A tungsten target is struck by electrons that have been accelerated from rest through a 40.0 - kV potential difference. Find the shortest wavelength of the radiation emitted.
> White light is incident on a diffraction grating with 475 lines/ mm. (a) Calculate the angle θr2 to the second - order maximum for a wavelength of 675 nm. (b) Calculate the wavelength of light with a third - order maximum at the same angle θr2.
> Light from an argon laser strikes a diffraction grating that has 5310 grooves/cm. The central and first - order principal maxima are separated by 0.488 m on a wall 1.72 m from the grating. Determine the wavelength of the laser light.
> White light is spread out into its spectral components by a diffraction grating. If the grating has 2.00 x 103 lines/cm, at what angle does red light of wavelength 6.40 x 102 nm appear in the first - order spectrum?
> A helium–neon laser (λ = 632.8 nm) is used to calibrate a diffraction grating. If the first - order maximum occurs at 20.5°, what is the spacing between adjacent grooves in the grating?
> Consider an array of parallel wires with uniform spacing of 1.30 cm between centers. In air at 20.0°C, ultrasound with a frequency of 37.2 kHz from a distant source is incident perpendicular to the array. (Take the speed of sound to be 343 m/s.) (a) Find
> The hydrogen spectrum has a red line at 656 nm and a violet line at 434 nm. What angular separations between these two spectral lines can be obtained with a diffraction grating that has 4.50 x 103 lines/cm?
> Intense white light is incident on a diffraction grating that has 600. lines/mm. (a) What is the highest order in which the complete visible spectrum can be seen with this grating? (b) What is the angular separation between the violet edge (400. nm) and
> Light of wavelength 620. nm falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 15.0° from the central maximum. Find the separation between the slits.
> Three discrete spectral lines occur at angles of 10.1°, 13.7°, and 14.8°, respectively, in the first - order spectrum of a diffraction - grating spectrometer. (a) If the grating has 3660 slits/cm, what are the wavelengths of the light? (b) At what angles
> The second - order dark fringe in a single - slit diffraction pattern is 1.40 mm from the center of the central maximum. Assuming the screen is 85.0 cm from a slit of width 0.800 mm and assuming monochromatic incident light, calculate the wavelength of t
> A slit of width 0.50 mm is illuminated with light of wavelength 5.00 x 102 nm, and a screen is placed 1.20 x 102 cm in front of the slit. Find the widths of the first and second maxima on each side of the central maximum.
> A screen is placed 50.0 cm from a single slit that is illuminated with light of wavelength 6.80 x 102 nm. If the distance between the first and third minima in the diffraction pattern is 3.00 mm, what is the width of the slit?
> A beam of monochromatic light is diffracted by a slit of width 0.600 mm. The diffraction pattern forms on a wall 1.30 m beyond the slit. The width of the central maximum is 2.00 mm. Calculate the wavelength of the light.
> Microwaves of wavelength 5.00 cm enter a long, narrow window in a building that is otherwise essentially opaque to the incoming waves. If the window is 36.0 cm wide, what is the distance from the central maximum to the first - order minimum along a wall
> Light of wavelength 587.5 nm illuminates a slit of width 0.75 mm. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.85 mm from the central maximum? (b) Calculate the width of the centr
> A student and his lab partner create a single slit by carefully aligning two razor blades to a separation of 0.500 mm. When a helium–neon laser at 633 nm illuminates the slit, a diffraction pattern is observed on a screen 1.25 m beyond the slit. Calculat
> Light of wavelength 5.40 x 102 nm passes through a slit of width 0.200 mm. (a) Find the width of the central maximum on a screen located 1.50 m from the slit. (b) Determine the width of the first - order bright fringe.
