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physics
modern physics

Questions and Answers of Modern Physics

Continuation of Problem 67 uses the result of part (b) in Problem 67 for the motion along a single axis in the following situation. Frame A in Figure is attached to a particle that moves with
Continuation of Problem 67 let reference frame C in Figure move past reference frame D (not shown). (a) Show that MAD = MABMBCMCD, (b) Now put this general result to work: Three particles move
The total energy of a proton passing through a laboratory apparatus is 10.611nJ. What is its speed parameter β? Use the proton mass given in Appendix B under "Best Value," not the commonly
If we intercept an electron having total energy 1533 MeV that came from Vega, which is 26ly from us, how far in light years was the trip in the rest frame of the electron?
A pion is created in the higher reaches of Earth's atmosphere when an incoming high-energy cosmic ray particle collides with an atomic nucleus. A pion so formed descends toward Earth with a speed of,
What is the momentum in MeV/c of an electron with a kinetic energy of 2.00 MeV?
Find the speed parameter of a particle that takes 2.0 y longer than light to travel a distance of 6.0ly.
How much work is needed to accelerate a proton from a speed of 0.9850c to a speed of 0.9860c?
An airplane whose rest length is 40.0 m is moving at uniform velocity with respect to Earth, at a speed of 630 m/s.(a) By what fraction of its rest length is it shortened to an observer on Earth?(b)
To circle Earth in low orbit, a satellite must have a speed of about 2.7 x 104 km/h suppose that two such satellites orbit Earth in opposite directions.(a) What is their relative speed as they pass,
A radar transmitter Z is fixed to a reference frame S' that is moving to the right with speed v relative to reference frame S (Figure). A mechanical timer (essentially a clock) in frame S', having a
A particle with mass m has speed c/2 relative to inertial frame S. The particle collides with an identical particle at rest relative to frame S. Relative to S, what is the speed of a frame S' in
An elementary particle produced in a laboratory experiment travels 0.230 mm through the lab at a relative speed of 0.960c before it decays (becomes another particle).(a) What is the proper lifetime
What are?(a) K,(b) E, and(c) p (in GeV/c) for a proton moving at speed 0.990c? What are?(d) K,(e) E, and(f) p (in MeV/c) f or an electron moving at speed 0.990c?
In the red shift of radiation from a distant galaxy, a certain radiation, known to have a wavelength of 434 nm when observed in the laboratory, has a wavelength of 462 nm.(a) What is the radial speed
(a) What potential difference would accelerate an electron to speed c according to classical physics?(b) With this potential difference, what speed would the electron actually attain?
The radius of Earth is 6370 km, and its orbital speed about the Sun is 30 km/s. Suppose Earth moves past an observer at this speed. To the observer, by how much does Earth's diameter contract along
A spaceship at rest in a certain reference frame S is given a speed increment of 0.50c. Relative to its new rest frame, it is then given a further 0.50c increment. This process is continued until its
A Foron cruiser moving directly toward a Reptilian scout ship fires a decoy toward the scout ship relative to the scout ship, the speed of the decoy is 0.980c and the speed of the Foron cruiser is
One cosmic -ray particle approaches Earth along Earth's north-south axis with a speed of 0.80c toward the geographic North Pole and other approaches with a speed of 0.60c toward the geographic south
(a) How much energy is released in the explosion of a fission bomb containing 3.0 kg of fissionable material? Assume that 0.10% of the mass is converted to released energy.(b) What mass of TNT would
At what rate does the Sun emit photons? For simplicity, assume that the Sun's entire emission at the rate of 3.9 x 1026 W is at the single wavelength of 550 nm.
A helium-neon laser emits red light at wavelength λ = 633 nm in a beam of diameter 3.5 mm and at an energy-emission rate of 5.0mW. A detector in the beam's path totally absorbs the beam. At what
The meter was once defined as 1,650,763.73 wavelengths of the orange light emitted by a source containing krypton-86 atoms. What is the photon energy of that light?
The yellow-colored light from a highway sodium lamp is brightest at a wavelength of 589 nm. What is the photon energy for light at that wavelength?
