- The charge on a capacitor in an ac circuit is q(t) = Q sin ωt. Using a small-angle approximation (Appendix A.9), we can write q(t) ≈ Qωtfor times |t| ≪ 1/ω. What is the slope of the graph of
- X-rays illuminate a target and the scattered x-rays are detected. Given the wavelength λ of the incident x-rays and the scattering angle θ, rank the scattered x-rays from largest wavelength to
- A 100 W incandescent lightbulb radiates visible light at a rate of about 10 W; the rest of the EM radiation is mostly infrared. Assume that the lightbulb radiates uniformly in all directions. Under
- Follow the steps outlined in this problem to estimate the time lag (predicted classically but not observed experimentally) in the photoelectric effect. Let the intensity of the incident radiation be
- Exposure to ultraviolet light is one method used to sterilize medical equipment, disinfect drinking water, and pasteurize fruit juices. Microorganisms are typically small enough that UV light can
- Rhodopsin is the molecule responsible for the reception of light in the rod cells of the mammalian retina. Absorption of a photon changes the 11-cis-retinal part of the molecule to all-trans-retinal.
- One of the first signs of sunburn is the reddening of the skin (called erythema). As a very rough rule of thumb, erythema occurs if 13 mJ of ultraviolet light of approximately 300 nm wavelength
- A surgeon is attempting to correct a detached retina by using a pulsed laser. (a) If the pulses last for 20.0 ms and if the output power of the laser is 0.500 W, how much energy is in each
- The photoelectric effect is studied using a tungsten target. The work function of tungsten is 4.5 eV. The incident photons have energy 4.8 eV. (a) What is the threshold frequency? (b) What
- When photons with a wavelength of 120.0 nm are incident on a metal, electrons are ejected that can be stopped with a stopping potential of 6.00 V. (a) What stopping potential is needed when the
- (a) Light of wavelength 300 nm is incident on a metal that has a work function of 1.4 eV. What is the maximum speed of the emitted electrons? (b) If light of wavelength 800 nm is incident on a
- A 220 W laser fires a 0.250 ms pulse of light with a wavelength of 680 nm. (a) What is the energy of each photon in the laser beam? (b) How many photons are in this pulse?
- These data are obtained for photoelectric stopping potentials using light of four different wavelengths. (a) Plot a graph of the stopping potential versus the reciprocal of the
- What is the ground state energy, according to Bohr theory, for (a) He+, (b) Li2+, (c) deuterium (an isotope of hydrogen whose nucleus contains a neutron as well as a proton)?
- Nuclei in a radium-226 radioactive source emit photons whose energy is 186 keV. These photons are scattered by the electrons in a metal target; a detector measures the energy of the scattered photons
- During a Compton scattering experiment, an electron that was initially at rest recoils at 180° (i.e., in the direction of motion of the incident x-ray photon). If the recoil electron has a kinetic
- In gamma-ray astronomy, the existence of positrons (e+) can be inferred by characteristic gamma-ray photons that are emitted when a positron and an electron (e−) annihilate. For simplicity, assume
- UV light with a wavelength of 180 nm is incident on a metal and electrons are ejected. Instead of determining the maximum kinetic energy of the electrons with a stopping potential, the maximum
- Which one of these statements is true?(a) The principal quantum number of the electron in a hydrogen atom does not affect its energy.(b) The principal quantum number of an electron in its ground
- In the Bohr model, the electron in the ground state of the hydrogen atom is in a circular orbit of radius 0.0529 nm. How does the quantum mechanical picture of the H atom differ from the Bohr model?
