Question: An unstable particle is created in the

> If a muon is traveling at 0.999c, what are its momentum and kinetic energy? (The mass of such a muon at rest in the laboratory is 207 times the electron mass.)

> Calculate the magnitude of the force required to give a 0.145-kg baseball an acceleration a = 1.00 m/s2 in the direction of the baseball’s initial velocity when this velocity has a magnitude of a. 10.0 m/s; b. 0.900c; c. 0.990c. d. Repeat parts (a),

> Three thin lenses, each with a focal length of 40.0 cm, are aligned on a common axis; adjacent lenses are separated by 52.0 cm. Find the position of the image of a small object on the axis, 80.0 cm to the left of the first lens.

> A source of electromagnetic radiation is moving in a radial direction relative to you. The frequency you measure is 1.25 times the frequency measured in the rest frame of the source. What is the speed of the source relative to you? Is the source moving t

> A convex spherical mirror with a focal length of magnitude 24.0 cm is placed 20.0 cm to the left of a plane mirror. An object 0.250 cm tall is placed midway between the surface of the plane mirror and the vertex of the spherical mirror. The spherical mir

> a. Repeat the derivation of Eq. (34.19) for the case in which the lens is totally immersed in a liquid of refractive index nliq. b. A lens is made of glass that has refractive index 1.60. In air, the lens has focal length +18.0 cm. What is the focal len

> When an object is placed at the proper distance to the left of a converging lens, the image is focused on a screen 30.0 cm to the right of the lens. A diverging lens is now placed 15.0 cm to the right of the converging lens, and it is found that the scre

> a. Prove that when two thin lenses with focal lengths f1 and f2 are placed in contact, the focal length Æ’ of the combination is given by the relationship b. A converging meniscus lens (see Fig. 34.32a) has an index of refraction of 1.55 and

> You may have noticed a small convex mirror next to your bank’s ATM. Why is this mirror convex, as opposed to flat or concave? What considerations determine its radius of curvature?

> As shown in Fig. P34.89, the candle is at the center of curvature of the concave mirror, whose focal length is 10.0 cm. The converging lens has a focal length of 32.0 cm and is 85.0 cm to the right of the candle. The candle is viewed looking through the

> A screen is placed a distance d to the right of an object. A converging lens with focal length f is placed between the object and the screen. In terms of f, what is the smallest value d can have for an image to be in focus on the screen?

> A convex mirror and a concave mirror are placed on the same optic axis, separated by a distance L = 0.600 m. The radius of curvature of each mirror has a magnitude of 0.360 m. A light source is located a distance x from the concave mirror, as shown in Fi

> An object is placed 22.0 cm from a screen. a. At what two points between object and screen may a converging lens with a 3.00-cm focal length be placed to obtain an image on the screen? b. What is the magnification of the image for each position of the 

> An object to the left of a lens is imaged by the lens on a screen 30.0 cm to the right of the lens. When the lens is moved 4.00 cm to the right, the screen must be moved 4.00 cm to the left to refocus the image. Determine the focal length of the lens.

> The radii of curvature of the surfaces of a thin converging meniscus lens are R1 = +12.0 cm and R2 = +28.0 cm. The index of refraction is 1.60. a. Compute the position and size of the image of an object in the form of an arrow 5.00 mm tall, perpendicula

> a. How fast must you be approaching a red traffic light (λ = 675 nm) for it to appear yellow (λ = 575 nm)? Express your answer in terms of the speed of light. b. If you used this as a reason not to get a ticket for running a red light, how much of a fin

> A transparent rod 30.0 cm long is cut flat at one end and rounded to a hemispherical surface of radius 10.0 cm at the other end. A small object is embedded within the rod along its axis and halfway between its ends, 15.0 cm from the flat end and 15.0 cm

> An imperial spaceship, moving at high speed relative to the planet Arrakis, fires a rocket toward the planet with a speed of 0.920c relative to the spaceship. An observer on Arrakis measures that the rocket is approaching with a speed of 0.360c. What is

> Figure P34.80 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 P34.80 Object Imag

> For a spherical mirror, if s = f, then s′ =∞, and the lateral magnification m is infinite. Does this make sense? If so, what does it mean?

> A lens forms a real image that is 214 cm away from the object and 1 2 3 times its height. What kind of lens is this, and what is its focal length?

> You place an object alongside a white screen, and a plane mirror is 60.0 cm to the right of the object and the screen, with the surface of the mirror tilted slightly from the perpendicular to the line from object to mirror. You then place a converging le

> In high-energy physics, new particles can be created by collisions of fast-moving projectile particles with stationary particles. Some of the kinetic energy of the incident particle is used to create the mass of the new particle. A protonâ€&#1

> Both ends of a glass rod with index of refraction 1.60 are ground and polished to convex hemispherical surfaces. The radius of curvature at the left end is 6.00 cm, and the radius of curvature at the right end is 12.0 cm. The length of the rod between ve

> a. Consider the Galilean transformation along the x-direction : x′ = x - vt and t′ = t. In frame S the wave equation for electromagnetic waves in a vacuum is where E represents the electric field in the wave. Show th

> A microscope is focused on the upper surface of a glass plate. A second plate is then placed over the first. To focus on the bottom surface of the second plate, the microscope must be raised 0.780 mm. To focus on the upper surface, it must be raised anot

> A pinhole camera is just a rectangular box with a tiny hole in one face. The film is on the face opposite this hole, and that is where the image is formed. The camera forms an image without a lens. a. Make a clear ray diagram to show how a pinhole camer

> Figure P34.72 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is 2.0 cm along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram for t

> A mirror on the passenger side of your car is convex and has a radius of curvature with magnitude 18.0 cm. a. Another car is behind your car, 9.00 m from the mirror, and this car is viewed in the mirror by your passenger. If this car is 1.5 m tall, what

> A layer of benzene (n = 1.50) that is 4.20 cm deep floats on water (n = 1.33) that is 5.70 cm deep. What is the apparent distance from the upper benzene surface to the bottom of the water when you view these layers at normal incidence?

> Two events occur at the same space point in a particular inertial frame of reference and are simultaneous in that frame. Is it possible that they may not be simultaneous in a different inertial frame? Explain.

> You are in your car driving on a highway at 25 m/s when you glance in the passenger-side mirror (a convex mirror with radius of curvature 150 cm) and notice a truck approaching. If the image of the truck is approaching the vertex of the mirror at a speed

> Many of the stars in the sky are actually binary stars, in which two stars orbit about their common center of mass. If the orbital speeds of the stars are high enough, the motion of the stars can be detected by the Doppler shifts of the light they emit.

> Two particles in a high-energy accelerator experiment approach each other head-on with a relative speed of 0.890c. Both particles travel at the same speed as measured in the laboratory. What is the speed of each particle, as measured in the laboratory?

> Two particles in a high-energy accelerator experiment are approaching each other head-on, each with a speed of 0.9380c as measured in the laboratory. What is the magnitude of the velocity of one particle relative to the other?

> If you run away from a plane mirror at 3.60 m/s, at what speed does your image move away from you?

> What is the size of the smallest vertical plane mirror in which a woman of height h can see her full-length image?

> 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

> 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?

> Find the longest and shortest wavelengths in the Lyman and Paschen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?

> 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