Question: Find the longest and shortest wavelengths in

> Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the seco

> An enemy spaceship is moving toward your starfighter with a speed, as measured in your frame, of 0.400c. The enemy ship fires a missile toward you at a speed of 0.700c relative to the enemy ship (Fig. E37.18). a. What is the speed of the missile relativ

> A telescope is constructed from two lenses with focal lengths of 95.0 cm and 15.0 cm, the 95.0-cm lens being used as the objective. Both the object being viewed and the final image are at infinity. a. Find the angular magnification for the telescope. b

> A pursuit spacecraft from the planet Tatooine is attempting to catch up with a Trade Federation cruiser. As measured by an observer on Tatooine, the cruiser is traveling away from the planet with a speed of 0.600c. The pursuit ship is traveling at a spee

> If simultaneity is not an absolute concept, does that mean that we must discard the concept of causality? If event A is to cause event B, A must occur first. Is it possible that in some frames A appears to be the cause of B, and in others B appears to be

> The focal length of the eyepiece of a certain microscope is 18.0 mm. The focal length of the objective is 8.00 mm. The distance between objective and eyepiece is 19.7 cm. The final image formed by the eyepiece is at infinity. Treat all lenses as thin. a

> Space pilot Mavis zips past Stanley at a constant speed relative to him of 0.800c. Mavis and Stanley start timers at zero when the front of Mavis’s ship is directly above Stanley. When Mavis reads 5.00 s on her timer, she turns on a bright light under th

> A rocket ship flies past the earth at 91.0% of the speed of light. Inside, an astronaut who is undergoing a physical examination is having his height measured while he is lying down parallel to the direction in which the ship is moving. a. If his height

> As measured by an observer on the earth, a spacecraft runway on earth has a length of 3600 m. a. What is the length of the runway as measured by a pilot of a spacecraft flying past at a speed of 4.00 * 107 m/s relative to the earth? b. An observer on e

> If the person in Exercise 34.54 chooses ordinary glasses over contact lenses, what power lens (in diopters) does she need to correct her vision if the lenses are 2.0 cm in front of the eye? From Exercise 34.54 A person can see clearly up close but canno

> A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. a. Is she nearsighted or farsighted? b. What type of lens (converging or diverging) is needed to correct her vision? c. Wh

> Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their p

> An unstable particle is created in the upper atmosphere from a cosmic ray and travels straight down toward the surface of the earth with a speed of 0.99540c relative to the earth. A scientist at rest on the earth’s surface measures that the particle is c

> a. Where is the near point of an eye for which a contact lens with a power of +2.75 diopters is prescribed? b. Where is the far point of an eye for which a contact lens with a power of -1.30 diopters is prescribed for distant vision?

> Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 µs. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth’s surface, and they travel very close to the speed of light. The pr

> An object 0.600 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0 cm. a. Draw a principal-ray diagram showing the formation of the image. b. Determine the position, size, orientation,

> A camera lens has a focal length of 180.0 mm and an aperture diameter of 16.36 mm. a. What is the ƒ-number of the lens? b. If the correct exposure of a certain scene is 1/30 s at f/11, what is the correct exposure at f/2.8?

> An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.150 s. The first officer on the spacecraft measures that the searchlight is on for 12.0 ms. a. Which of these two measured t

> A spacecraft flies away from the earth with a speed of 4.80 * 106 m/s relative to the earth and then returns at the same speed. The spacecraft carries an atomic clock that has been carefully synchronized with an identical clock that remains at rest on ea

> As you pilot your space utility vehicle at a constant speed toward the moon, a race pilot flies past you in her spaceracer at a constant speed of 0.800c relative to you. At the instant the spaceracer passes you, both of you start timers at zero. a. At t

> The negative pion (π-) is an unstable particle with an average lifetime of 2.60 * 10-8 s (measured in the rest frame of the pion). a. If the pion is made to travel at very high speed relative to a laboratory, its average lifetime is measured in the labo

> The crystalline lens of the human eye is a double-convex lens made of material having an index of refraction of 1.44 (although this varies). Its focal length in air is about 8.0 mm, which also varies. We shall assume that the radii of curvature of its tw

> Two thin lenses with a focal length of magnitude 12.0 cm, the first diverging and the second converging, are located 9.00 cm apart. An object 2.50 mm tall is placed 20.0 cm to the left of the first (diverging) lens. a. How far from this first lens is th

> Repeat Exercise 34.41 using the same lenses except for the following changes: a. The second lens is a diverging lens having a focal length of magnitude 60.0 cm. b. The first lens is a diverging lens having a focal length of magnitude 40.0 cm. c. Both

> You are standing on a train platform watching a high-speed train pass by. A light inside one of the train cars is turned on and then a little later it is turned off. a. Who can measure the proper time interval for the duration of the light: you or a pas

> What do you think would be different in everyday life if the speed of light were 10 m/s instead of 3.00 * 108 m/s ?

