Question: The Bohr theory of the hydrogen atom

> A warm pitcher of lemonade is put into an ice chest. Describe what happens to the entropies of lemonade and ice as heat flows from the lemonade to the ice within the chest.

> Can a heat engine be made to operate without creating any “thermal pollution,” that is, without making its cold reservoir get warmer in the long run? The net work output must be greater than zero.

> A magnetic dipole antenna has its axis aligned with the vertical. The antenna sends out radio waves. If you are due south of the antenna, what is the polarization state of the radio waves that reach you?

> An x-ray diffraction experiment using 16 keV x-rays is repeated using electrons instead of x-rays. What should the kinetic energy of the electrons be in order to produce a diffraction pattern with maxima at the same angles as the x-rays (using the same c

> An 81 kg student who has just studied matter waves is concerned that he may be diffracted as he walks through a doorway that is 81 cm across and 12 cm thick. (a) If the wavelength of the student must be about the same size as the doorway to exhibit diff

> A cylindrical disk has volume 8.97 × 10−3 m3 and mass 8.16 kg. The disk is floating on the surface of some water with its flat surfaces horizontal. The area of each flat surface is 0.640 m2. (a) What is the specific gravity of the disk? (b) How far belo

> The mass density of diamond (a crystalline form of carbon) is 3500 kg/m3. How many carbon atoms per cubic centimeter are there?

> A toy car with a mass of 120 g moves to the right with a speed of 0.75 m/s. A small child drops a 30.0 g piece of clay onto the car. The clay sticks to the car and the car continues to the right. What is the change in speed of the car? Consider the frict

> A solar cell provides an emf of 0.45 V. (a) If the cell supplies a constant current of 18.0 mA for 9.0 h, how much electric energy does it supply? (b) What is the power—the rate at which it supplies electric energy?

> A voltmeter with a resistance of 670 kΩ is used to measure the voltage across the 83.0 kΩ resistor in the figure with Problems 79 and 80. What is the voltmeter reading?

> Is it possible to make a heat pump with a coefficient of performance equal to 1? Explain.

> Lars, of mass 82.4 kg, can do work for about 2.0 min at the rate of 1.0 hp (746 W). How long will it take him to climb three flights of stairs, a vertical height of 12.0 m?

> In an amusement park rocket ride, cars are suspended from 4.25 m cables attached to rotating arms at a distance of 6.00 m from the axis of rotation. The cables swing out at a constant angle of 45.0° when the ride is operating. What is the angu

> A wire with cross-sectional area A carries a current I. Assuming the wire is ohmic, show that the electric field strength E in the wire is proportional to the current per unit area (I/A) and identify the constant of proportionality.

> 1. The image of an object in a plane mirror (a) is always smaller than the object. (b) is always the same size as the object. (c) is always larger than the object. (d) can be larger, smaller, or the same size as the object, depending on the distance betw

> A meson with charge +e composed of up and/or strange quarks and/or antiquarks.

> Light rays travel from left to right through a lens. If a virtual image is formed, on which side of the lens is it? On which side would a real image be found?

> Six wooden blocks (mass m) float in a barrel of water. The blocks are not all made from the same type of wood. The bottom of each block is submerged to a depth d below the water surface. Rank the blocks in order of the buoyant force on them, largest to s

> Michelle is enjoying a picnic across the valley from a cliff. She claps her hands and the echo takes 1.5 s to return. Given that the speed of sound in air is 343 m/s on that day, how far away is the cliff?

> /is radioactive; it decays to / . / is itself radioactive and has a half-life of 4.6 s. At t = 0, a sample contains 4.00 mol of / and 1.50 mol of/. At t = 25 µs, the sample contains 3.00 mol of/ and 2.50 mol of /. How much/ will there be at t = 50 µs?

> What is the purpose of having fins on an automobile or motorcycle radiator?

> Geraldine uses a 423 nm coherent light source and a double slit with a slit separation of 20.0 µm to display three interference maxima on a screen that is 20.0 cm wide. If she wants to spread the three bright fringes across the full width of the screen,

> The posture of small animals may prevent them from being blown over by the wind. For example, with wind blowing from the side, a small insect stands with bent legs; the more bent the legs, the lower the body and the smaller the angle θ. The

> The radioisotope 131I, used to diagnose and treat thyroid conditions, can be produced by neutron activation of tellurium inside a nuclear reactor. A hospital receives a shipment of 131I with an initial activity of 3.7 × 1010 Bq. After 2.5 days, several p

> A highway is made of concrete slabs that are 15 m long at 20.0°C. (a) If the temperature range at the location of the highway is from−20.0°C to +40.0°C, what size expansion gap should be left (at 20.0°C) to prevent buckling of the highway? (b) How larg

> Three equal charges are placed on three corners of a square. If the force that Qa exerts on Qb has magnitude Fba and the force that Qa exerts on Qc has magnitude Fca, what is the ratio of Fca to Fba?

