1cc. The number of lines in the Brackett series that have
wavelengths greater than the maximum wavelength in the Paschen series
isa) 1.b) 2.c) 4.d) 8.e) ∞. Get solution
1mcq. The wavelength of the fourth line in the Lyman series of the hydrogen spectrum isa) 80.0 nm.b) 85.0 nm.c) 90.2 nm.d) 94.9 nm. Get solution
2cc. How many wave functions are possible in the n = 5 shell?a) 9b) 14c) 16d) 21e) 25 Get solution
2mcq. The electron in a certain hydrogen atom is in the n = 5 state. Which of the following could be the EBμ and m values for the electron?a) 5, –3b) 4, –5c) 3, –2d) 4, –6 Get solution
3cc. Element 111 was discovered in 1994 and named roentgenium in 2004. It exists for only a few seconds before it decays. The electron configuration of roentgenium has not been determined yet. What would you predict it to be?a) [Xe]4f145d106s26p6b) [Rn]4f145d106s26p6c) [Rn]5f146d97s2d) [Xe]5f146d97s2 Get solution
3mcq. A muon has the same charge as an electron but a mass that is 207 times greater. The negatively charged muon can bind to a proton to form a new type of hydrogen atom. How does the binding energy, EBμ, of the muon in the ground state of a muonic hydrogen atom compare with the binding energy, EBe, of an electron in the ground state of a conventional hydrogen atom?a) |EBμ| ≈ |EBe|b) |EBμ| ≈ 100 |EBe|c) |EBμ| ≈ |EBe|/100d) |EBμ| ≈ 200 |EBe|e) |EBμ| ≈ |EBe|/200 Get solution
4cc. Element 118 was discovered in 2006 and exists for approximately 1 millisecond before it decays. Only a few atoms of this element have been produced. The ionization energy for element 118 has not been measured yet. What would you predict it to be?a) approximately 0 eV (the atom is unstable)b) approximately 2 eVc) approximately 5 eVd) approximately 10 eVe) approximately 20 eV Get solution
4mcq. Which of the following can be used to explain why you can’t walk through walls?a) Coulomb repulsive forceb) the strong nuclear forcec) gravityd) Pauli Exclusion Principlee) none of the above Get solution
5cc. In the X-ray spectrum in Figure 38.22, suppose one of the peaks corresponds to a K-shell transition and the other to an L-shell transition. Which of the following is true?a) The peak with the higher photon energy corresponds to the K-shell transition.b) The peak with the higher photon energy corresponds to the L-shell transition.c) Either peak could correspond to either transition, depending on the electrostatic potential difference applied in the X-ray tube.d) The peaks cannot be identified, without knowing what material was used for the anode.Figure 38.22 Sketch of an X-ray spectrum with a bremsstrahlung continuum plus sharp peaks due to electron transitions between atomic shells.... Get solution
5mcq. How many antinodes are there in a system with the quantum number n = 6?a) 12b) 6c) 3d) 5 Get solution
6cc. What is the population ratio of the 5s state relative to the 3p state at a temperature of 5000 K?a) 1.2·10–33b) 4.3·10–23c) 0.011d) 0.51e) 2.4 Get solution
6mcq. Transition metals can be defined as the elements in which the d subshells go from empty to full. How many transition metals are there in each period?a) 2b) 6c) 10d) 14 Get solution
7mcq. What is the shortest wavelength photon that can be emitted by singly ionized helium (He+)?a) 0.00 nmb) 22.8 nmc) 46.0 nmd) 91.0 nme) 365 nm Get solution
9cq. The common depiction of an atom, with electrons tracing elliptical orbits centered on the nucleus, is an icon of the Atomic Age. Given what you know of the physics of atoms, what’s wrong with this picture? Get solution
10cq. Given that the hydrogen atom has an infinite number of energy levels, why can’t a hydrogen atom in the ground state absorb all possible wavelengths of light? Get solution
12cq. What would happen to the energy levels of a hydrogen atom if the Coulomb force doubled in strength? What would happen to the sizes of atoms? Get solution
13cq. Which model of the hydrogen atom—the Bohr model or the quantum mechanical model—predicts that the electron spends more time near the nucleus? Get solution
14cq. For ... > 4, which values of ... and m correspond to wave functions that have their maximum probability in the xy-plane? Get solution
15cq. Hund’s rule, a component of the Aufbauprinzip (construction principle), states that as one moves across the periodic table, with increasing atomic number, the available subshells are filled successively with one electron in each orbital, their spins all parallel; only when all orbitals in a subshell contain one electron are second electrons, with spins opposite to the first, placed in the orbitals. Explain why the ground-state electron configurations of successive elements should follow this pattern. Get solution