Monochromatic light (that is, light of a single wavelength) is to be absorbed by a sheet of photographic find and thus recorded on the film. Photon absorption will occur if the photon energy equals
How fast must an electron move to have a kinetic energy equal to the photon energy of sodium light at wavelength 590 nm?
An ultraviolet lamp emits light of wavelength 400 nm at the rate of 400 W. An infrared lamp emits light of wavelength 700nm, also at the rate of 400 W. (a) Which lamp emits photons at the greater
A satellite in Earth orbit maintains a panel of solar cells of area 2.60 m2 perpendicular to the direction of the Sun's light rays. The intensity of the light at the panel is 1.39kW/m2.(a) At what
A special kind of light bulb emits monochromatic light of wavelength 630 nm. Electrical energy is supplied to it at the rate of 60 W, and the bulb is 93% efficient at converting that energy to light
Under ideal conditions, a visual sensation can occur in the human visual system if light of wavelength 550 nm is absorbed by the eye's retina at a rate as low as 100 photons per second. What is the
A 100 W sodium lamp (λ = 589 nm) radiates energy uniformly in all directions. (a) At what rate are photons emitted by the lamp? (b) At what distance from the lamp will a totally absorbing
A light detector has an absorbing area of 2.00 x 10-6 m2?and absorbs 50% of the incident light, which is at wavelength 600nm. The detector faces an isotropic source, 12.0 m from the source. The
A light detector (your eye) has an area of 2.00 x 10-6 m2 and absorbs 80% of the incident light, which is at wavelength 500 nm. The detector faces an isotropic source, 3.00 m from the source. If the
The beam emerging from a 1.5 W argon laser (λ = 515 nm) has a diameter d of 3.0 mm. The beam is focused by a lens system with an effective focal length fL of 2.5 mm. The focused beam strikes a
The work function of tungsten is 4.50eV. Calculate the speed of the fastest electrons ejected from a tungsten surface when light whose photon energy is 5.80eV shines on the surface.
You wish to pick an element for a photocell that will operate via the photoelectric effect with visible light. Which of the following are suitable (work functions are in parentheses): tantalum
Light strikes a sodium surface, causing photoelectric emission. The stopping potential for the ejected electrons is 5.0 V and the work function of sodium is 2.2eV. What is the wavelength of the
Find the maximum kinetic energy of electrons ejected from a certain material if the material's work function is 2.3eV and the frequency of the incident radiation is 3.0 x 1015 Hz.
The stopping potential for electrons emitted from a surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is
The wavelength associated with the cutoff frequency for silver is 325 nm. Find the maximum kinetic energy of electrons ejected from a silver surface by ultraviolet light of wavelength 254 nm.
Light of wavelength 200 nm shines on an aluminum surface; 4.20eV is required to eject an electron. What is the kinetic energy of? (a) The fastest and (b) The slowest ejected electrons? (c) What is
An orbiting satellite can become charged by the photoelectric effect when sunlight ejects electrons from its outer surface. Satellites must be designed to minimize such charging. Suppose a satellite
(a) If the work function for a certain metal is 1.8eV, what is the stopping potential for electrons ejected from the metal when light of wavelength 400 nm shines on the metal? (b) What is the maximum
Suppose the fractional efficiency of a cesium surface (with work function 1.80eV) is 1.0 x 10-16 that is, on average one electron is ejected for every 1016 photons that reach the surface. What would
X rays with a wavelength of 71 pm are directed onto a gold foil and eject tightly bound electrons from the gold atoms. The ejected electrons then move in circular paths of radius r in a region of
In a photoelectric experiment using a sodium surface, you find a stopping potential of 1.85 V for a wavelength of 300 nm and a stopping potential of 0.820 V for a wavelength of 400 nm. From these
What (a) Frequency, (b) Photon energy, and (c) Photon momentum magnitude (in keV/c) is associated with x rays having wavelength 35.0 pm?