- Which of the lettered transitions on the energy level diagram would be the best candidate for light amplification by stimulated emission? C a b d - Excited state Metastable state f - Ground state
- Which of these statements about electron energy levels in hydrogen atoms is true?(a) An electron in the hydrogen atom is best represented as a traveling wave.(b) An electron with positive total
- An electron and a neutron have the same de Broglie wavelength. Which is true?(a) The electron has more kinetic energy and a higher speed.(b) The electron has less kinetic energy but a higher
- Which one of these statements is true?(a) The atomic spacing in crystals is too fine to produce observable diffraction effects with matter waves.(b) Only charged particles have matter waves
- A particle is incident from the left on a slit of width w and the particle passes through the slit opening. The uncertainty principle restricts which of these quantities?(a) The product of the width
- The exclusion principle:(a) Implies that in an atom no two electrons can have identical sets of quantum numbers.(b) Says that no two electrons in an atom can have the same orbit.(c) Excludes
- Describe some differences between the beam of light from a flashlight and from a laser.
- What happens to the energy level spacings for a particle in a box when the box is made longer?(a) The spacings decrease.(b) The spacings increase.(c) The spacings stay the same.(d) Insufficient
- If a particle is confined to a three-dimensional, cubical region of length L on each side:(a) The particle has a minimum uncertainty in each component of momentum of about h/(πL).(b) The particle
- A bullet is fired from a rifle. The end of the barrel is a circular aperture. Is diffraction a measurable effect?(a) No, because only charged particles have de Broglie wavelengths.(b) No, because a
- To resolve details of a cell using an ordinary microscope, you must use a wavelength that is about the same size, or smaller, than the details of the cell you want to observe. Suppose you want to be
- What technique could Becquerel and others have used to determine that alpha rays are positively charged, beta rays negatively charged, and gamma rays uncharged? Explain how they could find that alpha
- The activity of a radioactive sample (with a single radioactive nuclide) decreases to one eighth its initial value in a time interval of 96 days. What is the half-life of the radioactive nuclide
- For all stable nuclei, (a) the mass of the nucleus is less than Zmp + (A - Z)mn- (b) the mass of the nucleus is greater than Zmp + (A - Z)mn. (c) the mass of the nucleus is equal to Zmp + (A -
- Rank these nuclides in decreasing order of the number of neutrons: (a) He (b) He (c) H (d) Li (e) B (f) Li
- Radioactive decays into . Which of these particles is released in the decay?(a) A proton(b) An electron(c) A positron(d) An alpha particle(e) A neutron(f) None of the above 215, 83 Bj
- Which of these are appropriate units for the decay constant λ of a radioactive nuclide?(a) s(b) Ci(c) rad(d) s−1(e) rem(f) MeV
- Show that c2 = 931.494 MeV/u.
- How much energy is released in the fusion reaction 2H + 3H - 4He + n?
- Estimate the minimum total kinetic energy of the 2H and 3H nuclei necessary to allow the fusion reaction of Eq. (29-49) to take place. u + ³H₂ + H₂ + H₂
- Strontium-90 is a radioactive element that is produced in nuclear fission. It decays by β− decay to yttrium (Y) with a half-life of 28.8 yr. (a) Write down the decay scheme for
- An ultraviolet microscope locates an electron in an atom to within a distance of 0.5 nm. What is the order of magnitude of the minimum uncertainty in the momentum of the electron located in this way?
- A particle traveling at a speed of 6.50 × 106 m/s has the uncertainty in its position given by its de Broglie wavelength. What is the minimum uncertainty in the speed of the particle?
- The particle in a box model is often used to make rough estimates of energy level spacings. For a metal wire 10 cm long, treat a conduction electron as a particle confined to a one-dimensional box of
- A particle is confined to & finite box of length L. In the nth state, the wave function has n − 1 nodes. The wave function must make a smooth transition from sinusoidal inside the box to a
- (a) Show that the number of electron states in a sub-shell is 4ℓ + 2.(b) By summing the number of states in each of subshells, show that the number of states in a shell is 2n2. Use the fact that
- The neutrons produced in fission reactors have a wide range of kinetic energies. After the neutrons make several collisions with atoms, they give up their excess kinetic energy and are left with the
- What is the ground-state electron configuration of a K+ ion?
- An electron in an atom has an angular momentum quantum number of 2. (a) What is the magnitude of the angular momentum of this electron in terms of ħ? (b) What are the possible values for
- An electron in a hydrogen atom has quantum numbers: n = 8; mℓ = 4. What are the possible values for the orbital angular momentum quantum number ℓ of the electron?