> A lens made of glass (ng = 1.52) is coated with a thin film of MgF2 (ns = 1.38) of thickness t. Visible light is incident normally on the coated lens as in Figure P24.30. (a) For what minimum value of t will the reflected light of wavelength 5.40 x 102 n
> Light at 633 nm from a helium–neon laser shines on a pair of parallel slits separated by 1.45 x 10-5 m and an interference pattern is observed on a screen 2.00 m from the plane of the slits. (a) Find the angle from the central maximum to the first bright
> A thin film of glycerin (n = 1.473) of thickness 524 nm with air on both sides is illuminated with white light at near normal incidence. What wavelengths will be strongly reflected in the range 300 nm to 700 nm?
> Nonreflective coatings on camera lenses reduce the loss of light at the surfaces of multi-lens systems and prevent internal reflections that might mar the image. Find the minimum thickness of a layer of magnesium fluoride (n = 1.38) on flint glass (n = 1
> A thin film of oil (n = 1.45) of thickness 425 nm with air on both sides is illuminated with white light at normal incidence. Determine (a) The most strongly and (b) The most weakly reflected wavelengths in the range 400 nm to 600 nm.
> A plano - convex lens with radius of curvature R = 3.0 m is in contact with a flat plate of glass. A light source and the observer’s eye are both close to the normal, as shown in Figure 24.10a. The radius of the 50th bright Newtonâ
> An investigator finds a fiber at a crime scene that he wishes to use as evidence against a suspect. He gives the fiber to a technician to test the properties of the fiber. To measure the diameter of the fiber, the technician places it between two flat gl
> A spacer is cut from a playing card of thickness 2.90 x 10-4 m and used to separate one end of two rectangular, optically flat, 3.00 - cm long glass plates with n = 1.55, as in Figure P24.24. Laser light at 594 nm shines straight down on the top plate. T
> Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength 656.3 nm, called the Hα line. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glas
> An oil film (n = 1.45) floating on water is illuminated by white light at normal incidence. The film is 2.80 x 102 nm thick. Find (a) The wavelength and color of the light in the visible spectrum most strongly reflected and (b) The wavelength and color o
> A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 3.00 cm and the index of refraction of the polymer is n = 1.50, how thick would you make the coating? Assu
> Krypton (atomic number 36) has how many electrons in its next - to - outer shell (n = 3)? (a) 2 (b) 4 (c) 8 (d) 18
> When the principal quantum number is n = 5, how many different values of (a) ℓ and (b) mℓ are possible? (c) How many states have distinct pairs of values of ℓ and mℓ?
> Consider a hydrogen atom and a singly ionized helium atom. Which atom has the lower ground state energy? (a) Hydrogen (b) Helium (c) The ground state energy is the same for both.
> The “size” of the atom in Rutherford’s model is about 1.0 x 10-10 m. (a) Determine the attractive electrostatic force between an electron and a proton separated by this distance. (b) Determine (in eV) the electrostatic potential energy of the atom.
> A transparent oil with index of refraction 1.29 spills on the surface of water (index of refraction 1.33), producing a maximum of reflection with normally incident orange light (wavelength 6.00 x 102 nm in air). Assuming the maximum occurs in the first o
> In a Young’s double - slit experiment, a set of parallel slits with a separation of 0.100 mm is illuminated by light having a wavelength of 589 nm, and the interference pattern is observed on a screen 4.00 m from the slits. (a) What is the difference in
> The wavelengths of the Paschen series for hydrogen are given by 1/λ = RH(1/32 - 1/n2) n = 4, 5, 6, . . . . . (a) Calculate the wavelengths of the first three lines in this series. (b) Identify the region of the electromagnetic spectrum in which these lin
> The wavelengths of the Lyman series for hydrogen are given by 1/λ = RH(1 - 1/n2) n = 2, 3, 4, . . . . . (a) Calculate the wavelengths of the first three lines in this series. (b) Identify the region of the electromagnetic spectrum in which these lines ap
> Suppose the ionization energy of an atom is 4.100 eV. In this same atom, we observe emission lines that have wavelengths of 310.0 nm, 400.0 nm, and 1378 nm. Use this information to construct the energy level diagram with the least number of levels. Assum
> Use Bohr’s model of the hydrogen atom to show that when the atom makes a transition from the state n to the state n - 1, the frequency of the emitted light is given by
> An electron has a de Broglie wavelength equal to the diameter of a hydrogen atom in its ground state. (a) What is the kinetic energy of the electron? (b) How does this energy compare with the magnitude of the ground - state energy of the hydrogen atom?
