are scattered from electrons in an aluminum foil. The frequency of the scattered X-rays is 1.203 × 1018 Hz. (a) What is the scattering angle? (b) What is the recoiling speed of the electrons?
34. •• X-rays of wavelength 0.01520 nm are scattered from a carbon atom. The wavelength shift is measured to be 0.000326 nm. (a) What is the scattering angle? (b) How much energy, in eV, does each photon impart to each electron?
33. IE •• A photon with an energy of 5.0 KeV is scattered by a free electron. (a) The recoiling electron could have an energy of (1) zero, (2) less than 5.0 KeV, but not zero, (3) 5.0 keV. Explain. (b) If the wavelength of the scattered photon is 0.25 nm, what is the recoiling electron’s
32. •• X-rays with a wavelength of 0.0045 nm are used in a Compton scattering experiment. If they are scattered at 45°, what is the wavelength of the scattered radiation?
31. • A monochromatic beam of X-rays with a wavelength of 0.280 nm is scattered by a metal foil. If the scattered beam has a wavelength of 0.281 nm, what is the scattering angle?
30. • What is the change in wavelength when monochromatic X-rays are scattered by electrons through an angle of 30°?
29. • When the wavelength shift for Compton scattering from a free electron is a maximum, what is the scattering angle?
28. • What is half the maximum wavelength shift for Compton scattering from a free electron?
27. ••• When a material is illuminated with red light(λ = 700 nm) and then blue light (λ = 400 nm), it is found that the maximum kinetic energy of the photoelectrons resulting from the blue light is twice that from the red light. What is the work function of the material?
25. •• Blue light with a wavelength of 420 nm is incident on a certain material and causes the emission of photoelectrons with a maximum kinetic energy of 1.00 × 10−19 J. (a) What is the stopping voltage? (b) What is the material’s work function? (c) What is the stopping voltage if red
24. •• The work function of a material is 3.5 eV. If it is illuminated with monochromatic light (λ = 300 nm), what are (a) the stopping potential and (b) the cutoff frequency?
23. •• When light of wavelength of 250 nm is incident on a metal, the maximum speed of the photoelectrons is 4.0 × 105 m/s. What is the work function of this metal in eV?
22. •• The photoelectric effect threshold wavelength for a metal is 400 nm. Calculate the maximum speed of photoelectrons if the light used has a wavelength of(a) 300 nm, (b) 400 nm, and (c) 500 nm.
20. IE •• The work function of metal A is less than that of metal B. (a) The threshold wavelength for metal A is(1) shorter than, (2) the same as, (3) longer than that of metal B. Why? (b) If the threshold wavelength for metal B is 620 nm and the work function of metal A is twice that of metal
19. •• A metal with a work function of 2.40 eV is illuminated by a beam of monochromatic light. If the stopping potential is 2.50 V, what is the wavelength of that light?
18. •• Assume that a 100-W lightbulb gives off 2.50% of its energy as visible light. How many photons of visible light are given off in 1.00 min? (Use an average visible wavelength of 550 nm.)
17. • What is the longest wavelength light that can cause the emission of electrons from a metal that has a work function of 3.50 eV?
16. • The photoelectrons ejected from a material require a stopping voltage of 5.0 V. If the intensity of the light is tripled, what is the new stopping voltage?
15. • When light of a wavelength of 200 nm is incident on a material’s surface, the maximum kinetic energy of the photoelectrons is 6.0 × 10−19 J. What is the work function of that material?
14. • The work function of a material is 5.0 × 10−19 J. If light of wavelength of 300 nm is incident on the surface, what is the maximum kinetic energy of the photoelectrons ejected during the photoelectric effect?
13. • A source of UV light has a wavelength of 150 nm. How much energy does one of its photons have expressed in(a) joules and (b) electron-volts?
12. IE • (a) Compared with a quantum of red light(λ = 700 nm), a photon of violet light (λ = 400 nm)has (1) more, (2) the same amount of, (3) less energy.Why? (b) Determine the ratio of the photon energy associated with violet light to that of red light.
11. • Each photon in a beam of light has an energy of 6.50 × 10−19 J. What is the light’s wavelength? What type of light is this?
10. ••• The wavelength at which the Sun emits its most intense light is about 550 nm. Assuming the Sun radiates ideally, estimate (a) its surface temperature and (b) its total emitted power. [Hint: The Sun’s data can be found in the inside back cover of the book.]
9. •• The temperature of an object is 500°C. If the intensity of the emitted radiation, 2.0 W/m2, were due entirely to the most intense frequency component, how many quanta of radiation would be emitted per second per square meter?
8. IE •• The temperature of an object increases from 200°C to 400°C. (a) Will the frequency of the most intense spectral component emitted (1) increase, but not double; (2) double; (3) be reduced in half; or(4) decrease, but not by half? Why? (b) What is the change in the frequency of the
7. •• The minimum energy of an atomic oscillator in a blackbody is 3.5 × 10−19 J while emitting at that body’s most intense wavelength. What is the Celsius temperature of the object?
6. •• What is the minimum energy of a atomic oscillator in an object producing the radiation at λmax if the object’s temperature is 212°F?
5. •• A “red-hot” object emits thermal radiation with a maximum at frequency of 1.0 × 1014 Hz. What is the Celsius temperature of the object?
4. IE • (a) If you have a fever, is the wavelength of the radiation component of maximum intensity emitted by your body (1) greater, (2) the same, or (3) smaller as compared with its value when your temperature is normal? Why? (b) Assume that human skin has a temperature of 34°C. What is the
3. • What are the wavelength and frequency of the most intense radiation component emitted by a thermal radiator at a temperature of 0°C?
2. • Find the approximate temperature of a red star that emits light with a wavelength of maximum emission of 700 nm (deep red).
1. • A warm solid is at 27°C. What is the wavelength of the radiation at maximum intensity?
17. Explain the difference between spontaneous emission and stimulated emission.
16. In what sense is a laser an “amplifier” of energy? Explain why this concept does not violate conservation of energy.
15. “Pumping” is a necessary process in laser light production. Briefly describe what it is.
14. Very accurate measurements of the wavelengths emitted by a hydrogen atom indicate that they are all slightly longer than expected from the Bohr theory.Explain how conservation of linear momentum explains this. [Hint: Photons carry linear momentum and energy, and both need to be conserved.]
13. Does it take more or less energy to ionize a hydrogen atom if the electron is in an excited state than if it is in the ground state? Explain.
12. List the physical quantities of a hydrogen atom determined by the principal quantum number?
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