Question: The “size” of the atom in Rutherford’

> Light from a helium–neon laser (λ = 632.8 nm) is incident on a single slit. What is the maximum width of the slit for which no diffraction minima are observed?

> Light with a wavelength in vacuum of 546.1 nm falls perpendicularly on a biological specimen that is 1.000 μm thick. The light splits into two beams polarized at right angles, for which the indices of refraction are 1.320 and 1.333, respectively. (a) Cal

> Light of intensity I0 is polarized vertically and is incident on an analyzer rotated at an angle θ from the vertical. Find the angle θ if the transmitted light has intensity (a) I = (0.750)I0, (b) I = (0.500)I0, (c) I = (0.250)I0, and (d) I = 0.

> A double slit separated by 0.058 0 mm is placed 1.50 m from a screen. (a) If yellow light of wavelength 588 nm strikes the double slit, what is the separation between the zeroth - order and first - order maxima on the screen? (b) If blue light of wavelen

> Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are shown in Figure P24.59. A linearly polarized beam of light with plane of polarization p

> Plane - polarized light is incident on a single polarizing disk, with the direction of E0 parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity in the transmitted beam is reduced by a fact

> Equation 24.14 assumes the incident light is in air. If the light is incident from a medium of index n1 onto a medium of index n2, follow the procedure used to derive Equation 24.14 to show that tan θp = n2/n1.

> The critical angle for total internal reflection for sapphire surrounded by air is 34.4°. Calculate the Brew ster’s angle for sapphire if the light is incident from the air.

> A light beam is incident on a piece of fused quartz (n = 1.458) at the Brewster’s angle. Find a) The value of Brewster’s angle and (b) The angle of refraction for the transmitted ray.

> At what angle above the horizon is the Sun if light from it is completely polarized upon reflection from water?

> The index of refraction of a glass plate is 1.52. What is the Brewster’s angle when the plate is (a) In air and (b) In water?

> Unpolarized light passes through two Polaroid sheets. The transmission axis of the analyzer makes an angle of 35.0° with the axis of the polarizer. (a) What fraction of the original unpolarized light is transmitted through the analyzer? (b) What fraction

> The angle of incidence of a light beam in air onto a reflecting surface is continuously variable. The reflected ray is found to be completely polarized when the angle of incidence is 48.0°. (a) What is the index of refraction of the reflecting material?

> Light containing two different wavelengths passes through a diffraction grating with 1.20 x 103 slits/cm. On a screen 15.0 cm from the grating, the third - order maximum of the shorter wavelength falls midway between the central maximum and the first sid

> In a location where the speed of sound is 354 m/s, a 2.00 kHz sound wave impinges on two slits 30.0 cm apart. (a) At what angle is the first maximum located? (b) If the sound wave is replaced by 3.00 - cm microwaves, what slit separation gives the same a

> Light of wavelength 5.00 x 102 nm is incident normally on a diffraction grating. If the third - order maximum of the diffraction pattern is observed at 32.0°, (a) What is the number of rulings per centimeter for the grating? (b) Determine the total numbe

> Monochromatic light at 577 nm illuminates a diffraction grating with 325 lines/mm. Determine (a) The angle to the first - order maximum, (b) The highest order that can be observed with this grating at the given wavelength, and (c) The angle to this highe

> Sunlight is incident on a diffraction grating that has 2750 lines/ cm. The second - order spectrum over the visible range (400.– 700. nm) is to be limited to 1.75 cm along a screen that is a distance L from the grating. What is the required value of L?

> 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 Newton&acirc

> 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.

> 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.

> 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.

> 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.