Explain the difference between speed and velocity.
> In an optically pumped laser, the light that causes optical pumping is always shorter in wavelength than the laser beam. Explain.
> Describe some differences between the beam of light from a flashlight and from a laser.
> A 0.500 kg block of iron at 60.0°C is placed in contact with a 0.500 kg block of iron at 20.0°C. (a) The blocks soon come to a common temperature of 40.0°C. Estimate the entropy change of the universe when this occurs. [Hint: Assume that all the heat flo
> How should we interpret electron cloud representations of electron states in atoms?
> A steel sphere with radius 1.0010 cm at 22.0°C must slip through a brass ring that has an internal radius of 1.0000 cm at the same temperature. To what temperature must the brass ring be heated so that the sphere, still at 22.0°C, can just slip through?
> What is the length of a simple pendulum whose horizontal position is described by What assumption do you make when answering this question?
> Light of wavelength 0.500 µm (in air) enters the water in a swimming pool. The speed of light in water is 0.750 times the speed in air. What is the wavelength of the light in water?
> Why does a particle confined to a finite box have only a finite number of bound states?
> We often refer to the state of the hydrogen atom as “the n = 3 state,” for example. Under what circumstances do we only need to specify one of the four quantum numbers? Under what circumstances would we have to be more specific?
> The uncertainty principle does not allow us to think of the electron in an atom as following a well-defined trajectory. Why, then, are we able to define trajectories for golf balls, comets, and the like? [Hint: How are the uncertainties in momentum and v
> It is sometimes said that, at absolute zero, all molecular motion, vibration, and rotation would cease. Do you agree? Explain.
> 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? In what ways are the two similar?
> When aluminum is exposed to oxygen, a very thin layer of aluminum oxide forms on the outside. Aluminum oxide is a good insulator. Nevertheless, if two aluminum wires are twisted together, electric current can flow from one to the other, even if the oxide
> 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 (referred to as UVB radiation) is incident on the skin per s
> Explain why the electrical resistivity of a semiconductor decreases with increasing temperature.
> When a particle's kinetic energy increases, what happens to its de Broglie wavelength?
> How can we demonstrate the existence of matter waves?
> (a) If the bottom of a thundercloud has a potential of −1.00 × 109 V with respect to Earth and a charge of −20.0 C is discharged from the cloud to Earth during a lightning strike, how much electric potential energy is released? (Assume that the system ac
> A car with mass of 1000.0 kg accelerates from 0 m/s to 40.0 m/s in 10.0 s. Ignore air resistance. The engine has a 22% efficiency, which means that 22% of the energy released by the burning gasoline is converted into mechanical energy. (a) What is the a
> A gymnast of mass 52 kg is jumping on a trampoline. She jumps so that her feet reach a maximum height of 2.5 m above the trampoline and, when she lands, her feet stretch the trampoline down 75 cm. How far does the trampoline stretch when she stands on it
> Why does a confined particle have quantized energy levels?
> Central to the operation of a photocopy machine (see Section 16.2) is a drum coated with a photoconductor—a semiconductor that is a good insulator in the dark but allows charge to flow freely when illuminated with light. How does light allow charge to fl
> What do the ground-state electron configurations of the noble gases have in common? Why are the noble gases chemically nonreactive?
> The Nd:YAG laser operates in a four-state cycle as shown in the figure, and the ruby laser operates in a three-state cycle (compare with Fig. 28.21b). In which laser is it easier to maintain a population inversion? Why? Explain why the Nd:YAG laser can p
> Explain why a population inversion is necessary in a laser.
> An electron diffraction experiment gives maxima at the same angles as an x-ray diffraction experiment with the same sample. How do we know the wavelengths of the electrons and x-rays are the same? Would they give the same pattern if their energies were t
> What is the shortest wavelength x-ray produced by a 0.20 MV x- ray machine?
> List the assumptions of the Bohr theory of the hydrogen atom.
> A traveling sine wave is the result of the superposition of two sine waves with equal amplitudes, wavelengths, and frequencies: y1 = A sin (ωt + kx) and y2 = A sin (ωt + kx −ϕ). The two component waves each have amplitude A = 5.00 cm. If the superpositio
> A darkroom used for developing black-and-white film can be dimly lit by red light without ruining the film. Why is red light used rather than white or blue or some other color?