> A laser used in eye surgery emits a 3.00 - mJ pulse in 1.00 ns, focused to a spot 30.0 μm in diameter on the retina. (a) Find (in SI units) the power per unit area at the retina. (This quantity is called the irradiance.) (b) What energy is delivered per
> As the Earth moves around the Sun, its orbits are quantized. (a) Follow the steps of Bohr’s analysis of the hydrogen atom to show that the allowed radii of the Earth’s orbit are given by where n is an integer quantum
> An electron in chromium moves from the n 5 2 state to the n 5 1 state without emitting a photon. Instead, the excess energy is transferred to an outer electron (one in the n 5 4 state), which is then ejected by the atom. In this Auger (pronounced “ohjay”
> A pulsed ruby laser emits light at 694.3 nm. For a 14.0 - ps pulse containing 3.00 J of energy, find (a) The physical length of the pulse as it travels through space and (b) The number of photons in it. (c) If the beam has a circular cross section 0.600
> (a) How much energy is required to cause an electron in hydrogen to move from the n = 1 state to the n = 2 state? (b) If the electrons gain this energy by collision between hydrogen atoms in a high - temperature gas, find the minimum temperature of the h
> A thin film of glass (n = 1.52) of thickness 0.420 µm is viewed under white light at near normal incidence. What wavelength of visible light is most strongly reflected by the film when surrounded by air?
> In a hydrogen atom, what is the principal quantum number of the electron orbit with a radius closest to 1.0 μm?
> The K series of the discrete spectrum of tungsten contains wavelengths of 0.0185 nm, 0.0209 nm, and 0.0215 nm. The K - shell ionization energy is 69.5 keV. Determine the ionization energies of the L, M, and N shells.
> When an electron drops from the M shell (n = 3) to a vacancy in the K shell (n = 1), the measured wavelength of the emitted x - ray is found to be 0.101 nm. Identify the element.
> A bismuth target is struck by electrons, and x - rays are emitted. Estimate (a) The M - to L - shell transitional energy for bismuth and (b) The wavelength of the x - ray emitted when an electron falls from the M shell to the L shell.
> Zirconium (Z = 40) has two electrons in an incomplete d subshell. (a) What are the values of n and ℓ for each electron? (b) What are all possible values of mℓ and ms? (c) What is the electron configuration in the ground state of zirconium?
> Two electrons in the same atom have n = 3 and ℓ = 1. (a) List the quantum numbers for the possible states of the atom. (b) How many states would be possible if the exclusion principle did not apply to the atom?
> A certain element has its outermost electron in a 3p subshell. It has valence +3 because it has three more electrons than a certain noble gas. What element is it?
> (a) Write out the electronic configuration of the ground state for nitrogen (Z = 7). (b) Write out the values for the possible set of quantum numbers n, ℓ, mℓ, and ms for the electrons in nitrogen.
> Apply the Pauli exclusion principle to determine the number of electrons that could occupy the quantum states described by (a) n = 3, ℓ = 2, mℓ = -1 and (b) n = 3, ℓ = 1, and (c) n = 4.
> A thin film of oil (n = 1.25) is located on smooth, wet pavement. When viewed from a direction perpendicular to the pavement, the film reflects most strongly red light at 6.40 x 102 nm and reflects no green light at 512 nm. (a) What is the minimum thickn
> A hydrogen atom is immersed in a magnetic field so that its energy levels split according to the Zeeman effect. Neglecting any effects due to electron spin, how many unique energy levels are available to an electron in the 4f subshell?
> The r - meson has a charge of -e, a spin quantum number of 1, and a mass 1507 times that of the electron. If the electrons in atoms were replaced by ρ - mesons, list the possible sets of quantum numbers for ρ - mesons in the 3d subshell.