> A pencil that is 9.0 cm long is held perpendicular to the surface of a plane mirror with the tip of the pencil lead 12.0 cm from the mirror surface and the end of the eraser 21.0 cm from the mirror surface. What is the length of the image of the pencil t

> Consider a particle with mass m moving in a potential U = 1/2 kx2, as in a mass–spring system. The total energy of the particle is E =(p2/2m)+ 1/2 kx2. Assume that p and x are approximately related by the Heisenberg uncertainty principle, so px ≈ h. a.

> To investigate the structure of extremely small objects, such as viruses, the wavelength of the probing wave should be about one-tenth the size of the object for sharp images. But as the wavelength gets shorter, the energy of a photon of light gets great

> The neutral pion (π0) is an unstable particle produced in high-energy particle collisions. Its mass is about 264 times that of the electron, and it exists for an average lifetime of 8.4 * 10-17 s before decaying into two gamma-ray photons. Using the rela

> Suppose that the uncertainty of position of an electron is equal to the radius of the n = 1 Bohr orbit for hydrogen. Calculate the simultaneous minimum uncertainty of the corresponding momentum component, and compare this with the magnitude of the moment

> High-speed electrons are used to probe the interior structure of the atomic nucleus. For such electrons the expression l = h/p still holds, but we must use the relativistic expression for momentum, p = mv/ 1 −v2/c2 . a. Show that the

> What is the de Broglie wavelength of a red blood cell, with mass 1.00 * 10-11 g, that is moving with a speed of 0.400 cm/s? Do we need to be concerned with the wave nature of the blood cells when we describe the flow of blood in the body?

> A beam of 40-eV electrons traveling in the +xdirection passes through a slit that is parallel to the y-axis and 5.0 µm wide. The diffraction pattern is recorded on a screen 2.5 m from the slit. a. What is the de Broglie wavelength of the el

> a. Write the Planck distribution law in terms of the frequency f, rather than the wavelength λ, to obtain I(f). b. Show that where I(λ) is the Planck distribution formula of Eq. (39.24). Hint: Change the integration variable

> In the Bohr model of the hydrogen atom, what is the de Broglie wavelength of the electron when it is in a. the n = 1 level and b. the n = 4 level? In both cases, compare the de Broglie wavelength to the circumference 2prn of the orbit.

> a. What is the smallest amount of energy in electron volts that must be given to a hydrogen atom initially in its ground level so that it can emit the Ha line in the Balmer series? b. How many different possibilities of spectral-line emissions are there

> Repeat Exercise 34.38 for the case in which the lens is diverging, with a focal length of -48.0 cm. From Exercise 34.38: A converging lens with a focal length of 12.0 cm forms a virtual image 8.00 mm tall, 17.0 cm to the right of the lens. Determine the

> A large number of hydrogen atoms are in thermal equilibrium. Let n2/n1 be the ratio of the number of atoms in an n = 2 excited state to the number of atoms in an n = 1 ground state. At what temperature is n2 /n1 equal to a. 10-12; b. 10-8; c. 10-4? d

> Calculate the de Broglie wavelength of a 5.00-g bullet that is moving at 340 m/s. Will the bullet exhibit wavelike properties?

> What is the de Broglie wavelength for an electron with speed a. v = 0.480c and b. v = 0.960c? (Hint: Use the correct relativistic expression for linear momentum if necessary.)

> a. A nonrelativistic free particle with mass m has kinetic energy K. Derive an expression for the de Broglie wavelength of the particle in terms of m and K. b. What is the de Broglie wavelength of an 800-eV electron?

> An electron is moving with a speed of 8.00 * 106 m/s. What is the speed of a proton that has the same de Broglie wavelength as this electron?

> a. The uncertainty in the y-component of a proton’s position is 2.0 * 10-12 m. What is the minimum uncertainty in a simultaneous measurement of the y-component of the proton’s velocity? b. The uncertainty in the z-component of an electron’s velocity is

> The wavelength 10.0 mm is in the infrared region of the electromagnetic spectrum, whereas 600 nm is in the visible region and 100 nm is in the ultraviolet. What is the temperature of an ideal blackbody for which the peak wavelength lm is equal to each of

> The shortest visible wavelength is about 400 nm. What is the temperature of an ideal radiator whose spectral emittance peaks at this wavelength?

> An alpha particle (m = 6.64 * 10-27 kg) emitted in the radioactive decay of uranium-238 has an energy of 4.20 MeV. What is its de Broglie wavelength?