> The temperature at which liquid nitrogen boils (at atmospheric pressure) is 77 K. Express this temperature in (a) °C and (b) °F.
> Describe the process by which a continuous spectrum of x-rays is produced. Does the spectrum have a maximum wavelength or a minimum wavelength? Explain.
> In the photoelectric effect, what is the relationship between the maximum kinetic energy of ejected electrons and the frequency of the light incident on the surface?
> A coal-fired electrical generating station can use a higher TH than a nuclear plant; for safety reasons the core of a nuclear reactor is not allowed to get as hot as burning coal. Suppose that TH = 727°C for a coal station but TH = 527°C for a nuclear st
> How does the observation of the sharp lines seen in the hydrogen emission spectrum verify the notion that all electrons have the same charge?
> Some stars are reddish in color, others bluish, and others yellowish- white (like the Sun). How is the color related to the surface temperature of the star? What color are the hottest stars? What color are the coolest?
> An experiment shines visible light on a target and measures the wavelengths of light scattered at different angles. Would the experiment show that the scattered photons are Compton-shifted? Explain.
> What happens to the energies of the characteristic x-rays when the potential difference accelerating the electrons in an x-ray tube is doubled?
> When a plot is made of x-ray intensity versus wavelength for a particular x-ray tube, two sharp peaks are superimposed on the continuous x-ray spectrum. These sharp peaks are called “characteristic” x-rays. Explain the origin of this name. In other words
> A block of birch wood floats in oil with 90.0% of its volume submerged. What is the density of the oil? The density of the birch is 0.67 g/cm3.
> 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. The molecule absorbs light most strongly at a waveleng
> In a photoelectric effect experiment, two different metals (1 and 2) are subjected to EM radiation. Metal 1 produces photoelectrons for both red and blue light; metal 2 produces photoelectrons for blue light but not for red. Which metal produces photoele
> Consider the situation described in Problem 18. (a) Take into account the expansion of the glass and calculate how much water will spill out of the glass. Compare your answer with the case where the expansion of the glass was not considered. (b) By wha
> Explain why the annihilation of an electron and a positron creates a pair of photons rather than a single photon.
> Use the photon model to explain why ultraviolet radiation can be harmful to your skin, but visible light is not.
> The photoresponse of the retina of the human eye at low light levels depends on individual photosensitive molecules in rod cells being excited by the incident light. When excited, these molecules change shape, leading to other changes in the cell that tr
> A solar cell is used to generate electricity when sunlight falls on it. How would you expect the current produced by a solar cell to depend on the intensity of the incident light? How would you expect the current to depend on the wavelength of the incide
> You shoot a 51 g pebble straight up with a catapult whose spring constant is 320 N/m. The catapult is initially stretched by 0.20 m. How high above the starting point does the pebble fly? Ignore air resistance.
> According to Figure 30.3, higher energies correspond with times that are closer to the origin of the universe, so particle accelerators at higher energies probe conditions that existed shortly after the Big Bang. At Fermilab's Tevatron, protons and antip
> A parallel plate capacitor used in a flash for a camera must be able to store 32 J of energy when connected to 300 V. (Most electronic flashes actually use a 1.5 to 6.0 V battery, but increase the effective voltage using a dc-dc inverter.) (a) What shou
> Explain why every line in the absorption spectrum of hydrogen is present in the emission spectrum, but not every line in the emission spectrum is present in the absorption spectrum. [Hint: The excited states are very short-lived.]
> A fluorescent substance absorbs EM radiation of one wavelength and then emits EM radiation of a different wavelength. Which wavelength is longer? Explain.
> 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 penetrate to the cell nucleus and damage their DNA molecul
> An ordinary drinking glass is filled to the brim with water (268.4 mL) at 2.0°C and placed on the sunny pool deck for a swimmer to enjoy. If the temperature of the water rises to 32.0°C before the swimmer reaches for the glass, how much water will have s
> In a photoelectric effect experiment, how is the stopping potential determined? What does the stopping potential tell us about the electrons emitted from the metal surface?
> Explain how Rutherford's experiment, in which alpha particles are incident on a thin gold foil, refutes the plum pudding model of the atom.
> What process becomes especially important for photons with energies in excess of 1.02 MeV?
> Why is the Compton shift more noticeable for an incident x-ray photon than for a photon of visible light?
> In both Compton scattering and the photoelectric effect, an electron gains energy from an incident photon. What is the essential difference between the two processes?