- (a) Find the magnitude of the orbital angular momentum L for an electron with n = 2 and I = 1 in terms of ħ. (b) What are the allowed values for Lz? (c) What are the angles between the
- The figure shows the lowest six energy levels of the outer electron in sodium. In the ground state, the electron is in the “3s” level. (a) What is the ionization energy of sodium? (b)
- A light-emitting diode (LED) has the property that electrons can be excited into the conduction band by the electrical energy from a battery; a photon is emitted when the electron drops back to the
- A proton and a deuteron (which has the same charge as the proton but 2.0 times the mass) are incident on a barrier of thickness 10.0 fm and “height” 10.0 MeV. Each particle has a kinetic energy
- Before the discovery of the neutron, one theory of the nucleus proposed that the nucleus contains protons and electrons. For example, the helium-4 nucleus would contain 4 protons and 2 electrons
- Electrons are accelerated through a potential difference of 8.95 kV and pass through a single slit of width 6.6 × 10−10 m. How wide is the central maximum on a screen that is 2.50 m from the slit?
- How could Henri Becquerel and other scientists determine that there were three different kinds of radiation before having determined the electric charges or masses of the alpha, beta, and gamma rays?
- Solid lead has more than four times the mass density of solid aluminum. What is the main reason that lead is so much more dense?(a) The Pb atom is smaller than the Al atom.(b) The Pb nucleus is
- Light passes from one medium (in which the speed of light is v1) into another (in which the speed of light is v2). If v1 < v2, as the light crosses the boundary, (a) both fand λ decrease. (b)
- If the wavelength of an electromagnetic wave is about the diameter of an apple, what type of radiation is it?(a) X-ray(b) UV(c) Infrared(d) Microwave(e) Visible light(f) Radio wave
- Prove that, in an EM wave traveling in vacuum, the electric and magnetic energy densities are equal; that is, prove that at any point and at any instant of time. 1 2012 1 = Β 2μο
- A light wave passes through a hazy region in the sky. If the electric field vector of the emerging wave is one quarter that of the incident wave, what is the ratio of the transmitted intensity to the
- Light travels through tanks filled with various substances. The indices of refraction of the substances n and the lengths of the tanks are given. Rank them in order of the time it takes light to
- Randomly polarized light with intensity I0 passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles θ1 and θ2, respectively,
- Unpolarized light is incident on four ideal polarizing sheets with their transmission axes oriented as shown in the figure. What percentage of the initial light intensity is transmitted through this
- Horizontally polarized light with intensity I0 passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles θ1 and θ2,
- A police car’s radar gun emits microwaves with a frequency of f1 = 7.50 GHz. The beam reflects from a speeding car, which is moving toward the police car at 48.0 m/s with respect to the police car.
- Consider the three ideal polarizing filters shown in the figure. The angles listed indicate the direction of the transmission axis of each polarizer with respect to the vertical. (a) If
- Suppose some astronauts have landed on Mars. When the astronauts ask a question of mission control personnel on Earth, what is the shortest possible time they have to wait for a response? The average
- A useful measure of the quality of a fiber-optic cable such as those used in endoscopes and other medical equipment is the numerical aperture. The larger the numerical aperture, the more light will
- Calculate the frequency of an EM wave with a wavelength the size of(a) The thickness of a piece of paper (60 μm), (b) A 91 m long soccer field, (c) The diameter of Earth, and (d) the
- The figure shows a schematic diagram of a defective eye and some lenses. Which of the lenses shown can correct for this defect? ID (a) (b) (c) (d) (e)
- If a piece of white cardboard is placed at the location of a virtual object, what (if anything) would be seen on the cardboard?