> When the principal quantum number is n = 4, how many different values of (a) ℓ and (b) mℓ are possible?
> List the possible sets of quantum numbers for electrons in the 3d subshell.
> For an electron in a 3d state, determine (a) The principle quantum number and (b) The orbital quantum number. (c) How many different magnetic quantum numbers are possible for an electron in that state?
> Hydrogen’s single electron can occupy any of the atom’s distinct quantum states. Determine the number of distinct quantum states in the (a) n = 1, (b) n = 2, and (c) n = 3 energy levels.
> Using the concept of standing waves, de Broglie was able to derive Bohr’s stationary orbit postulate. He assumed a confined electron could exist only in states where its de Broglie waves form standing wave patterns, as in Figure 28.6. C
> A general expression for the energy levels of one – electron atoms and ions is Here μ is the reduced mass of the atom, given by μ = m1m2 / (m1 + m2), where m1 is the mass of the electron and m2 is the mass of
> Consider a Bohr model of doubly ionized lithium. (a) Write an expression similar to Equation 28.14 for the energy levels of the sole remaining electron. (b) Find the energy corresponding to n = 4. (c) Find the energy corresponding to n = 2. (d) Calculate
> The orbital radii of a hydrogen - like atom is given by the equation rn = n2ħ2/Zmekee2 What is the radius of the first Bohr orbit in (a) He+, (b) Li2+, and (c) Be3+?
> A thin layer of liquid methylene iodide (n = 1.756) is sandwiched between two flat, parallel plates of glass (n = 1.50). What is the minimum thickness of the liquid layer if normally incident light with λ = 6.00 x 102 nm in air is to be strongly reflecte
> (a) Write an expression relating the kinetic energy KE of the electron and the potential energy PE in the Bohr model of the hydrogen atom. (b) Suppose a hydrogen atom absorbs a photon of energy E, resulting in the transfer of the electron to a higher - e
> An electron is in the second excited orbit of hydrogen, corresponding to n = 3. Find (a) The radius of the orbit and (b) The wavelength of the electron in this orbit.
> (a) Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 x 108 m as the average Earth–Moon distance and 2.36 x 106 s as the period of the Moon in its orbit. (b) If the angular momentum of the Moon
> A photon with energy 2.28 eV is absorbed by a hydrogen atom. Find (a) The minimum n for a hydrogen atom that can be ionized by such a photon and (b) The speed of the electron released from the state in part (a) when it is far from the nucleus.
> Consider a large number of hydrogen atoms, with electrons all initially in the n = 4 state. (a) How many different wavelengths would be observed in the emission spectrum of these atoms? (b) What is the longest wavelength that could be observed? (c) To wh
> (a) If an electron makes a transition from the n = 4 Bohr orbit to the n = 2 orbit, determine the wavelength of the photon created in the process. (b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when this
> A particle of charge q and mass m, moving with a constant speed v, perpendicular to a constant magnetic field B, follows a circular path. If in this case the angular momentum about the center of this circle is quantized so that mvr = 2nħ, show
> The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number n = 2 as shown in Figure P28.19. Consider the photon of longest wavelength corresponding to a transition shown in the figure. De
> A hydrogen atom initially in its ground state (n = 1) absorbs a photon and ends up in the state for which n = 3. (a) What is the energy of the absorbed photon? (b) If the atom eventually returns to the ground state, what photon energies could the atom em
> What is the energy of a photon that, when absorbed by a hydrogen atom, could cause an electronic transition from (a) The n = 2 state to the n = 5 state and (b) The n = 4 state to the n = 6 state?
> A soap bubble (n = 1.33) having a wall thickness of 120 nm is floating in air. (a) What is the wavelength of the visible light that is most strongly reflected? (b) Explain how a bubble of different thickness could also strongly reflect light of this same
> Following are four possible transitions for a hydrogen atom (a) Which transition will emit the shortest - wavelength photon? (b) For which transition will the atom gain the most energy? (c) For which transition(s) does the atom lose energy?