> If green light causes the ejection of electrons from a metal in a photoelectric effect experiment and yellow light does not, what would you expect to happen if red light were used to illuminate the same metal? Do you expect more intense yellow light to e
> Two sine waves are described by y1 = A sin (ωt + kx) and y2 = A sin (ωt + kx + π/3). Plot graphs of y1 versus t and y2 versus t on the same axes for the point x = 0. Plot y versus t for the superposition of the two waves at x = 0 and estimate its amplitu
> Describe the photoelectric effect and four aspects of the experimental results that were puzzling to nineteenth-century physicists. How does the photon model of light explain the experimental results in each case?
> In Section 26.2, suppose that another astronaut, Celia, moves in a spaceship to the left with respect to Abe (see Fig. 26.4). What would Celia conclude about the time order of the two flashes?
> A copper bar of thermal conductivity 401 W/(m·K) has one end at 104°C and the other end at 24°C. The length of the bar is 0.10 m, and the cross-sectional area is 1.0 × 10−6 m2. (a) What is the rate of heat conduction along the bar? (b) What is the te
> In an Earth laboratory, an astronaut measures the length of a rod to be 1.00 m. The astronaut takes the rod aboard a spaceship and flies away from Earth at speed 0.5c. Is the length of the rod measured by an observer on Earth greater than, less than, or
> 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 decaying exponential outsideâ€&#
> A pendulum passes x = 0 with a speed of 0.50 m/s; it swings out to A = 0.20 m. What is the period T of the pendulum? (Assume the amplitude is small.)
> A thin soap film (n = 1.35) is suspended in air. The spectrum of light reflected from the film is missing two visible wavelengths of 500.0 nm and 600.0 nm, with no missing wavelengths between the two. (a) What is the thickness of the soap film? (b) Are
> Harry and Sally are on opposite sides of the room at a wedding reception. They simultaneously (in the frame of the room) take flash pictures of the bride and groom cutting the cake in the center of the room. What would an observer moving at constant velo
> A constant force is applied to a particle initially at rest. Sketch qualitative graphs of the particle's speed, momentum, and acceleration as functions of time. Assume that the force acts long enough so the particle achieves relativistic speeds.
> An astronaut in top physical condition has an average resting pulse on Earth of about 52 beats per minute. Suppose the astronaut is in a spaceship traveling at 0.87c (γ = 2) with respect to Earth when he takes his own resting pulse. Does he measure about
> A proton (mass 1.67 × 10−27 kg, charge +e) is fired directly at a lithium nucleus (mass 1.16 × 10−26 kg, charge +3e). If the proton's velocity is 5.24 × 105 m/s when it is far from the nucleus, how far apart will the two particles be when the proton is a
> A particle with nonzero mass m can never move faster than the speed of light. Is there also a maximum momentum that the particle can have? A maximum kinetic energy? Explain.
> As you talk on a cell phone, does the mass of the phone's battery change at all? If so, does it increase or decrease?
> An electron is moving at nearly light speed. A constant force of magnitude F is acting on the electron in the direction of its motion. Is the acceleration of the electron less than, equal to, or greater in magnitude than F/m? Explain.
> A quasar is a bright center in a far distant galaxy where some energetic action is taking place (probably due to energy being released as matter falls into a black hole at the center of the galaxy). Through her telescope Mavis observes a quasar 12 × 109
> Does a stretched spring have the same mass as when it is relaxed? Explain.
> A cylindrical brass container with a base of 75.0 cm2 and height of 20.0 cm is filled to the brim with water when the system is at 25.0°C. How much water overflows when the temperature of the water and the container is raised to 95.0°C?
> Explain why it is impossible for a particle with mass to move faster than the speed of light.
> When the spring on a toy gun is compressed by a distance x, it will shoot a rubber ball straight up to a height of h. Ignoring air resistance, how high will the gun shoot the same rubber ball if the spring is compressed by an amount 2x? Assume x ≪ h.
> A particle with charge +e has a total energy of 0.638 MeV when it is moving at 0.600c. If this particle then enters a linear accelerator, what is its speed after it has been accelerated through a 2.6 MV potential difference?
> A friend argues with you that relativity is absurd: “It's obvious that moving clocks don't run slow and that moving objects aren't shorter than when they're at rest.” How would you reply?