> An electron has a de Broglie wavelength of 2.80 * 10-10 m. Determine a. the magnitude of its momentum and b. its kinetic energy (in joules and in electron volts).

> Why do you think the development of Newtonian mechanics preceded the more refined relativistic mechanics by so many years?

> a. Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. b. Calculate the orbital period in each of these levels. c. The average lifetime of the first excited level of a hydrogen atom is 1.0 * 10-8

> A hydrogen atom initially in its ground level absorbs a photon, which excites the atom to the n = 3 level. Determine the wavelength and frequency of the photon.

> For crystal diffraction experiments (discussed in Section 39.1), wavelengths on the order of 0.20 nm are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is a. a photon; b. an electron; c. an alp

> A hydrogen atom is in a state with energy -1.51 eV. In the Bohr model, what is the angular momentum of the electron in the atom, with respect to an axis at the nucleus?

> The silicon–silicon single bond that forms the basis of the mythical silicon-based creature the Horta has a bond strength of 3.80 eV. What wavelength of photon would you need in a (mythical) phasor disintegration gun to destroy the Horta?

> A CD-ROM is used instead of a crystal in an electron diffraction experiment. The surface of the CD-ROM has tracks of tiny pits with a uniform spacing of 1.60 mm. a. If the speed of the electrons is 1.26 * 104 m/s, at which values of θ will the m = 1 and

> a. In an electron microscope, what accelerating voltage is needed to produce electrons with wavelength 0.0600 nm? b. If protons are used instead of electrons, what accelerating voltage is needed to produce protons with wavelength 0.0600 nm? (Hint: In e

> A beam of neutrons that all have the same energy scatters from atoms that have a spacing of 0.0910 nm in the surface plane of a crystal. The m = 1 intensity maximum occurs when the angle θ in Fig. 39.2 is 28.6°. What is the kinetic energy (in electron vo

> Through what potential difference must electrons be accelerated if they are to have a. the same wavelength as an x ray of wavelength 0.220 nm and b. the same energy as the x ray in part (a)?

> In principle, does a hot gas have more mass than the same gas when it is cold? Explain. In practice, would this be a measurable effect? Explain.

> a. An electron moves with a speed of 4.70 * 106 m/s. What is its de Broglie wavelength? b. A proton moves with the same speed. Determine its de Broglie wavelength.

> Elements in the gaseous state emit line spectra with well-defined wavelengths. But hot solid bodies always emit a continuous spectrum—that is, a continuous smear of wavelengths. Can you account for this difference?

> How might the energy levels of an atom be measured directly—that is, without recourse to analysis of spectra?

> Galaxies tend to be strong emitters of Lyman-α photons (from the n = 2 to n = 1 transition in atomic hydrogen). But the intergalactic medium—the very thin gas between the galaxies— tends to absorb Lyman-α photons. What can you infer from these observatio

> Does a photon have a de Broglie wavelength? If so, how is it related to the wavelength of the associated electromagnetic wave? Explain.

> If a proton and an electron have the same kinetic energy, which has the longer de Broglie wavelength? Explain.

> Equation (39.30) states that the energy of a system can have uncertainty. Does this mean that the principle of conservation of energy is no longer valid? Explain.

> Does the uncertainty principle have anything to do with marksmanship? That is, is the accuracy with which a bullet can be aimed at a target limited by the uncertainty principle? Explain.

> Why go through the expense of building an electron microscope for studying very small objects such as organic molecules? Why not just use extremely short electromagnetic waves, which are much cheaper to generate?

> You have been asked to design a magnet system to steer a beam of 54-eV electrons like those described in Example 39.1 (Section 39.1). The goal is to be able to direct the electron beam to a specific target location with an accuracy of ±1.0

> A high-speed train passes a train platform. Larry is a passenger on the train, Adam is standing on the train platform, and David is riding a bicycle toward the platform in the same direction as the train is traveling. Compare the length of a train car as

> Do the planets of the solar system obey a distance law (rn = n2r1) as the electrons of the Bohr atom do? Should they? Why (or why not)? (Consult Appendix F for the appropriate distances.)

> If a proton and an electron have the same speed, which has the longer de Broglie wavelength? Explain.

> a. Show that in the Bohr model, the frequency of revolution of an electron in its circular orbit around a stationary hydrogen nucleus is f = me4/4ϵ02n3h3. b. In classical physics, the frequency of revolution of the electron is equal to the f

> You have entered a contest in which the contestants drop a marble with mass 20.0 g from the roof of a building onto a small target 25.0 m below. From uncertainty considerations, what is the typical distance by which you will miss the target, given that y

> A pulsed dye laser emits light of wavelength 585 nm in 450-ms pulses. Because this wavelength is strongly absorbed by the hemoglobin in the blood, the method is especially effective for removing various types of blemishes due to blood, such as port-wine–

> While interacting with molecules (mainly water) in the tumor tissue, each Compton electron or photoelectron causes a series of ionizations, each of which takes about 40 eV. Estimate the maximum number of ionizations that one photon generated by this line

> When ultraviolet light with a wavelength of 400.0 nm falls on a certain metal surface, the maximum kinetic energy of the emitted photoelectrons is measured to be 1.10 eV. What is the maximum kinetic energy of the photoelectrons when light of wavelength 3

> What would the minimum work function for a metal have to be for visible light (380–750 nm) to eject photoelectrons?