16cq. The energy-level diagram for a four-level laser is presented in the figure, which includes information about the relative times required for the various transitions involved in the operation of such a laser. Explain why the nonradiative transitions have to be fast (higher rate of transitions per second) compared to the slower laser transition.... Get solution
17cq. The hydrogen atom wave function ψ200 is zero when r = 2a0. Does this mean that the electron in that state can never be observed at a distance of 2a0 from the nucleus or that the electron can never be observed passing through the spherical surface defined by r = 2a0? Is there a difference between those two descriptions? Get solution
18cq. A 10-eV electron collides with (but is not captured by) a hydrogen atom in its ground state. Calculate the wavelengths of all photons that might be emitted. Get solution
19. What is the shortest wavelength of light that a hydrogen atom will emit? Get solution
20. Determine the wavelength of the second line in the Paschen series. Get solution
21. The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen atom to/from the n = 5 energy level from/to higher energy levels. What are the shortest and longest wavelengths of lines in the Pfund series? Are any of these in the visible portion of the electromagnetic spectrum? Get solution
22. An electron in the second excited state of a hydrogen atom jumps to the ground state. What are the possible colors and wavelengths of the light emitted as a result of the jump? Get solution
23. Calculate the energy of the fifth excited state of a hydrogen atom. Get solution
24. Hydrogen atoms are bombarded with 13.1-eV electrons. Determine the shortest wavelength of light the atoms will emit. Get solution
25. The Rydberg constant with a finite mass of the nucleus is given by Rmodified = RH/(1+m/M), where m and M are the masses of an electron and a nucleus, respectively. Calculate the modified value of the Rydberg constant fora) a hydrogen atom, andb) a positronium (in a positronium, the “nucleus” is a positron, which has the same mass as an electron). Get solution
26. A muon is a particle very similar to an electron. It has the same charge but its mass is 1.88·10–28 kg.a) Calculate the reduced mass for a hydrogen-like muonic atom consisting of a single proton and a muon.b) Calculate the ionization energy for such an atom, assuming that the muon is initially in its ground state. Get solution
27. An excited hydrogen atom emits a photon with an energy of 1.133 eV. What were the initial and final states of the hydrogen atom before and after emitting the photon? Get solution
28. An 8.00-eV photon is absorbed by an electron in the n = 2 state of a hydrogen atom. Calculate the final speed of the electron. Get solution
29. Assume that Bohr’s quantized energy levels apply to planetary orbits. Derive an equation similar to equation 38.6 that gives the allowed radii of those orbits, and estimate the principal quantum number for the Earth’s orbit. Get solution
30. Prove that the period of an electron in the nth Bohr orbit is given by T = n3/(2cRH), with n = 1,2,3, ... . Get solution
31. What are the largest and smallest possible values for the angular momentum L of an electron in the n = 5 shell? Get solution
32. Electrons with the same value of the quantum number n are said to occupy the same electron shell, K, L, M, N, or higher. Calculate the maximum allowed number of electrons for thea) κ shell,b) L shell, andc) M shell. Get solution
33. What is the angle between the total angular momentum vector and the z-axis for a hydrogen atom in the stationary state (3, 2, 1)? Get solution
34. A hydrogen atom is in its fifth excited state, with principal quantum number n = 6. The atom emits a photon with a wavelength of 410 nm. Determine the maximum possible orbital angular momentum of the electron after emission. Get solution
35. The radial wave function for hydrogen in the 1s state is given by R1s = A1e–r/a0 where the normalization constant, A1, was found in Example 38.2.a) Calculate the probability density at r = a0/2.b) The 1s wave function has a maximum at r = 0 but the 1s radial probability density peaks at r = a0. Explain this difference.Example 38.2 Normalization of the Hydrogen Wave Function... Get solution
36. For the wave function ψ100(r) in equation 38.30, find the value of r for which the function P(r) = 4πr2|ψ100(r)|2 is a maximum. Get solution
37. An electron in a hydrogen atom is in the 2s state. Calculate the probability of finding the electron within a Bohr radius (a0 = 0.05295 nm) of the proton. The 2s wave function for hydrogen is...Evaluating the integral is a bit tedious, so you may want to consider using a program such as Mathcad or Mathematica or finding the integral online at http://integrals.wolfram.com/index.jsp. Get solution