> The drawing shows a snapshot of a transverse wave traveling along a string at 10.0 m/s. The equation for the wave is y(x, t) = A cos (ωt + kx). (a) Is the wave moving to the right or to the left? (b) What are the numerical values of A, Ï
> In a double-slit experiment, what is the linear distance on the screen between adjacent maxima if the wavelength is 546 nm, the slit separation is 0.100 mm, and the slit-screen separation is 20.0 cm?
> A spherical rain drop of radius 1.0 mm has a charge of +2.0 nC. The electric field in the vicinity is 2.0 kN/C downward. The terminal speed of an identical but uncharged drop is 6.5 m/s. The drag force is related to the drop’s speed by
> In an experiment to measure the Coulomb constant, a tiny sphere with charge +7.0 nC is suspended from a spring. When two other tiny charged spheres, each with a charge of −4.0 µC, are placed in the positions shown in the figure, the spring stretches 0.50
> The graph shows the position x of a switch engine in a rail yard as a function of time t. At which of the labeled times t0 to t7 is (a) ax 0, (d) vx = 0, (e) the speed decreasing?
> Humans cool off by perspiring; the evaporating sweat removes heat from the body. If the skin temperature is 35.0°C and the air temperature is 28.0°C, what is the entropy change of the universe due to the evaporation of 150 mL of sweat? Take the latent he
> In gel electrophoresis, the mobility μ of a molecule in a particular gel matrix is defined as μ = v1/E, where v1 is the terminal speed of the molecule and E is the applied electric field strength. In one case, a molecule has mobility 3.0 × 10−8 C·m/(N·s)
> A student eats 2000 kcal per day. (a) Assuming that all of the food energy is released as heat, what is the rate of heat released (in watts)? (b) What is the rate of change of entropy of the surroundings if all of the heat is released into air at room t
> The Bohr model of the hydrogen atom proposed that the electron orbits around the proton in a circle of radius 5.3 × 10−11 m. The electric force is responsible for the radial acceleration of the electron. What is the speed of the electron in this model?
> (a) Which has the larger buoyant force acting on it when immersed in water, 1.0 kg of lead or 1.0 kg of aluminum? Explain. (b) Which has the larger buoyant force acting on it, 1.0 kg of steel that is sinking to the bottom of a lake or 1.0 kg of wood with
> Within an insulated system, 418.6 kJ of heat is conducted through a copper rod from a hot reservoir at +200.0°C to a cold reservoir at +100.0°C. (The reservoirs are so big that this heat exchange does not change their temperatures appreciably.) What is t
> A very small charged block with a mass of 2.35 g is placed on an insulated, frictionless plane inclined at an angle of 17.0° with respect to the horizontal. The block does not slide down the plane because of a 465 N/C uniform electric field th
> Rank these in order of increasing entropy: (a) 1 mol of water at 20°C and 1 mol of ethanol at 20°C in separate containers; (b) a mixture of 1 mol of water at 20°C and 1 mol of ethanol at 20°C; (c) 0.5 mol of water at 20°C and 0.5 mol of ethanol at 20°
> The energy-time uncertainty principle allows for the creation of virtual particles that appear from a vacuum for a very brief period of time Δt, then disappear again. This can happen as long as ΔE Δt = ħ/2, where ΔE is the rest energy of the particle. (
> (a) Write an expression for the magnitude of the electric field at a point (x, 0) on a line perpendicular to the dipole axis. State the direction of the field for x > 0 and for x < 0. (b) Show that when x ≫ d, E ≈ kqd/x3. (c) The field is inversely pro
> Rank these in order of increasing entropy: (a) 0.5 kg of ice and 0.5 kg of (liquid) water at 0°C; (b) 1 kg of ice at 0°C; (c) 1 kg of (liquid) water at 0°C; (d) 1 kg of water at 20°C.
> A pilot wants to fly from Dallas to Oklahoma City, a distance of 330 km at an angle of 10.0° west of north. The pilot heads directly toward Oklahoma City with an airspeed of 200 km/h. After flying for 1.0 h, the pilot finds that he is 15 km off course to
> (a) Write an expression for the electric field at a point (0, y) on the dipole axis for y > d/2. What is the direction of the field? (b) Show that when y ≫ d, E ≈ 2kqd/y3. [Hint: Use the binomial approximation from Appendix A.9.] (c) The field is inverse
