Question: There is a certain probability that a

> 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 Does this mean that the principle of conservation of energy is no longer valid?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

> In a photoelectric-effect experiment, the photocurrent i for large positive values of VAC has the same value no matter what the light frequency f (provided that f is higher than the threshold frequency f0). Explain why.

> Human skin is relatively insensitive to visible light, but ultraviolet radiation can cause severe burns. Does this have anything to do with photon energies? Explain.

> A double-convex thin lens has surfaces with equal radii of curvature of magnitude 2.50 cm. Using this lens, you observe that it forms an image of a very distant tree at a distance of 1.87 cm from the lens. What is the index of refraction of the lens?

> Would you expect effects due to the photon nature of light to be generally more important at the low-frequency end of the electromagnetic spectrum (radio waves) or at the high-frequency end (x rays and gamma rays)? Why?

> According to the photon model, light carries its energy in packets called quanta or photons. Why then don’t we see a series of flashes when we look at things?

> Some lasers emit light in pulses that are only 10-12 s in duration. The length of such a pulse is (3 * 108 m/s)(10-12 s) = 3 * 10-4 m = 0.3 mm. Can pulsed laser light be as monochromatic as light from a laser that emits a steady, continuous beam? Explain

> Why must engineers and scientists shield against x-ray production in high-voltage equipment?

> The cornea of the eye has a radius of curvature of approximately 0.50 cm, and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the cornea itself is small enough that we shall neglect it. The depth of a typical human eye is

> Can Compton scattering occur with protons as well as electrons? For example, suppose a beam of x rays is directed at a target of liquid hydrogen. (Recall that the nucleus of hydrogen consists of a single proton.) Compared to Compton scattering with elect

> Figure P34.81 shows an object and its image formed by a thin lens. a. What is the focal length of the lens, and what type of lens (converging or diverging) is it? b. What is the height of the image? Is it real or virtual? Figure P34.81 Image Objec

> In a photoelectric-effect experiment, which of the following will increase the maximum kinetic energy of the photoelectrons? a. Use light of greater intensity; b. use light of higher frequency; c. use light of longer wavelength; d. use a metal surfac

> In a particle accelerator a proton moves with constant speed 0.750c in a circle of radius 628 m. What is the net force on the proton?

> A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall 6.00 m to the right of the slide. The image is 80.0 times the size of the slide. a. How far is the slide from the lens? b. Is the image erect or inverted

> One of the wavelengths of light emitted by hydrogen atoms under normal laboratory conditions is l = 656.3 nm, in the red portion of the electromagnetic spectrum. In the light emitted from a distant galaxy this same spectral line is observed to be Doppler

> a. You want to use a lens with a focal length of 35.0 cm to produce a real image of an object, with the height of the image twice the height of the object. What kind of lens do you need, and where should the object be placed? b. Suppose you want a virtu

> In certain radioactive beta decay processes, the beta particle (an electron) leaves the atomic nucleus with a speed of 99.95% the speed of light relative to the decaying nucleus. If this nucleus is moving at 75.00% the speed of light in the laboratory re

> What should be the index of refraction of a transparent sphere in order for paraxial rays from an infinitely distant object to be brought to a focus at the vertex of the surface opposite the point of incidence?

> A nuclear bomb containing 12.0 kg of plutonium explodes. The sum of the rest masses of the products of the explosion is less than the original rest mass by one part in 104. a. How much energy is released in the explosion? b. If the explosion takes pla

> In our universe, the rest energy of an electron is approximately 8.2 * 10-14 J. What would it be in the alternate universe? a. 8.2 * 10-8 J; b. 8.2 * 10-26 J; c. 8.2 * 10-2 J; d. 0.82 J.

> Scientists working with a particle accelerator determine that an unknown particle has a speed of 1.35 * 108 m/s and a momentum of 2.52 * 10-19 kg.m/s. From the curvature of the particle’s path in a magnetic field, they also deduce that it has a positive

> The Russian physicist P. A. Cerenkov discovered that a charged particle traveling in a solid with a speed exceeding the speed of light in that material radiates electromagnetic radiation. (This is analogous to the sonic boom produced by an aircraft movin

> Physicists and engineers from around the world came together to build the largest accelerator in the world, the Large Hadron Collider (LHC) at the CERN Laboratory in Geneva, Switzerland. The machine accelerates protons to high kinetic energies in an unde

> Inside a spaceship flying past the earth at three-fourths the speed of light, a pendulum is swinging. a. If each swing takes 1.80 s as measured by an astronaut performing an experiment inside the spaceship, how long will the swing take as measured by a

> A spaceship is traveling toward the earth from the space colony on Asteroid 1040A. The ship is at the halfway point of the trip, passing Mars at a speed of 0.9c relative to the Mars frame of reference. At the same instant, a passenger on the spaceship re

> A light bulb is 3.00 m from a wall. You are to use a concave mirror to project an image of the bulb on the wall, with the image 3.50 times the size of the object. How far should the mirror be from the wall? What should its radius of curvature be?

> A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.00 m from the mirror. The filament is 6.00 mm tall, and the image is to be 24.0 cm tall. a. How far in front of the vertex of the mirror should the filament be placed

> Where must you place an object in front of a concave mirror with radius R so that the image is erect and 2 1 2 times the size of the object? Where is the image?