38. Calculate the energy needed to change a single ionized helium atom into a double ionized helium atom (that is, change it from He+ into He2+). Compare it to the energy needed to ionize the hydrogen atom. Assume that both atoms are in their ground state. Get solution
39. A He+ ion consists of a nucleus (containing two protons and two neutrons) and a single electron. Find the Bohr radius for this system. Get solution
40. Find the wavelengths of the three lowest-energy lines in the Paschen series of the spectrum of the He+ ion. Get solution
41. The binding energy of an extra electron added when As atoms are used to dope a Si crystal may be approximately calculated by considering the Bohr model of a hydrogen atom.a) Express the ground energy of the hydrogen-like atoms in terms of the dielectric constant, the effective mass of an extra electron, and the ground-state energy of a hydrogen atom.b) Calculate the binding energy of the extra electron in a Si crystal. The dielectric constant of Si is about 10.0, and the effective mass of extra electrons in a Si crystal is about 20.0% of that of free electrons. Get solution
42. What is the wavelength of the first visible line in the spectrum of doubly ionized lithium? Begin by writing the formula for the energy levels of the electron in doubly ionized lithium—then consider energy-level differences that give energies in the appropriate (visible) range. Express the answer as “the transition from state n to state n' produces the first visible line, with wavelength X.” Get solution
43. Following the steps used in the text for the hydrogen atom, apply the Bohr model of the atom to derive an expression fora) the radius of the nth orbit,b) the speed of the electron in the nth orbit, andc) the energy levels in a hydrogen-like ionized atom with charge number Z that has lost all of its electrons except for one. Compare the results with the corresponding ones for the hydrogen atom. Get solution
44. Apply the results of Problem 38.43 to determine the maximum and minimum wavelengths of the spectral lines in the Lyman, Balmer, and Paschen series for a singly ionized helium atom (He+). Get solution
45. Consider an electron in a hydrogen atom. If you are able to excite the electron from the n = 1 shell to the n = 2 shell with laser light of a given wavelength, what wavelength of laser light will excite that electron again from the n = 2 to the n = 3 shell? Explain. Get solution
46. A low-power laser has a power of 0.50 mW and a beam diameter of 3.0 mm.a) Calculate the average light intensity of the laser beam.b) Compare the value from part (a) to the intensity of light from a 100-W light bulb viewed from 2.0 m. Get solution
47. A ruby in a laser consists mostly of alumina (Al2O3) and a small amount of chromium ions, responsible for its red color. A 3.00-kW ruby laser emits light pulses of duration 10.0 ns and wavelength 694 nm.a) What is the energy of each of the photons in a pulse?b) Determine the number of chromium atoms undergoing stimulated emission to produce a pulse. Get solution
48. You have both a green, 543-nm, 5.00-mW laser and a red, 633-nm, 4.00-mW laser. Which one will produce more photons per second, and why? Get solution
49. What is the shortest possible wavelength in the Lyman series in hydrogen? Get solution
50. How much energy is required to ionize a hydrogen atom when the electron is in the nth level? Get solution
51. By what percentage is the mass of the electron changed by using the reduced mass for the hydrogen atom? What would the reduced mass be if the proton had the same mass as the electron? Get solution
53. Section 38.2 established that an electron, if observed in the ground state of hydrogen, is expected to have a speed of 0.0073c. For what nuclear charge Z would an innermost electron have a speed of approximately 0.500c, when considered classically? Get solution
54. A collection of hydrogen atoms have all been placed into the n = 4 excited state. What wavelengths of photons will be emitted by the hydrogen atoms as they transition back to the ground state? Get solution
55. Consider a muonic hydrogen atom, in which the electron is replaced by a muon of mass 105.66 MeV/c2 that orbits the proton. What are the first three energy levels of the muon in this type of atom? Get solution
56. What is the ionization energy of a hydrogen atom excited to the n = 2 state? Get solution
57. He+ is a helium atom with one electron missing. Treating this ion like a hydrogen atom, what are its first three energy levels? Get solution
58. What is the energy of a transition capable of producing light of wavelength 10.6 μm? (This is the wavelength of light associated with a commonly available infrared laser.) Get solution