> A hydrogen atom emits a photon of wavelength 656 nm. From what energy orbit to what lower - energy orbit did the electron jump?
> A photon is emitted when a hydrogen atom undergoes a transition from the n = 5 state to the n = 3 state. Calculate (a) The wavelength, (b) The frequency, and (c) The energy (in eV) of the emitted photon.
> Show that the speed of the electron in the nth Bohr orbit in hydrogen is given by
> For a hydrogen atom in its ground state, use the Bohr model to compute (a) The orbital speed of the electron, (b) The kinetic energy of the electron, and (c) The electrical potential energy of the atom.
> A hydrogen atom is in its first excited state (n = 2). Using the Bohr theory of the atom, calculate (a) The radius of the orbit, (b) The linear momentum of the electron, (c) The angular momentum of the electron, (d) The kinetic energy, (e) The potential
> What is the (a) Energy in eV and (b) Wavelength in μm of a photon that, when absorbed by a hydrogen atom, could cause a transition from the n = 3 to the n = 6 energy level?
> Singly ionized helium (He+) is a hydrogen - like atom. Determine the energy in eV required to raise a He+ electron from the n = 1 to the n = 2 energy level.
> Determine the energies in eV of the (a) Second and (b) Third energy levels of the hydrogen atom. Calculate the orbital radius in nm of an electron in hydrogen’s (c) Second and (d) Third energy levels.
> The so - called Lyman - α photon is the lowest energy photon in the Lyman series of hydrogen and results from an electron transitioning from the n = 2 to the n = 1 energy level. Determine (a) The energy in eV and (b) The wavelength in nm of a Lyman - α p
> Waves from a radio station have a wavelength of 3.00 x 102 m. They travel by two paths to a home receiver 20.0 km from the transmitter. One path is a direct path, and the second is by reflection from a mountain directly behind the home receiver. What is
> In a Rutherford scattering experiment, an α - particle (charge = +2e) heads directly toward a gold nucleus (charge = +79e). The α - particle had a kinetic energy of 5.0 MeV when very far (r ( ∞) from the nucleus. Assuming the gold nucleus to be fixed in
> The “size” of the atom in Rutherford’s model is about 1.0 x 10-10 m. (a) Determine the speed of an electron moving about the proton using the attractive electrostatic force between an electron and a proton separated by this distance. (b) Does this speed
> An isolated atom of a certain element emits light of wavelength 520. nm when the atom falls from its fifth excited state into its second excited state. The atom emits a photon of wavelength 410. nm when it drops from its sixth excited state into its seco
> Does the light emitted by a neon sign constitute a continuous spectrum or only a few colors? Defend your answer.
> The ionization energies for Li, Na, K, Rb, and Cs are 5.390, 5.138, 4.339, 4.176, and 3.893 eV, respectively. Explain why these values are to be expected in terms of the atomic structures.
> List some ways in which quantum mechanics altered our view of the atom pictured by the Bohr theory.
> Can the electron in the ground state of hydrogen absorb a photon of energy less than 13.6 eV? Can it absorb a photon of energy greater than 13.6 eV? Explain.
> Why are three quantum numbers needed to describe the state of a one - electron atom (ignoring spin)?
> Suppose the electron in the hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why should such a hypothetical atom emit a continuous spectrum rather than the observed line spectrum?
> An energy of about 21 eV is required to excite an electron in a helium atom from the 1s state to the 2s state. The same transition for the He+ ion requires approximately twice as much energy. Explain.
> Monochromatic light of wavelength λ is incident on a pair of slits separated by 2.40 x 10-4 m, and forms an interference pattern on a screen placed 1.80 m away from the slits. The first - order bright fringe is 4.52 mm from the center of the central maxi
> A nonrelativistic electron and a nonrelativistic proton are moving and have the same de Broglie wavelength. Which of the following are also the same for the two particles? (a) Speed (b) Kinetic energy (c) Momentum (d) Frequency