> Diana is standing on a raft of mass 100.0 kg that is floating on a still lake. She decides to walk the length of the raft. If Diana's mass is 55 kg and she walks with a velocity of 0.91 m/s with respect to the shore, how fast and in what direction does t

> Near a large lake, in what direction does a breeze passing over the land tend to blow at night?

> The weight of a boat is listed on specification sheets as its “displacement.” Explain.

> A common flashlight bulb is rated at 0.300 A and 2.90 V (the values of current and voltage under operating conditions). If the resistance of the bulb's tungsten filament at room temperature (20.0°C) is 1.10 Ω, estimate the temperature of the tungsten fil

> Three point charges are placed at the corners of an equilateral triangle having sides of 0.150 m. (a) What is the total electric force on the 2.50 µC charge? (b) What is the electric potential energy of the three charges?

> The force that must be exerted to drive a nail into a wall is roughly as shown in the graph. The first 1.2 cm are through soft drywall; then the nail enters the solid wooden stud. How much work must be done to hammer the nail a horizontal distance of 5.0

> In the crossover network of the figure, the crossover frequency is found to be 252 Hz. The capacitance is C = 560 µF. Assume the inductor to be ideal. (a) What is the impedance of the tweeter branch (the capacitor in series with the 8.0 &Ic

> A soccer ball of diameter 31 cm rolls without slipping at a linear speed of 2.8 m/s. (a) Through how many revolutions has the soccer ball turned as it moves a linear distance of 18 m? (b) What is the ball’s angular speed?

> An elevator cable winds on a drum of radius 90.0 cm that is connected to a motor. (a) If the elevator moves down at 0.50 m/s, what is the angular speed of the drum? (b) If the elevator moves down 6.0 m, how many revolutions has the drum made? (c) What

> Suppose that it takes tensile forces of magnitude F to produce a given strain ΔL/L in a steel wire of cross-sectional area A. If you had two such wires side by side and stretched them simultaneously, what magnitude tensile forces would be required to pro

> 1. If the figure shows the wavefronts for a double-slit interference experiment with light, at which of the labeled points is the intensity zero? The wavefronts represent wave crests only (not crests and troughs). (a) A only (b) B only (c) C only (d) A a

> A metal plant stand on a wooden deck feels colder than the wood around it. Is it necessarily colder? Explain.

> Why are vineyards planted along lakeshores or river-banks in cold climates?

> (a) Use a graphing calculator or computer graphing program to plot y versus x for the function for the times t = 0, 1.0 s, and 2.0 s. Use the values k = (π/5.0) rad/cm and ω = (π/6.0) rad/s. (b) Is this a traveling wave?

> An electric heater is plugged into an ac outlet. Since the ac current changes polarity, there is no net movement of electrons through the heating element; the electrons just tend to oscillate back and forth. How, then, does the heating element heat up? D

> A pendulum bob hung from a string of length L is released from height h above the bottom of its swing. The pendulum’s swing is interrupted by a horizontal peg at height r above the bottom of the pendulum’s swing (point

> A photon is incident on an electron at rest. The scattered photon has a wavelength of 2.81 pm and moves at an angle of 29.5° with respect to the direction of the incident photon. (a) What is the wavelength of the incident photon? (b) What is the final

> Why are several layers of clothing warmer than one coat of equal weight?

> A certain pipe has resonant frequencies of 234 Hz, 390 Hz, and 546 Hz, with no other resonant frequencies between these values. (a) Is this a pipe open at both ends or closed at one end? (b) What is the fundamental frequency of this pipe? (c) How long

> Why is drinking water in a camp located near the equator often kept in porous jars?

> A 40 Hz sound wave is barely audible at a sound intensity level of 60 dB. What is the displacement amplitude of this sound wave? Compare it with the average distance between molecules in air at room temperature, about 3 nm.

> If the angle of incidence is greater than the angle of refraction for a light beam passing an interface, what can be said about the relative values of the indices of refraction and the speed of light in the first and second media?

> In the diagram, regions A and C extend far to the left and right, respectively. The electric field due to the two point charges is zero at some point in which region or regions? Explain.

> The tension in a guitar string is increased by 15%. What happens to the fundamental frequency of the string?