59. What is the energy of the orbiting electron in a hydrogen atom with a radial quantum number of 45? Get solution
60. Find the energy difference between the ground state of hydrogen and the ground state of deuterium (hydrogen with an extra neutron in the nucleus). Get solution
61. An excited hydrogen atom, whose electron is in the n = 4 state, is motionless. When the electron drops to the ground state, does it set the atom in motion? If so, with what speed? Get solution
62. The radius of the n = 1 orbit in the hydrogen atom is a0 = 0.053 nm.a) Compute the radius of the n = 6 orbit. How many times larger is this than the n = 1 radius?b) If an electron in the n = 6 orbit drops to the n = 1 orbit (ground state), what are the frequency and the wavelength of the emitted radiation? What kind of radiation is emitted (visible, infrared, etc.)?c) How would your answer to part (a) change if the atom was a singly ionized helium atom (He+) instead? Get solution
63. An electron in a hydrogen atom is in the ground state (1s). Calculate the probability of finding the electron within a Bohr radius (a0 = 0.05295 nm) of the proton. The ground-state wave function for hydrogen is... Get solution
65. A beam of electrons with a speed of 676.01 km/s is incident on a system of excited hydrogen atoms. If an electron hits a hydrogen atom in the n = 3 state, what is the highest level n, to which this hydrogen atom can be excited in this collision? (In the collision of the electron with the hydrogen atom, you may neglect the recoil energy of the hydrogen atom, because it has a mass much greater than that of the electron.) Get solution
66. A beam of electrons with a speed of 378.92 km/s is incident on a system of excited hydrogen atoms. If an electron hits a hydrogen atom and excites it to the n = 10 state, what is the lowest level n in which this hydrogen atom could have been before the collision? (In the collision of the electron with the hydrogen atom, you may neglect the recoil energy of the hydrogen atom, because it has a mass much greater than that of the electron.)... Get solution
67. Find the ratio of the number of hydrogen atoms in the n = 3 state to the number of hydrogen atoms in the n = 7 state at a temperature of 528.3 K. Get solution
68. At what temperature is the ratio of the number of hydrogen atoms in the n = 3 state to the number of hydrogen atoms in the n = 8 state equal to 5.1383·105? Get solution
1mcq. The wavelength of the fourth line in the Lyman series of the hydrogen spectrum isa) 80.0 nm.b) 85.0 nm.c) 90.2 nm.d) 94.9 nm. Get solution
2cc. How many wave functions are possible in the n = 5 shell?a) 9b) 14c) 16d) 21e) 25 Get solution
2mcq. The electron in a certain hydrogen atom is in the n = 5 state. Which of the following could be the EBμ and m values for the electron?a) 5, –3b) 4, –5c) 3, –2d) 4, –6 Get solution
3cc. Element 111 was discovered in 1994 and named roentgenium in 2004. It exists for only a few seconds before it decays. The electron configuration of roentgenium has not been determined yet. What would you predict it to be?a) [Xe]4f145d106s26p6b) [Rn]4f145d106s26p6c) [Rn]5f146d97s2d) [Xe]5f146d97s2 Get solution
3mcq. A muon has the same charge as an electron but a mass that is 207 times greater. The negatively charged muon can bind to a proton to form a new type of hydrogen atom. How does the binding energy, EBμ, of the muon in the ground state of a muonic hydrogen atom compare with the binding energy, EBe, of an electron in the ground state of a conventional hydrogen atom?a) |EBμ| ≈ |EBe|b) |EBμ| ≈ 100 |EBe|c) |EBμ| ≈ |EBe|/100d) |EBμ| ≈ 200 |EBe|e) |EBμ| ≈ |EBe|/200 Get solution
4cc. Element 118 was discovered in 2006 and exists for approximately 1 millisecond before it decays. Only a few atoms of this element have been produced. The ionization energy for element 118 has not been measured yet. What would you predict it to be?a) approximately 0 eV (the atom is unstable)b) approximately 2 eVc) approximately 5 eVd) approximately 10 eVe) approximately 20 eV Get solution
4mcq. Which of the following can be used to explain why you can’t walk through walls?a) Coulomb repulsive forceb) the strong nuclear forcec) gravityd) Pauli Exclusion Principlee) none of the above Get solution
5cc. In the X-ray spectrum in Figure 38.22, suppose one of the peaks corresponds to a K-shell transition and the other to an L-shell transition. Which of the following is true?a) The peak with the higher photon energy corresponds to the K-shell transition.b) The peak with the higher photon energy corresponds to the L-shell transition.c) Either peak could correspond to either transition, depending on the electrostatic potential difference applied in the X-ray tube.d) The peaks cannot be identified, without knowing what material was used for the anode.Figure 38.22 Sketch of an X-ray spectrum with a bremsstrahlung continuum plus sharp peaks due to electron transitions between atomic shells.... Get solution
