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college physics reasoning
College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions
If a measurement of an electron’s energy takes 3.0 ns (3.0x10-9 s), what is the minimum possible uncertainty in the energy?
Crystals can be used to do interference experiments with electrons. Consider a crystal with a spacing between atoms of 0.30 nm. If the electron wavelength must be approximately this size to observe interference, what is the electron energy?
Consider a double-slit interference experiment employing electrons. If the separation between two very narrow slits is 150 nm and the electron energy is 10 eV, what is the angle at which the first bright interference fringe is found?
Electrons are used in a single-slit diffraction experiment. We saw in Chapter 25 that such an experiment works well if the slit has a width of 10 times the wavelength. If the slit in an experiment with electrons has a width of 10 nm, what is the electron energy?
In principle, a baseball could be used to do a diffraction experiment. (a) If this experiment were to use a doorway as the diffraction slit, estimate the approximate speed that would be required for the baseball. First estimate the necessary wavelength for the baseball. (b) If the doorway is 10
The mass of an electron is approximately 1800 times smaller than the mass of a proton. If an electron and proton have the same wavelength, what is the ratio of their energies?
X-rays, electrons, and neutrons can all be used in diffraction experiments with crystals. In all three cases, the wavelength must be smaller than the spacing between atoms. Assuming this spacing is d 0.30 nm, calculate the energies of an X-ray photon, an electron, and a neutron with wavelengths
Photons with a frequency of 3.0x1015 Hz shine on a piece of aluminum (work function=4.3 eV). What are the energy and the de Broglie wavelength of the ejected electrons?
Oxygen molecules (O2) in the atmosphere are described by kinetic theory (Chapter 15). What is the average de Broglie wavelength of these molecules at room temperature?
A “thermal neutron” is a neutron whose kinetic energy is equal to kBT, with T = room temperature 300 K. (a) What is the speed of a thermal neutron?(b) What is the wavelength of a thermal neutron?(c) How does the wavelength compare with the spacing between atoms in a solid (about 0.3 nm)? To
If the wavelength of an electron is 150 nm, what is its speed?
(a) What is the wavelength of a photon whose momentum is equal to that of an electron with a speed of 2000 m/s? (b) What is the ratio of their energies?
An electron and a neutron have the same wavelength. What is the ratio of (a) Their kinetic energies (b) Their momenta? Assume the speeds are low enough that you can ignore relativity.
A transmission electron microscope (TEM) operates by focusing electrons to a small spot on the object and then measuring the yield of electrons that pass through the object. Suppose the electrons in a TEM have energies of 5 MeV. (a) Find the electron wavelength. (b) Do you expect this TEM to have
One type of electron microscope, called a scanning electron microscope (SEM), forms an image of the surface of an object by focusing electrons to a small spot on the object and then measuring the yield of reflected electrons. (a) If the electron energy is 100 keV, what is the electron
An electron has the same energy as a photon of blue light (λ = 400 nm). (a) What is the momentum of the electron? (b) What is the ratio of the momentum of the electron to the momentum of the photon?
The kinetic energy of an electron in an atom such as hydrogen is typically around 10 eV. (a) What is the wavelength of an electron with this energy? (b) How does this wavelength compare with the size of an atom? (c) If the energy were decreased by a factor of 10, how much would the wavelength
Consider two particles with masses that differ by a factor of 210. If they have the same wavelengths, what is the ratio of their kinetic energies?
The kinetic energy of an electron is increased by a factor of two. By what factor does the wavelength change?
In Chapter 23 (Example 23.3), we discussed the use of a solar sail to propel a spacecraft. Such a sail would either absorb or reflect light from the Sun, using the resulting impulse to produce a force on the spacecraft. Consider a red laser that emits photons with a wavelength of 620 nm. (a) If
A red laser that operates at a wavelength of 650 nm is directed at a black surface, which completely absorbs the beam. If the laser exerts a force of 10 nN (1.0x10-8 N) on the surface, how many photons are striking the surface every second?
A hydrogen atom emits a photon of energy 3.4 eV. If the atom is at rest before emitting the photon, what is the speed of the atom after emission?
Two photons have different frequencies f1 and f2. If the ratio of their momenta is 3.0, what is the ratio of their frequencies?
The ionization energy of a hydrogen atom is 13.6 eV. When a hydrogen atom absorbs a photon with this energy, the electron is ejected from the atom. (a) What are the frequency and wavelength of a photon with this energy? Where does this photon lie in the electromagnetic spectrum? Could you see
The star Betelgeuse in the constellation Orion is one of the brightest stars in the night sky. It is classified as a “red giant” star, in part because of its color. What is the approximate surface temperature of Betelgeuse?