> A spacecraft of the Trade Federation flies past the planet Coruscant at a speed of 0.600c. A scientist on Coruscant measures the length of the moving spacecraft to be 74.0 m. The spacecraft later lands on Coruscant, and the same scientist measures the le

> a. Through what potential difference does an electron have to be accelerated, starting from rest, to achieve a speed of 0.980c? b. What is the kinetic energy of the electron at this speed? Express your answer in joules and in electron volts.

> A reflecting telescope (Fig. E34.63) is to be made by using a spherical mirror with a radius of curvature of 1.30 m and an eyepiece with a focal length of 1.10 cm. The final image is at infinity. a. What should the distance between the eyepiece and the

> The eyepiece of a refracting telescope (see Fig. 34.53) has a focal length of 9.00 cm. The distance between objective and eyepiece is 1.20 m, and the final image is at infinity. What is the angular magnification of the telescope? From Fig. 34.53 34

> When a particle meets its antiparticle, they annihilate each other and their mass is converted to light energy. The United States uses approximately 1.0 * 1020 J of energy per year. a. If all this energy came from a futuristic antimatter reactor, how mu

> The image formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. a. What is the angular magnification of the microscope? b. The unaided eye can distinguish two

> What is the speed of a particle whose kinetic energy is equal to a. its rest energy and b. five times its rest energy?

> A person swimming 0.80 m below the surface of the water in a swimming pool looks at the diving board that is directly overhead and sees the image of the board that is formed by refraction at the surface of the water. This image is a height of 5.20 m abov

> The laws of optics also apply to electromagnetic waves invisible to the eye. A satellite TV dish is used to detect radio waves coming from orbiting satellites. Why is a curved reflecting surface (a “dish”) used? The dish is always concave, never convex;

> You want to view through a magnifier an insect that is 2.00 mm long. If the insect is to be at the focal point of the magnifier, what focal length will give the image of the insect an angular size of 0.032 radian?

> The focal length of a simple magnifier is 8.00 cm. Assume the magnifier is a thin lens placed very close to the eye. a. How far in front of the magnifier should an object be placed if the image is formed at the observer’s near point, 25.0 cm in front of

> A thin lens with a focal length of 6.00 cm is used as a simple magnifier. a. What angular magnification is obtainable with the lens if the object is at the focal point? b. When an object is examined through the lens, how close can it be brought to the

> An electron is acted upon by a force of 5.00 * 10-15 N due to an electric field. Find the acceleration this force produces in each case: a. The electron’s speed is 1.00 km/s. b. The electron’s speed is 2.50 * 108 m/s and the force is parallel to the ve

> How fast must a rocket travel relative to the earth so that time in the rocket “slows down” to half its rate as measured by earth based observers? Do present-day jet planes approach such speeds?

> a. At what speed is the momentum of a particle twice as great as the result obtained from the nonrelativistic expression mv? Express your answer in terms of the speed of light. b. A force is applied to a particle along its direction of motion. At what

> Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 45.0 cm from hi

> As you have seen, relativistic calculations usually involve the quantity γ. When γ is appreciably greater than 1, we must use relativistic formulas instead of Newtonian ones. For what speed v (in terms of c) is the value of γ a. 1.0% greater than 1; b.

> In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the bending occurs at the cornea, whose vertex is 2.60 cm from the retina. What should be the radius of curvature of the cor

> A proton has momentum with magnitude p0 when its speed is 0.400c. In terms of p0, what is the magnitude of the proton’s momentum when its speed is doubled to 0.800c?

> A speck of dirt is embedded 3.50 cm below the surface of a sheet of ice (n = 1.309). What is its apparent depth when viewed at normal incidence?

> Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. a. For a distant

> When a camera is focused, the lens is moved away from or toward the digital image sensor. If you take a picture of your friend, who is standing 3.90 m from the lens, using a camera with a lens with an 85-mm focal length, how far from the sensor is the le

> You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. a. If the slide is placed 15.0 cm from the lens, what focal length lens is required? b. If the dimensions of the picture on a 35-mm color slide are 24 mm *

> A camera lens has a focal length of 200 mm. How far from the lens should the subject for the photo be if the lens is 20.4 cm from the sensor?

> Electromagnetic radiation from a star is observed with an earth-based telescope. The star is moving away from the earth at a speed of 0.520c. If the radiation has a frequency of 8.64 * 1014 Hz in the rest frame of the star, what is the frequency measured

> An observer in frame S′ is moving to the right (+x-direction) at speed u = 0.600c away from a stationary observer in frame S. The observer in S′ measures the speed v′ of a particle moving to the right away from her. What speed v does the observer in S me

> A meter stick moves past you at great speed. Its motion relative to you is parallel to its long axis. If you measure the length of the moving meter stick to be 1.00 ft (1 ft = 0.3048 m)—for example, by comparing it to a 1-foot ruler that is at rest relat

> A 1.20-cm-tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. a. Find the loc

> An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. a. What is the focal length of the lens? Is the lens converging or diverging? b. If the object is 8.00 mm tall, how tall is the image? Is it erect or