- Siu-Ling has a far point of 25 cm. Which statement here is true?(a) She may have normal vision.(b) She is myopic and requires diverging lenses to correct her vision.(c) She is myopic and requires
- Verify the locations and sizes of the images formed by the two lenses in Fig. 24.2 using the lens equation and the following data: f1 = +4.00 cm, f2 = −2.00 cm, s = 8.00 cm (where s is the distance
- What causes chromatic aberration?(a) Light is an electromagnetic wave and has intrinsic diffraction properties.(b) Different wavelengths of light give different angles of refraction at the
- An astronomical telescope has an angular magnification of 10. The barrel length is 33 cm. What are the focal lengths of the objective and the eyepiece, in that order respectively, from the choices
- A compound microscope has three possible objective lenses (focal lengths fo) and two eyepiece lenses (focal lengths fe). For maximum angular magnification, the objective and eyepiece should be chosen
- What causes spherical aberration?(a) Light is an electromagnetic wave and has intrinsic diffraction properties.(b) Different wavelengths of light give different angles of refraction at the lens-air
- A nearsighted person wears corrective lenses. One of the focal points of the corrective lenses should be(a) At the cornea.(b) At the retina.(c) At infinity.(d) Past the retina.(e) At the near
- Reducing the aperture on a camera(a) Reduces the depth of field and requires a longer exposure time.(b) Reduces the depth of field and requires a shorter exposure time.(c) Increases the depth of
- A camera uses a 200.0 mm focal length telephoto lens to take pictures from a distance of infinity to as close as 2.0 m. What are the minimum and maximum distances from the lens to the sensor?
- A statue is 6.6 m from the opening of a pinhole camera, and the screen is 2.8 m from the pinhole. (a) Is the image erect or inverted?(b) What is the magnification of the image? (c) To get a
- Draw a diagram of the human eye, labeling the cornea, the lens, the iris, the retina, and the aqueous and vitreous fluids.
- Esperanza uses a camera with a lens of focal length 50.0 mm to take a photo of her son Carlos, who is 1.2 m tall and standing 3.0 m away. (a) What must be the distance between the lens and the
- The figure shows a schematic diagram of a defective eye. What is this defect called? E
- Color printers always use at least three different colors of ink or toner. Televisions and computer monitors have pixels of at least three different colors. Why are at least three necessary?
- If rays from points on an object are converging as they enter a lens, is the object real or virtual?
- If the distance from the lens to the retina is 2.00 cm, show that the focal length of the lens must vary between 1.85 cm and 2.00 cm to see objects from 25.0 cm to infinity.
- The distance from the lens of a particular eye to the retina is 1.75 cm. What is the focal length of the lens when the eye produces a clear image of an object 25.0 cm away?
- One can estimate the size of the blind spot on the retina by treating the eye as a camera obscura. Suppose your friend Julie's eye can be approximated as a sphere of diameter 2.5 cm. She notices that
- Joe is told by his ophthalmologist that he requires glasses with a refractive power of −4.50 D to correct his vision. His previous prescription was −4.00 D. (a) Is Joe nearsighted or
- Suppose that the lens in a particular eye has a focal length that can vary between 1.85 cm and 2.00 cm, but the distance from the lens to the retina is only 1.90 cm. (a) Is this eye nearsighted
- Five converging lenses are used as simple magnifiers. In each case, the focal length f and the distance between the lens and the object p are given. Rank them in order of the angular magnification,
- Anne's retina is 1.8 cm from the lens. The nearest object she can see clearly without corrective lenses is 2.0 m away. (a) Sketch a ray diagram to show (qualitatively) what happens when she
- Suppose the distance from the lens to the retina is 18 mm. (a) What must the refractive power of the lens be when looking at distant objects? (b) What must the refractive power of the lens
- Two radio towers are a distance d apart as shown in the overhead view. Each antenna by itself would radiate equally in all directions in a horizontal plane. The radio waves have the same wavelength
- (a) What is the focal length of a magnifying glass that gives an angular magnification of 8.0 when the image is at infinity? (b) How far must the object be from the lens?
- Which of these statements correctly describes the orientation of the electric field, the magnetic field , and the velocity of propagation of an electromagnetic wave? (E)
- Repeat Problem 25 assuming that n1 < n2 < n3.Data From Problem 25A thin film is viewed both in reflected and transmitted light at normal incidence. The figure shows the strongest two rays for

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