What is the approximate surface temperature of stars with the color (a) Blue (b) Red
A nuclear fission bomb reaches a temperature of about 108 K when it explodeAs. What is the approximate photon energy at which the blackbody radiation has its highest intensity?
Molybdenum has a work function of 4.2 eV. If light of frequency 2.0x1015 Hz strikes the surface of molybdenum, what is the energy of the ejected electrons?
A device called a photocell detects light by letting it fall onto a metal and then measuring the current from the ejected electrons. You are designing a photocell to work with visible light and are considering the use of either aluminum (work function = 4.3 eV) or cesium (work function = 2.1
The work function of gold is 4.6 eV. Photons of a certain energy are found to eject electrons with a kinetic energy of 2.3 eV. (a) What is the speed of the ejected electrons? (b) What is the photon frequency? (c) If the photon energy is increased by a factor of two, what is the kinetic energy of
The work function for a metal is 5.0 eV. What is the minimum photon frequency that can just eject an electron from the metal?
How many photons does a green laser (λ = 510 nm) with a power rating of 2.0 W emit in 1 microsecond?
A sodium lamp emits light with a wavelength of 590 nm. If the light radiates with a power of 30 W, how many photons does it emit each second?
A hydrogen atom that is initially at rest absorbs a photon with an energy of 2.0 eV. What is the momentum of the atom after it absorbs the photon?
The energy carried by 300 photons is 2.5x 10-16 J. What is the frequency of one of these photons? Where do these photons fall in the electromagnetic spectrum?
Radiation from outer space that reaches the Earth follows a blackbody spectrum with a temperature of about 2.7 K. (a) What is the energy of a typical photon from outer space? (b) Where does this photon fall in the electromagnetic spectrum?
The power absorbed by the receiving antenna for an FM radio is found to be 10 pW (1.0x10-11 W). Approximately how many photons are absorbed by the antenna each second?
An FM radio station transmits at a frequency of 95 MHz and a total power of 100 kW. How many photons does this station emit each second?
How many photons of red light (λ = 600 nm) does it take to have a total energy of 1 J?
Suppose a blackbody emits photons most strongly with a frequency near 2.0 GHz. (a) What is the photon energy? (b) What is the approximate temperature of the blackbody? (c) In what region of the electromagnetic spectrum does this radiation fall?
A photon has an energy of 6.0 eV. What is the frequency of the radiation?
The highest-energy photons emitted by a hydrogen atom have an energy of 13.6 eV. Find the energy, in joules, of one of these photons.
X-rays used by your dentist have a wavelength near 0.070 nm. (a) What is the frequency of this radiation? (b) What is the energy of a single X-ray photon with this wavelength?
A helium–neon laser (λ = 632.8 nm) emits radiation with a power of 100 mW. How many photons does it emit in 1 s?
A helium-neon laser emits red light with λ = 632.8 nm. Find (a) The energy of a single photon and (b) The momentum carried by a single photon.
Find the approximate photon energy for (a) An FM radio signal, (b) The radiation in your microwave oven, (c) Your cell phone signal,(d) The light emitted by a burning match.
Planck’s constant was first used to explain what phenomenon?
Explain why the existence of a cutoff frequency in the photoelectric effect cannot be explained with the wave theory of light.
Suppose the human eye were so sensitive that it could detect a single photon. With input of just a single photon, could our system of rods and cones detect the color of this light?
Human color vision is based on the absorption of light by three different types of cone cells, which are most sensitive to red light, green light, and blue light. (a) Explain how the output of these cells can be used to determine the color of the incident light. (b) Could an eye with just two
Color vision can only be understood using a particle (photon) model of light. Compare color vision to the photoelectric effect, explaining how they are similar and how they differ.
In Section 28.4, we gave a classical explanation of the electron’s spin magnetic moment using the picture of an electron as a spinning ball of electric charge. The neutron has zero net charge, yet it also has a magnetic moment. Explain how a spinning ball with zero net charge can still have a
Explain why the particle nature of light is not apparent in everyday life.
Explain why the wave nature of baseballs and cars is not apparent in everyday life. Provide a calculation to justify your answer.
Which of the following experiments or phenomena are evidence (a) for the wave nature of light, and (b) which are evidence for the existence of photons? (i) Single-slit diffraction (ii) Photoelectric effect (iii) Double-slit interference (iv) Color vision
Astronomers classify the color of stars as red, yellow, white, and blue. Why are green stars never seen? Consider how the eye perceives a mixture of different colors of light.