> A clean nickel surface is exposed to light of wavelength 235 nm. What is the maximum speed of the photoelectrons emitted from this surface? Use Table 38.1. From table 38.1: Work Functions of TABLE 38.1 Several Elements Element Work Function (eV) Al

> A laser produces light of wavelength 625 nm in an ultrashort pulse. What is the minimum duration of the pulse if the minimum uncertainty in the energy of the photons is 1.0%?

> The cornea behaves as a thin lens of focal length approximately 1.8 cm, although this varies a bit. The material of which it is made has an index of refraction of 1.38, and its front surface is convex, with a radius of curvature of 5.0 mm. a. If this fo

> A horizontal beam of laser light of wavelength 585 nm passes through a narrow slit that has width 0.0620 mm. The intensity of the light is measured on a vertical screen that is 2.00 m from the slit. a. What is the minimum uncertainty in the vertical com

> An ultrashort pulse has a duration of 9.00 fs and produces light at a wavelength of 556 nm. What are the momentum and momentum uncertainty of a single photon in the pulse?

> A 16.0-cm-long pencil is placed at a 45.0° angle, with its center 15.0 cm above the optic axis and 45.0 cm from a lens with a 20.0-cm focal length as shown in Fig. P34.106. (Note that the figure is not drawn to scale.) Assume that the diameter

> X rays with an initial wavelength of 0.900 * 10-10 m undergo Compton scattering. For what scattering angle is the wavelength of the scattered x rays greater by 1.0% than that of the incident x rays?

> A photon scatters in the backward direction (ɸ = 180°) from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0% change in wavelength as a result of the scattering?

> The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a single photon of green light will trigger receptor cells in the rods of the ret

> If a photon of wavelength 0.04250 nm strikes a free electron and is scattered at an angle of 35.0° from its original direction, find a. the change in the wavelength of this photon; b. the wavelength of the scattered light; c. the change in energy of th

> A photon with wavelength λ = 0.1385 nm scatters from an electron that is initially at rest. What must be the angle between the direction of propagation of the incident and scattered photons if the speed of the electron immediately after the collision is

> X rays are produced in a tube operating at 24.0 kV. After emerging from the tube, x rays with the minimum wavelength produced strike a target and undergo Compton scattering through an angle of 45.0°. a. What is the original x-ray wavelength? b. What is

> An x ray with a wavelength of 0.100 nm collides with an electron that is initially at rest. The x ray’s final wavelength is 0.110 nm. What is the final kinetic energy of the electron?

> The average life span in the United States is about 70 years. Does this mean that it is impossible for an average person to travel a distance greater than 70 light-years away from the earth? (A light-year is the distance light travels in a year.) Explain

> A certain very nearsighted person cannot focus on anything farther than 36.0 cm from the eye. Consider the simplified model of the eye described in Exercise 34.50. If the radius of curvature of the cornea is 0.75 cm when the eye is focusing on an object

> In one form of cataract surgery the person’s natural lens, which has become cloudy, is replaced by an artificial lens. The refracting properties of the replacement lens can be chosen so that the person’s eye focuses on distant objects. But there is no ac

> A camera with a 90-mm-focal-length lens is focused on an object 1.30 m from the lens. To refocus on an object 6.50 m from the lens, by how much must the distance between the lens and the sensor be changed? To refocus on the more distant object, is the le

> a. what is the minimum potential difference between the filament and the target of an x-ray tube if the tube is to produce x rays with a wavelength of 0.150 nm? b. What is the shortest wavelength produced in an x-ray tube operated at 30.0 kV?

> The smallest object we can resolve with our eye is limited by the size of the light receptor cells in the retina. In order for us to distinguish any detail in an object, its image cannot be any smaller than a single retinal cell. Although the size depend

> Protons are accelerated from rest by a potential difference of 4.00 kV and strike a metal target. If a proton produces one photon on impact, what is the minimum wavelength of the resulting x rays? How does your answer compare to the minimum wavelength if

> The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.0 kV, what are the shortest-wavelength x rays produced by the television?

> The photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find a. the stopping potential in volts; b. the kinetic energy, in electron volts, of the most energetic electrons ejected; c. the spe