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 velocity related?]
> Hilda holds a gardening book of weight 10 N at a height of 1.0 m above her patio for 50 s. How much work does she do on the book during that 50 s?
> As shown in the top-view diagram, a 46.4 N force is applied to the outer edge of a door of width 1.26 m in such a way that it acts (a) perpendicular to the door, (b) at an angle of 43.0° with respect to the door surface, (c) so that the line
> The natural abundance of deuterium in water is 0.0156% (i.e., 0.0156% of the hydrogen nuclei in water are 2H). If the fusion reaction (2H + 2H) yields 3.65 MeV of energy on average, how much energy could you get from 1.00 L of water? (There are two react
> The string in a yo-yo is wound around an axle of radius 0.500 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.200 kg and outer radius 2.00 cm. Starting from rest, it rotates and falls a distance of 1.00 m
> Radon gas (Rn) is produced by the alpha decay of radium / . (a) How many neutrons and how many protons are present in the nucleus of the isotope of Rn produced by this decay? (b) The air in a student’s basement apartment contains 1.0 × 107 Rn nuclei. T
> A solid sphere of mass 0.600 kg rolls without slipping along a horizontal surface with a translational speed of 5.00 m/s. It comes to an incline that makes an angle of 30° with the horizontal surface. Ignoring energy losses due to friction, to what verti
> A neutron star is a star that has collapsed into a collection of tightly packed neutrons. Thus, it is something like a giant nucleus; but since it is electrically neutral, there is no Coulomb repulsion to break it up. The force holding it together is gra
> A solid sphere is released from rest and allowed to roll down a board that has one end resting on the floor and is tilted at 30° with respect to the horizontal. If the sphere is released from a height of 60 cm above the floor, what is the sphere's speed
> Repeat Problem 50 if the magnetic field is 2.5 T in the plane of the loop, 60.0° below the +x-axis.
> Suppose a charge q is placed at point x = 0, y = 0. A second charge q is placed at point x = 8.0 m, y = 0. What charge must be placed at the point x = 4.0 m, y = 0 in order that the field at the point x = 4.0 m, y = 3.0 m be zero?
> Explain why an ideal spring must exert forces of equal magnitude on the objects attached to each end, even if the spring itself has a nonzero acceleration. [Hint: Use one of Newton’s laws of motion and remember that an ideal spring has zero mass.] Is the
> You drop a stone into a deep well and hear it hit the bottom 3.20 s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about 3
> The invention of the cannon in the fourteenth century made the catapult unnecessary and ended the safety of castle walls. Stone walls were no match for balls shot from cannons. Suppose a cannonball of mass 5.00 kg is launched from a height of 1.10 m, at
> A hydrogen atom in its ground state is immersed in a continuous spectrum of ultraviolet light with wavelengths ranging from 96 nm to 110 nm. After absorbing a photon, the atom emits one or more photons to return to the ground state. (a) What wavelength(
> A hollow cylinder, a uniform solid sphere, and a uniform solid cylinder all have the same mass m. The three objects are rolling on a horizontal surface with identical translational speeds v. Find their total kinetic energies in terms of m and v and order
> Can the velocity of an object be zero and the acceleration be nonzero at the same time? Explain.
> Any pair of equal and opposite forces acting on the same object is called a couple. Consider the couple in part (a) of the figure. The rotation axis is perpendicular to the page through point P. (a) Show that the magnitude of the net torque is equal to
> Suppose that you have a glass tube filled with atomic hydrogen gas (H, not H2).Assume that the atoms start out in their ground states. You illuminate the gas with monochromatic light of various wavelengths, ranging through the entire IR, visible, and UV
> A solid cylinder (mass 160 g, radius 2.0 cm) rolls without slipping at a speed of 5.0 cm/s. What is its total kinetic energy?
> 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 0.01 W/m2. (a) If the area of the atom is (0.1 nm)2, f
> A solid sphere is rolling without slipping down a board that is tilted at an angle of 35° with respect to the horizontal. What is its acceleration?
> A spaceship passes over an observation station on Earth. Just as the nose of the ship passes the station, a light in the nose of the ship flashes. As the tail of the ship passes the station, a light flashes in the ship's tail. According to an Earth obser
> When is the first time for t > 0 that the string looks exactly as it does at t = 0?
> A town is planning on using the water flowing through a river at a rate of 5.0 × 106 kg/s to carry away the heat from a new power plant. Environmental studies indicate that the temperature of the river should only increase by 0.50°C. The maximum design e
> Why would we expect atmospheric testing of nuclear weapons to increase the relative abundance of carbon-14 in the atmosphere? Why would we expect the widespread burning of fossil fuels to decrease the relative abundance of carbon-14 in the atmosphere?
> Why can we ignore the binding energies of the atomic electrons in calculations such as Example 29.4? Isn’t there a mass defect due to the binding energy of the electrons?
> In a CRT television, electrons of kinetic energy 2.0 keV strike the screen. No EM radiation is emitted below a certain wavelength. Calculate this wavelength.
> Explain why neutron-activated nuclides tend to decay by β− rather than β+.
> Jorge is going to bungee jump from a bridge that is 55.0 m over the river below. The bungee cord has an unstretched length of 27.0 m. To be safe, the bungee cord should stop Jorge’s fall when he is at least 2.00 m above the river. If Jorge has a mass of
> Why is a slow neutron more likely to induce a nuclear reaction (as in neutron activation and induced fission) than a proton with the same kinetic energy?
> 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 rays have a charge-to-mass ratio half that of the H+ i
> Why does a fission reaction tend to release one or more neutrons? Why is the release of neutrons necessary in order to sustain a chain reaction?
> A square brass plate, 8.00 cm on a side, has a hole cut into its center of area 4.908 74 cm2 (at 20.0°C). The hole in the plate is to slide over a cylindrical steel shaft of cross-sectional area 4.910 00 cm2 (also at 20.0°C). To wha
> Why would a fusion reactor produce less radioactive waste than a fission reactor? [Hint: Compare the products of a fission reaction with those from a fusion reaction.]
> Fission reactors and cyclotrons tend to produce different kinds of isotopes. A reactor produces isotopes primarily through neutron activation; thus, the isotopes tend to be neutron-rich (high neutron-to- proton ratio). A cyclotron can only accelerate cha
> Hydrogen bonding is responsible for many of the unusual properties of water (see Sec. 16.1). A simplified model represents a hydrogen bond as the electrostatic interaction of four point charges arranged along a straight line, as shown in the figure. (a)
> Radioactive alpha emitters are relatively harmless outside the body, but can be dangerous if ingested or inhaled. Explain.
> Radon-222 is created in a series of radioactive decays starting with / and ending with / . The half-life of 222Rn is 3.8 days. (a) If the half-life is so short, why hasn’t all the 222Rn gas decayed by now? (b) If the half-life of 222Rn were much sho
> 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?
> The Lyman series in the hydrogen emission spectrum is formed by electron transitions from an excited state to the ground state. Calculate the longest three wavelengths in the Lyman series.
> 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?
> 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
> Explain the difference between speed and velocity.
> 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