A blacksmith heats a piece of metal in a furnace. The metal initially glows red and later yellow, and then it gets white hot while glowing brighter as more heat is applied. Is it possible for the metal to get “violet hot” and glow purple if it is hot enough? Why or why not?
The peak (maximum-intensity) wavelength emitted by a glowing piece of metal is found to decrease as time passes. Is the metal being heated, or is it being cooled?
Consider the following types of radiation: visible light, infrared radiation, gamma rays, X-rays, radio waves, and ultraviolet radiation. From smallest to largest, order them according to (a) Their frequency, (b) Their wavelength, (c) Their photon energy.
Apply the Heisenberg uncertainty principle to a car. If you are asked to measure the position of the car, estimate the best accuracy you could expect to achieve with a ruler. Then calculate the minimum possible uncertainty in the car’s momentum. Do you think it is feasible to measure the momentum
An electron and a proton have the same kinetic energy. Which one has the larger momentum?
Blocking ultraviolet radiation is effective in preventing sunburn. Using the concept of photons, describe why human skin is sensitive to ultraviolet frequencies, but much less so to those of visible light.
The (old-fashioned) fi lm used for black-and-white photography is not affected by infrared light, is somewhat sensitive to red light, and exposes rapidly to blue light to the extent that blue fi lters are sometimes used to obtain an appropriate contrast. Give a possible explanation for why the fi
No electrons are ejected when a dim source of red light is directed onto a metallic surface. The intensity of the red light source is increased by a factor of 100. Is it now possible for electrons to be ejected via the photoelectric effect? Why or why not?
Physicists often conduct experiments in which photons are counted one by one as they arrive at a detector. Explain why these experiments are relatively easy for photons of visible light, even easier for X-rays, and hardest for radio waves.
What has greater energy, an ultraviolet photon or an X-ray photon?
Consider a microscope that uses electrons instead of photons. Under what conditions will this microscope have better resolution than a microscope that uses visible light? Consider the electron’s energy and wavelength.
You have two lightbulbs: one gives off green light with a very low intensity, and the other emits red light with a very high intensity. (a) Which one emits photons with a higher energy? (b) If these two lightbulbs emit the same intensity, which one emits more photons each second?
Estimate the de Broglie wavelength of a car that (a) has a speed of 100 mi/h, (b) has a speed of 10,000 mi/h, (c) is at rest.
GPS and relativity. The Global Positioning System (GPS) consists of a network of about 30 satellites in orbit, each carrying atomic clocks on board. The orbital radius of the satellites is about four Earth radii (26,600 km). The orbits are nearly circular, with a typical eccentricity of less than
Suppose you take a trip to Mars, which is 80 million km from the Earth. You head directly toward Mars on your spaceship, traveling at 0.80c. Unbeknownst to you, your mortal enemy placed a bomb on your ship that has a 4-minute timer that was initiated upon your departure. Will you live long enough
Gravitational red shift. An important consequence of Einstein’s general relativity is that gravity must affect a light wave’s frequency and wavelength. As light moves upward from the Earth’s surface, the wavelength of the light increases and the frequency decreases as gravity “drains” the
By what amount is the diameter of the Moon shortened (as measured by a stationary observer on the Earth) due to its orbital motion around the Earth?
Thomas Jefferson National Accelerator Facility in Newport News, Virginia, is host to a continuous electron beam. Within the facility, electrons travel around a 7/8-mi-long tunnel five times in 23.5 millionths of a second. (Actually, the facility is capable of producing even higher speeds.) (a)
One consequence of general relativity is that a clock in a gravitational field runs slower. This time dilation is distinct from the time dilation from relative motion (special relativity) and is given by ∆t = ∆t0/√ 1 - 2 2GM/(Rc2), where ∆t is the dilated time, ∆t0 is the time when no
Suppose a rocket ship leaves the Earth in the year 2020. One of a set of twins born in 2000 remains on the Earth while the other rides in the rocket. The rocket ship travels at 0.90c in a straight line path for 10 years as measured by its own clock, turns around, and travels straight back at 0.90c
Suppose an electron is accelerated from rest through a potential difference of 100,000 volts. Determine the electron’s final kinetic energy, speed, and momentum (a) ignoring relativistic effects and (b) including relativistic effects.