> (a) Assume Earth is a uniform solid sphere. Find the kinetic energy of Earth due to its rotation about its axis. (b) Suppose we could somehow extract 1.0% of Earth's rotational kinetic energy to use for other purposes. By how much would that change the

> A 0.67 mH inductor and a 130Ω. resistor are placed in series with a 24 V battery. (a) How long will it take for the current to reach 67% of its maximum value? (b) What is the maximum energy stored in the inductor? (c) How long will it take for the ene

> A pendulum consists of a bob of mass m attached to the end of a cord of length L. The pendulum is released from a point at a height of L/2 above the lowest point of the swing. What is the tension in the cord as the bob passes the lowest point?

> In a game of pool, suppose that the cue ball initially moves in the −x- direction. After a collision with the 4-ball of equal mass, the cue ball moves at 52.0° above the −x-axis and the 4-ball moves at 38.0° below the −x-axis. Find the ratio of the balls

> A particle collides with a hydrogen atom in the n = 2 state, transferring 15.0 eV of energy to the atom. As a result, the electron breaks away from the hydrogen nucleus. What is the kinetic energy of the electron when it is far from the nucleus?

> A 750 kg automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. The car coasts down the hill and then continues coasting up the other side until it comes to rest. Ignoring frictional forces and air

> 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) What is the wavelength of the ra

> Two copper wires, one double the diameter of the other, have the same current flowing through them. If the thinner wire has a drift speed ν1 and the thicker wire has a drift speed ν2, how do the drift speeds of the charge carriers compare?

> Why do we call the temperature 0 K “absolute zero”? How is 0 K fundamentally different from 0°C or 0°F?

> A 60.0 kg woman stands at one end of a 120 kg raft that is 6.0 m long. The other end of the raft is 0.50 m from a pier. (a) The woman walks toward the pier until she gets to the other end of the raft and stops there. Now what is the distance between the

> When a virtual image is formed by a mirror, is it in front of the mirror or behind it? What about a real image?

> A capacitor and a resistor are connected in parallel across an ac source. The reactance of the capacitor is equal to the resistance of the resistor. Assuming that iC(t) = I sin ωt, sketch graphs of iC(t) and iR(t) on the same axes.

> A transverse wave on a string is described by Find the maximum velocity and the maximum acceleration of a point on the string. Plot graphs for displacement y versus t, velocity vy versus t, and acceleration ay versus t at x = 0.

> A neutron (mass 939.565 MeV/c2) disintegrates into a proton (mass 938.272 MeV/c2), an electron (mass 0.5110 MeV/c2), and an antineutrino (mass negligibly small). What is the sum of the kinetic energies of the particles produced, if the neutron was at res

> The diameter of a certain artery has decreased by 25% due to arteriosclerosis. (a) If the same amount of blood flows through it per unit time as when it was unobstructed, by what percentage has the blood pressure difference between its ends increased?

> An x-ray photon of initial frequency 3.0 × 1019 Hz collides with a free electron at rest; the scattered photon moves off at 90°. What is the frequency of the scattered photon?

> Two parallel long straight wires are suspended by strings of length L = 1.2 m. Each wire has mass per unit length 0.050 kg/m. When one wire carries 25.0 A of current and the other carries 100.0 A, the wires swing apart. (a) How far apart are the wires i

> Grant jumps 1.3 m straight up into the air to slam-dunk a basketball into the net. With what speed did he leave the floor?

> An electron beam in an oscilloscope is deflected by the electric field produced by oppositely charged metal plates. If the electric field between the plates is 2.00 × 105 N/C directed downward, what is the force on each electron when it passes between th

> Why do lakes and rivers freeze first at their surfaces?

> (a) Calculate the capacitance per unit length of an axon of radius 5.0 µm (see Fig. 17.14). The membrane acts as an insulator between the conducting fluids inside and outside the neuron. The membrane is 6.0 nm thick and has a dielectric constant of 7.0.

> (a) Why is the coolant fluid in an automobile kept under high pressure? (b) Why do radiator caps have safety valves, allowing you to reduce the pressure before removing the cap? [Hint: See Fig. 14.7a, the phase diagram for water.]

> Where would you place a third small object with the same charge so that the electric field is zero at the corner of the square labeled A?

> For human eyes, about 70% of the refraction occurs at the cornea; less than 25% occurs at the two surfaces of the lens. Why? [Hint: Consider the indices of refraction.] Is the same thing true for fish eyes?