(a) In MeV/c, what is the magnitude of the momentum associated with a photon having an energy equal to the electron rest energy? What are the (b) Wavelength and (c) Frequency of the corresponding
Light of wavelength 2.40 pm is directed onto a target containing free electrons. (a) Find the wavelength of light scattered at 30.0o from the incident direction. (b) Do the same for a scattering
X rays of wavelength 0.0100 nm are directed in the positive direction of an x axis onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of
Calculate the percentage change in photon energy during a collision like that in Fig. 38-5 for Φ = 90o and for radiation in (a) The microwave range, with λ = 3.0 cm; (b) The visible
Gamma rays of photon energy 0.511MeV are directed onto an aluminum target and are scattered in various directions by loosely bound electrons there. (a) What is the wavelength of the incident gamma
Calculate the Compton wavelength for (a) An electron and (b) A proton. What is the photon energy for an electromagnetic wave with a wavelength equal to the Compton wavelength of? (c) The electron and
Show that when a photon of energy E is scattered from a free electron at rest, the maximum kinetic energy of the recoiling electron is givenby
What are (a) The Compton shift ∆λ, (b) The fractional Compton shift ∆λ/λ, and (c) The change ∆E in photon energy for light of wavelength λ = 590 nm scattering from a free,
What is the maximum kinetic energy of electrons knocked out of a thin copper foil by Compton scattering of an incident beam of 17.5keV x rays? Assume the work function is negligible.
What percentage increase in wavelength leads to a 75% loss of photon energy in a photon-free electron collision?
A photon undergoes Compton scattering off a stationary free electron. The photon scatters at 90.0o from its initial direction; its initial wavelength is 3.00 x 10-12 m. What is the electron's kinetic
Consider a collision between an x-ray photon of initial energy 50.0keV and an electron at rest, in which the photon is scattered backward and the electron is knocked forward.(a) What is the energy of
What is the maximum wavelength shift for a Compton collision between a photon and a free proton?
Through what angle must a 200keV photon be scattered by a free electron so that the photon loses 10% of its energy?
Calculate the de Broglie wavelength of (a) A 1.00keV electron,(b) A 1.00 keV photon, and (c) A 1.00 keV neutron.
In an old-fashioned television set, electrons are accelerated through a potential difference of 25.0kV. What is the de Broglie wavelength of such electrons? (Relativity is not needed.)
A stream of protons, each with a speed of 0.9900c is directed into a two-slit experiment where the slit separation is 4.00 x 10-9 m. A two-slit interference pattern is built up on the viewing screen.
What is the wavelength of? (a) A photon with energy 1.00eV, (b) An electron with energy 1.00eV (c) A photon of energy 1.00GeV and (d) An electron with energy 1.00GeV?
An electron and a photon each have a wavelength of 0.20 nm. What is the momentum (in kg ∙ m/s) of the (a) Electron and (b) Photon? What is the energy (in eV) of the (c) Electron and (d)
Singly charged sodium ions are accelerated through a potential difference of 300 V. (a) What is the momentum acquired by such an ion? (b) What is its de Broglie wavelength?
The existence of the atomic nucleus was discovered in 1911 by Ernest Rutherford, who properly interpreted some experiments in which a beam of alpha particles was scattered from a metal foil of atoms
The wavelength of the yellow spectral emission line of sodium is 590 nm. At what kinetic energy would an electron have that wavelength as its de Broglie wavelength?
Electrons accelerated to an energy of 50GeV have a de Broglie wavelength λ small enough for them to probe the structure within a target nucleus by scattering from the structure. Assume that the
A non-relativistic particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813 x 10–4.By calculating its mass,
What are? (a) The energy of a photon corresponding to wavelength 1.00 nm, (b) The kinetic energy of an electron with de Broglie wavelength 1.00 nm, (c) The energy of a photon corresponding to
The highest achievable resolving power of a microscope is limited only by the wavelength used; that is, the smallest item that can be distinguished has dimensions about equal to the wavelength.
What accelerating voltage would be required for the electrons of an electron microscope if the microscope is to have the same resolving power as could be obtained using 100 keV gamma rays?
If the de Broglie wavelength of a proton is 100 fm,(a) What is the speed of the proton and (b) Through what electric potential would the proton have to be accelerated to acquire this speed?