Falling light. According to general relativity and the equivalence principle, light is bent by gravity. Suppose you stand two tall, perfectly reflecting mirrors exactly 1 m apart and facing each other. A beam of light is directed horizontally through a hole in one of the mirrors 10 m above the
As we’ll discuss in Chapter 30, radioactive decay involves the nucleus of an atom decaying by emitting either a particle or energy or both. The 216Po nucleus decays to 212Pb by emitting an alpha particle, which is a helium nucleus, 4He. Using the mass data given in Appendix A, find (a) The mass
Consider a proton moving at relativistic speed. (a) Determine the proton’s rest energy in electron volts (1 eV = 1.60 × 10-19 J). (b) Suppose the total energy of the proton is three times its rest energy. With what speed is the proton moving? (c) At this speed, determine the kinetic energy of
Like all stars, the Sun converts mass into energy that radiates out in all directions. The average rate at which this radiant energy reaches the Earth is approximately 1.4 × 103 W/m2. (a) Calculate the rate at which the Sun is losing mass. (b) Assuming this rate remains constant, how long will
Suppose two highly precise, identical clocks are synchronized and one clock is placed on the North Pole and the other on the equator. After 100 years, how much will the clocks differ in time? Assume the Earth is a perfect sphere.
An electron has a momentum equal to that of a baseball (m = 0.22 kg). If this baseball has a speed of 45 m/s (about 100 mi/h), what is the kinetic energy of the electron?
The space shuttle has a length of 37 m. (a) In its normal orbital motion around the Earth, the shuttle has speed of about 8000 m/s and an orbital period of about 90 minutes. Allowing for length contraction, what is the length of the shuttle as viewed by an observer at rest on the ground? (b)
The kinetic energy of a particle of rest mass m0 is equal to three times its rest energy. What is the momentum of the particle? Express your answer in terms of m0.
The Large Hadron Collider (LHC) is an accelerator at the Center for European Nuclear Research in Geneva, Switzerland. It uses collisions between protons to generate and study quarks and other elementary particles. If the kinetic energy of a proton in the LHC is 7.0 TeV ( 7.0 × 1012 eV), what
What is the relativistic momentum of an electron whose relativistic kinetic energy is 4.0 × 10-22 J?
The muon in Example 27.4 has a relativistic momentum of 4.0 × 10-19 kg m/s. The rest mass of a muon is m0 = 1.9 × 10-28 kg. Find the kinetic energy of the muon.
Cosmic rays are particles that bombard the Earth from space, and it is believed that most cosmic rays originate outside of our solar system. Some cosmic rays have extremely high energies. On the night of October 15, 1991, a cosmic-ray detector in Utah detected a cosmic-ray proton with an energy of
A 1.5-V battery is connected to a 10-W light bulb. After 1 day, how much has the mass of the battery changed?
In Chapter 23, we learned that an accelerating electric charge produces electromagnetic waves. In the same way, the general theory of relativity predicts that an accelerated mass produces gravitational waves. As the Earth moves in orbit around the Sun, it undergoes accelerated motion (i.e., uniform
In 2005, the total energy “consumed” by people on Earth was about 5 × 1020 J. About 85% of this was from the burning of fossil fuels. Equating this energy gained by burning fossil fuel in 2005 with mass (according to the mass–energy relation of relativity), how much mass was converted to
One kg of the chemical explosive TNT releases approximately 4.2 × 106 J of energy when it explodes. How much of the initial mass of TNT is converted to energy in such an explosion?
The most common helium nucleus in nature contains two protons and two neutrons. The mass of this nucleus is 6.64466 × 10-27 kg, while the mass of a proton is 1.67262 × 10-27 kg and the mass of a neutron is 1.67493 × 10-27 kg. Find the binding energy of this helium nucleus.
A chemical reaction that produces water molecules is2H2 + O2 → 2H2OThis reaction releases 570 kJ for each mole of oxygen molecules that is consumed. The relativistic relation between mass and energy then implies that the mass of two hydrogen molecules plus the mass of one oxygen molecule is
A proton has a kinetic energy of 1.5 × 107 eV. What is its speed?
Cosmic-ray protons have been observed with kinetic energies claimed to be as high as 1020 eV. What is the speed of these protons? Express your answer as c - v where v is the speed of the protons.
An electron in a television picture tube has a classical kinetic energy of 30 keV, which is the kinetic energy that Newton would calculate using the measured speed and rest mass of the electron. What is the actual kinetic energy of the electron; that is, what is the value found using the
An asteroid of mass 2500 kg has a (relativistic) kinetic energy of 1.5 × 1020 J. What is the speed of the asteroid?
Annihilate this. The anti-proton is a type of antimatter and is the antimatter “cousin” of the proton; the two particles have the same rest mass. It is possible for a proton and an anti-proton to annihilate each other, producing pure energy in the form of electromagnetic radiation (Chapter 31).
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