5mcq. How many antinodes are there in a system with the quantum number n = 6?a) 12b) 6c) 3d) 5 Get solution
6cc. What is the population ratio of the 5s state relative to the 3p state at a temperature of 5000 K?a) 1.2·10–33b) 4.3·10–23c) 0.011d) 0.51e) 2.4 Get solution
6mcq. Transition metals can be defined as the elements in which the d subshells go from empty to full. How many transition metals are there in each period?a) 2b) 6c) 10d) 14 Get solution
7mcq. What is the shortest wavelength photon that can be emitted by singly ionized helium (He+)?a) 0.00 nmb) 22.8 nmc) 46.0 nmd) 91.0 nme) 365 nm Get solution
9cq. The common depiction of an atom, with electrons tracing elliptical orbits centered on the nucleus, is an icon of the Atomic Age. Given what you know of the physics of atoms, what’s wrong with this picture? Get solution
10cq. Given that the hydrogen atom has an infinite number of energy levels, why can’t a hydrogen atom in the ground state absorb all possible wavelengths of light? Get solution
12cq. What would happen to the energy levels of a hydrogen atom if the Coulomb force doubled in strength? What would happen to the sizes of atoms? Get solution
13cq. Which model of the hydrogen atom—the Bohr model or the quantum mechanical model—predicts that the electron spends more time near the nucleus? Get solution
14cq. For ... > 4, which values of ... and m correspond to wave functions that have their maximum probability in the xy-plane? Get solution
15cq. Hund’s rule, a component of the Aufbauprinzip (construction principle), states that as one moves across the periodic table, with increasing atomic number, the available subshells are filled successively with one electron in each orbital, their spins all parallel; only when all orbitals in a subshell contain one electron are second electrons, with spins opposite to the first, placed in the orbitals. Explain why the ground-state electron configurations of successive elements should follow this pattern. Get solution
16cq. The energy-level diagram for a four-level laser is presented in the figure, which includes information about the relative times required for the various transitions involved in the operation of such a laser. Explain why the nonradiative transitions have to be fast (higher rate of transitions per second) compared to the slower laser transition.... Get solution
17cq. The hydrogen atom wave function ψ200 is zero when r = 2a0. Does this mean that the electron in that state can never be observed at a distance of 2a0 from the nucleus or that the electron can never be observed passing through the spherical surface defined by r = 2a0? Is there a difference between those two descriptions? Get solution
18cq. A 10-eV electron collides with (but is not captured by) a hydrogen atom in its ground state. Calculate the wavelengths of all photons that might be emitted. Get solution
19. What is the shortest wavelength of light that a hydrogen atom will emit? Get solution
20. Determine the wavelength of the second line in the Paschen series. Get solution
21. The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen atom to/from the n = 5 energy level from/to higher energy levels. What are the shortest and longest wavelengths of lines in the Pfund series? Are any of these in the visible portion of the electromagnetic spectrum? Get solution
22. An electron in the second excited state of a hydrogen atom jumps to the ground state. What are the possible colors and wavelengths of the light emitted as a result of the jump? Get solution
23. Calculate the energy of the fifth excited state of a hydrogen atom. Get solution
24. Hydrogen atoms are bombarded with 13.1-eV electrons. Determine the shortest wavelength of light the atoms will emit. Get solution
25. The Rydberg constant with a finite mass of the nucleus is given by Rmodified = RH/(1+m/M), where m and M are the masses of an electron and a nucleus, respectively. Calculate the modified value of the Rydberg constant fora) a hydrogen atom, andb) a positronium (in a positronium, the “nucleus” is a positron, which has the same mass as an electron). Get solution
26. A muon is a particle very similar to an electron. It has the same charge but its mass is 1.88·10–28 kg.a) Calculate the reduced mass for a hydrogen-like muonic atom consisting of a single proton and a muon.b) Calculate the ionization energy for such an atom, assuming that the muon is initially in its ground state. Get solution