(a) Write the wave function ψ (x) displayed in Eq. 38-19 in the form ψ(x) = a + ib, where a and b are real quantities. (Assume that r/o is real.) (b) Write the time-dependent wave
Show that Eq. 38-17 is indeed a solution of Eq. 38-16 by substituting ψ(x) and its second derivative into Eq. 38-16 and noting that an identity results.
(a) Let n = a + ib be a complex number, where a and b arc real (positive or negative) numbers. Show that the product nn* is always a positive real number. (b) Let m = c + id be another complex
Show that the angular wave number k for a non-relativistic free particle of mass m can be written as in which K is the particle's kineticenergy
Suppose we put A = 0 in Eq. 38-17 and relabeled B as ψ0. (a) What would the resulting wave function then describe? (b) How, if at all, would Figure be altered?
The function ?(x) displayed in Eq. 38-19 describes a free particle, for which we assumed that U(x) = 0 in Schrodinger's equation (Eq. 38-15). Assume now that U(x) = U0 = a constant in that equation.
In Eq.38-18 keep both terms, putting A - B ? ?0 the equation then describes the superposition of two matter waves of equal amplitude, traveling in opposite directions. (Recall that this is the
The uncertainty in the position of an electron along an x axis is given as 50 pm, which is about equal to the radius of a hydrogen atom. What is the least uncertainty in any simultaneous measurement
You will find in Chapter 39 that electrons cannot move in definite orbits within atoms, like the planets in our solar system. To see why, let us try to "observe" such an orbiting electron by using a
Figure shows a case in which the momentum component px of a particle is fixed so that ∆px = 0; then, from Heisenberg's uncertainty principle (Eq. 38-20), the position x of the particle is
(a) Suppose a beam of 5.0eV protons strikes a potential energy barrier of height 6.0eV and thickness 0.70 nm, at a rate equivalent to a current of 1000 A. How long would you have to wait-on
Consider the barrier-tunneling situation in Sample Problem 38-7. What percentage change in the transmission coefficient T occurs for a 1.0% change in (a) The barrier height, (b) The barrier
Consider a potential energy barrier like that of Figure but whose height Ub is 6.0eV and whose thickness L is 0.70 nm. What is the energy of an incident electron whose transmission coefficient is
A 3.0MeV proton is incident on a potential energy barrier of thickness 10 fm and height 10 MeV. What are? (a) The transmission coefficient T, (b) The kinetic energy K, the proton will have on the
In about 1916, R. A. Millikan found the following stopping potential data for lithium in his photoelectric experiments: Use these data to make a plot like Figure (which is for sodium) and then use
Derive Eq. 38-11, the equation for the Compton shift, from Eqs. 38-8, 38-9, and 38-10 by eliminating v and θ
Neutrons in thermal equilibrium with matter have an average kinetic energy of (3/2)kT, where k is the Boltzmann constant and Z, which may be taken to be 300 K, is the temperature of the environment
Consider a balloon filled with helium gas at room temperature and atmospheric pressure. Calculate (a) The average de Broglie wavelength of the helium atoms and (b) The average distance between atoms
(a) The smallest amount of energy needed to eject an electron from metallic sodium is 2.28eV. Does sodium show a photoelectric effect for red light, with λ = 680 nm? (b) What is the cutoff
A spectral emission line is electromagnetic radiation that is emitted in a wavelength range narrow enough to be taken as a single wavelength. One such emission line that is important in astronomy has
Using the classical equations for momentum and kinetic energy, show that an electron's de Broglie wavelength in nanometers can be written as λ = 1.226/√K, in which K is the electron's
A bullet of mass 40 g travels at 1000 m/s. Although the bullet is clearly too large to be treated as a matter wave, determine what Eq. 38-13 predicts for the de Broglie wavelength of the bullet at
Figure shows that because of Heisenberg's uncertainty principle, it is not possible to assign an x coordinate to the position of the electron. (a) Can you assign a y or a z coordinate? (b) Describe
Imagine playing baseball in a universe (not ours!) where the Planck constant is 0.60 J ∙ s. What would be the uncertainty in the position of a 0.50 kg baseball that is moving at 20m/s along an

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