> Objects that are at rest relative to Earth’s surface are in circular motion due to Earth’s rotation. (a) What is the radial acceleration of an object at the equator? (b) Is the object’s apparent weight greater or less than its weight? Explain. (c) By

> In a conventional exterior wall, a 2 × 6 wooden stud is placed every 16 in. (A stud is an upright support.) The stud runs all the way from the exterior siding to the interior wall and the spaces between studs are filled with insulation. In o

> A hollow metal sphere carries a charge of 6.0 µC. A second hollow metal sphere with a radius that is double the size of the first carries a charge of 18.0 µC. The two spheres are brought into contact with each other, then separated. How much charge is on

> For a capacitor in an ac circuit, explain why the current must be zero when the voltage across the capacitor is maximum.

> Why is the passenger's side mirror in many cars convex rather than plane or concave?

> A karate student hits downward on a stack of concrete blocks supported at both ends. A block breaks. Explain where it starts to break first, at the bottom or at the top. (The block experiences shear, compressive, and tensile stresses. Recall that concret

> Even though heat is not a fluid, Eq. (14-13) has a close analogy in Poiseuille's law, which describes the viscous flow of a fluid through a pipe (see Problem 9.68). (a) Explain the analogy. (b) For two or more thermal conductors in series, the total th

> Two objects with the same surface area are inside an evacuated container. The walls of the container are kept at a constant temperature. Suppose one object absorbs a larger fraction of incident radiation than the other. Explain why that object must emit

> The vertical displacement d of light rays parallel to the axis of a lens is measured as a function of the vertical displacement h of the incident ray from the principal axis as shown in part (a) of the figure. The data are graphed in part (b) of the fi

> In a nuclear reactor, a neutron moving at speed vi in the positive x- direction strikes a deuteron, which is at rest. The neutron is deflected by 90.0° and moves off with speed 0.577vi in the positive y-direction. Find the x- and y-components of the deut

> A thin circular hoop is suspended from a knife edge. Its rotational inertia about the rotation axis (along the knife) is I = 2mr2. Show that it oscillates with the same frequency as a simple pendulum of length equal to the diameter of the hoop.

> Many homes are heated with “radiators,” which are hollow metal devices filled with hot water or steam and located in each room of the house. They are sometimes painted with metallic, high-gloss silver paint so that they look well polished. Does this make

> A town is considering using its lake as a source of power. The average temperature difference from the top to the bottom is 15°C, and the average surface temperature is 22°C. (a) Assuming that the town can set up a reversible engine using the surface an

> The diagram shows a simplified household circuit. Resistor r1 = 240.0 Ω represents a lightbulb; resistor r2 = 12.0 Ω represents a hair dryer. The resistors r = 0.50 Ω (each) represent the resistance of the wiring in th

> How many moles of He are in 13 g of He?

> A plastic water bottle open at the top is three-fourths full of water and is placed on a scale. The bottle has an indentation for a label midway up the side, and a strap has been placed around this indentation. If the strap is tightened, so the bottle is

> A man with a mass of 70 kg stands on one foot. His femur has cross-sectional area of 8.0 cm2 and uncompressed length 50 cm. (a) How much shorter is the femur when he stands on one foot? (b) What is the fractional length change of the femur when the per

> What is the velocity of the scattered electron in Problem 26?

> A room in which the air temperature is held constant may feel warm in the summer but cool in the winter. Explain. [Hint: The walls are not necessarily at the same temperature as the air.]

> (a) Write an equation for a surface seismic wave moving in the −x- direction with amplitude 2.0 cm, period 4.0 s, and wavelength 4.0 km. Assume the wave is harmonic, x is measured in meters, and t is measured in seconds. (b) What is the maximum speed of

> The coefficient of linear expansion of brass is 1.9 × 10−5 °C−1. At 20.0°C, a hole in a sheet of brass has an area of 1.00 mm2. How much larger is the area of the hole at 30.0°C?

> The George Washington Bridge crosses the Hudson River between New York and New Jersey. The span of the steel bridge is about 1.6 km. If the temperature can vary from a low of −15°F in winter to a high of 105°F in summer, by how much might the length of t

> Suppose your handheld calculator will show six places beyond the decimal point. At what minimum speed would an object have to be traveling so that gamma can be seen to be different from 1 on your calculator display? That is, how fast should an object tra

> An astronaut has spent a long time in the International Space Station (ISS) traveling at 7.66 km/s. When he returns to Earth, he is 50 ms younger than his twin brother. How long was he on the ISS? [Hint: Use an approximation from Appendix A.9]

> An object connected to an ideal spring is oscillating without friction on a horizontal surface. Sketch graphs of the kinetic energy, potential energy, and total energy as functions of time for one complete cycle.

> A number of wires carry currents into or out of the page as indicated in the figure. (a) Using loop 1 for Ampere's law, what is the net current through the interior of the loop? (b) Repeat for loop 2.