27. An excited hydrogen atom emits a photon with an energy of 1.133 eV. What were the initial and final states of the hydrogen atom before and after emitting the photon? Get solution
28. An 8.00-eV photon is absorbed by an electron in the n = 2 state of a hydrogen atom. Calculate the final speed of the electron. Get solution
29. Assume that Bohr’s quantized energy levels apply to planetary orbits. Derive an equation similar to equation 38.6 that gives the allowed radii of those orbits, and estimate the principal quantum number for the Earth’s orbit. Get solution
30. Prove that the period of an electron in the nth Bohr orbit is given by T = n3/(2cRH), with n = 1,2,3, ... . Get solution
31. What are the largest and smallest possible values for the angular momentum L of an electron in the n = 5 shell? Get solution
32. Electrons with the same value of the quantum number n are said to occupy the same electron shell, K, L, M, N, or higher. Calculate the maximum allowed number of electrons for thea) κ shell,b) L shell, andc) M shell. Get solution
33. What is the angle between the total angular momentum vector and the z-axis for a hydrogen atom in the stationary state (3, 2, 1)? Get solution
34. A hydrogen atom is in its fifth excited state, with principal quantum number n = 6. The atom emits a photon with a wavelength of 410 nm. Determine the maximum possible orbital angular momentum of the electron after emission. Get solution
35. The radial wave function for hydrogen in the 1s state is given by R1s = A1e–r/a0 where the normalization constant, A1, was found in Example 38.2.a) Calculate the probability density at r = a0/2.b) The 1s wave function has a maximum at r = 0 but the 1s radial probability density peaks at r = a0. Explain this difference.Example 38.2 Normalization of the Hydrogen Wave Function... Get solution
36. For the wave function ψ100(r) in equation 38.30, find the value of r for which the function P(r) = 4πr2|ψ100(r)|2 is a maximum. Get solution
37. An electron in a hydrogen atom is in the 2s state. Calculate the probability of finding the electron within a Bohr radius (a0 = 0.05295 nm) of the proton. The 2s wave function for hydrogen is...Evaluating the integral is a bit tedious, so you may want to consider using a program such as Mathcad or Mathematica or finding the integral online at http://integrals.wolfram.com/index.jsp. Get solution
38. Calculate the energy needed to change a single ionized helium atom into a double ionized helium atom (that is, change it from He+ into He2+). Compare it to the energy needed to ionize the hydrogen atom. Assume that both atoms are in their ground state. Get solution
39. A He+ ion consists of a nucleus (containing two protons and two neutrons) and a single electron. Find the Bohr radius for this system. Get solution
40. Find the wavelengths of the three lowest-energy lines in the Paschen series of the spectrum of the He+ ion. Get solution
41. The binding energy of an extra electron added when As atoms are used to dope a Si crystal may be approximately calculated by considering the Bohr model of a hydrogen atom.a) Express the ground energy of the hydrogen-like atoms in terms of the dielectric constant, the effective mass of an extra electron, and the ground-state energy of a hydrogen atom.b) Calculate the binding energy of the extra electron in a Si crystal. The dielectric constant of Si is about 10.0, and the effective mass of extra electrons in a Si crystal is about 20.0% of that of free electrons. Get solution
42. What is the wavelength of the first visible line in the spectrum of doubly ionized lithium? Begin by writing the formula for the energy levels of the electron in doubly ionized lithium—then consider energy-level differences that give energies in the appropriate (visible) range. Express the answer as “the transition from state n to state n' produces the first visible line, with wavelength X.” Get solution
43. Following the steps used in the text for the hydrogen atom, apply the Bohr model of the atom to derive an expression fora) the radius of the nth orbit,b) the speed of the electron in the nth orbit, andc) the energy levels in a hydrogen-like ionized atom with charge number Z that has lost all of its electrons except for one. Compare the results with the corresponding ones for the hydrogen atom. Get solution
44. Apply the results of Problem 38.43 to determine the maximum and minimum wavelengths of the spectral lines in the Lyman, Balmer, and Paschen series for a singly ionized helium atom (He+). Get solution
45. Consider an electron in a hydrogen atom. If you are able to excite the electron from the n = 1 shell to the n = 2 shell with laser light of a given wavelength, what wavelength of laser light will excite that electron again from the n = 2 to the n = 3 shell? Explain. Get solution
46. A low-power laser has a power of 0.50 mW and a beam diameter of 3.0 mm.a) Calculate the average light intensity of the laser beam.b) Compare the value from part (a) to the intensity of light from a 100-W light bulb viewed from 2.0 m. Get solution
47. A ruby in a laser consists mostly of alumina (Al2O3) and a small amount of chromium ions, responsible for its red color. A 3.00-kW ruby laser emits light pulses of duration 10.0 ns and wavelength 694 nm.a) What is the energy of each of the photons in a pulse?b) Determine the number of chromium atoms undergoing stimulated emission to produce a pulse. Get solution
48. You have both a green, 543-nm, 5.00-mW laser and a red, 633-nm, 4.00-mW laser. Which one will produce more photons per second, and why? Get solution
49. What is the shortest possible wavelength in the Lyman series in hydrogen? Get solution
50. How much energy is required to ionize a hydrogen atom when the electron is in the nth level? Get solution
51. By what percentage is the mass of the electron changed by using the reduced mass for the hydrogen atom? What would the reduced mass be if the proton had the same mass as the electron? Get solution
53. Section 38.2 established that an electron, if observed in the ground state of hydrogen, is expected to have a speed of 0.0073c. For what nuclear charge Z would an innermost electron have a speed of approximately 0.500c, when considered classically? Get solution
54. A collection of hydrogen atoms have all been placed into the n = 4 excited state. What wavelengths of photons will be emitted by the hydrogen atoms as they transition back to the ground state? Get solution
55. Consider a muonic hydrogen atom, in which the electron is replaced by a muon of mass 105.66 MeV/c2 that orbits the proton. What are the first three energy levels of the muon in this type of atom? Get solution
56. What is the ionization energy of a hydrogen atom excited to the n = 2 state? Get solution
57. He+ is a helium atom with one electron missing. Treating this ion like a hydrogen atom, what are its first three energy levels? Get solution
58. What is the energy of a transition capable of producing light of wavelength 10.6 μm? (This is the wavelength of light associated with a commonly available infrared laser.) Get solution
59. What is the energy of the orbiting electron in a hydrogen atom with a radial quantum number of 45? Get solution
60. Find the energy difference between the ground state of hydrogen and the ground state of deuterium (hydrogen with an extra neutron in the nucleus). Get solution
61. An excited hydrogen atom, whose electron is in the n = 4 state, is motionless. When the electron drops to the ground state, does it set the atom in motion? If so, with what speed? Get solution
62. The radius of the n = 1 orbit in the hydrogen atom is a0 = 0.053 nm.a) Compute the radius of the n = 6 orbit. How many times larger is this than the n = 1 radius?b) If an electron in the n = 6 orbit drops to the n = 1 orbit (ground state), what are the frequency and the wavelength of the emitted radiation? What kind of radiation is emitted (visible, infrared, etc.)?c) How would your answer to part (a) change if the atom was a singly ionized helium atom (He+) instead? Get solution
63. An electron in a hydrogen atom is in the ground state (1s). Calculate the probability of finding the electron within a Bohr radius (a0 = 0.05295 nm) of the proton. The ground-state wave function for hydrogen is... Get solution
65. A beam of electrons with a speed of 676.01 km/s is incident on a system of excited hydrogen atoms. If an electron hits a hydrogen atom in the n = 3 state, what is the highest level n, to which this hydrogen atom can be excited in this collision? (In the collision of the electron with the hydrogen atom, you may neglect the recoil energy of the hydrogen atom, because it has a mass much greater than that of the electron.) Get solution
66. A beam of electrons with a speed of 378.92 km/s is incident on a system of excited hydrogen atoms. If an electron hits a hydrogen atom and excites it to the n = 10 state, what is the lowest level n in which this hydrogen atom could have been before the collision? (In the collision of the electron with the hydrogen atom, you may neglect the recoil energy of the hydrogen atom, because it has a mass much greater than that of the electron.)... Get solution
67. Find the ratio of the number of hydrogen atoms in the n = 3 state to the number of hydrogen atoms in the n = 7 state at a temperature of 528.3 K. Get solution
68. At what temperature is the ratio of the number of hydrogen atoms in the n = 3 state to the number of hydrogen atoms in the n = 8 state equal to 5.1383·105? Get solution
