Q&A Hero

Q: Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton. Then the ground state energy of a hydrogen atom is -13.6 eV. The minus sign indicates:A) the kinetic energy is negativeB) the potential energy is positiveC) the electron might escape from the atomD) the electron and proton are bound togetherE) none of the above

Q: The quantum number nis most closely associated with what property of the electron in a hydrogen atom? A) Energy B) Orbital angular momentum C) Spin angular momentum D) Magnetic moment E) zcomponent of angular momentum

Q: An electron is trapped in an infinitely deep rectangular well with sides of length Lx= Land Ly= 2L. The energy that the electron needs to move from the ground state to the state nx= 2, ny= 4 is: A) B) C) D) E)

Q: An electron is trapped in an infinitely deep rectangular well with sides of length Lx= Land Ly= 2L. The energy of the state nx= 2, ny= 4 is: A) B) C) D) E)

Q: The figure shows the energy levels for an electron in a finite potential energy well. If an electron in the n= 2 state absorbs a photon of wavelength 2.0 nm, what happens to the electron? A) It makes a transition to the n= 3 state. B) It makes a transition to then= 4 state. C) It escapes the well with a kinetic energy of 280eV. D) It escapes the well with a kinetic energy of 730eV. E) Nothing; this photon does not have an energy corresponding to an allowed transition so it is not absorbed.

Q: The figure shows the energy levels for an electron in a finite potential energy well. If the electron makes a transition from the n= 3 state to the ground state, what is the wavelength of the emitted photon? A) 6.0 nm B) 5.7 nm C) 5.3 nm D) 3.0 nm E) 2.3 nm

Q: A particle is trapped in a finite potential energy well that is deep enough so that the electron can be in the state with n= 4. For this state how many nodes does the probability density have? A) 0 B) 1 C) 3 D) 4 E) 5

Q: A particle in a certain finite potential energy well can have any of five quantized energy values and no more. Which of the following would allow it to have any of six quantized energy levels? A) Increase the momentum of the particle B) Decrease the momentum of the particle C) Decrease the well width D) Increase the well depth E) Decrease the well depth

Q: A particle is confined by finite potential energy walls to a one-dimensional trap fromx= 0 to x= L. Its wave function in the region x>Lhas the form:

Q: An electron is in a one-dimensional well with finite potential energy barriers at the walls. The matter wave: A) is zero at the barriers B) is zero everywhere within each barrier C) is zero in the well D) extends into the barriers E) is discontinuous at the barriers

Q: If a wave function for a particle moving along the xaxis is "normalized" then:

Q: A particle is confined to a one-dimensional trap by infinite potential energy walls. Of the following states, designed by the quantum number n, for which one is the probability density greatest near the center of the well? A) n= 2 B) n= 3 C) n= 4 D) n= 5 E) n= 6

Q: A particle is trapped in an infinite potential energy well. It is in the state with quantum number n= 14. How many maxima does the probability density have? A) 0 B) 7 C) 13 D) 14 E) 15

Q: A particle is trapped in an infinite potential energy well. It is in the state with quantum number n= 14. How many nodes does the probability density have (counting the nodes at the ends of the well)? A) 0 B) 7 C) 13 D) 14 E) 15

Q: An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. A graph of its probability density P(x) versus xis shown. The value of the quantum number nis: A) 0 B) 1 C) 2 D) 3 E) 4

Q: An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. A graph of its wave function versus xis shown. The value of quantum number nis:A) 0B) 1C) 2D) 4E) 8

Q: An electron in an atom initially has an energy 7.5 eV above the ground state energy. It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process. The momentum of the photon is:A) 1.7 x10-27kg .m/sB) 2.3 x10-27kg .m/sC) 4.0 x10-27kg .m/sD) 5.7 x10-27kg .m/sE) 8.0 x10-27kg .m/s

Q: An electron in an atom drops from an energy level at -1.1 x10-18J to an energy level at -2.4 x10-18J. The wave associated with the emitted photon has a frequency of:A) 2.0 x1017HzB) 2.0 x1015HzC) 2.0 x1013HzD) 2.0 x1011HzE) 2.0 x109Hz

Q: An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops to a state with energy 3.2 eV above the ground state energy and emits a photon in the process. The wave associated with the photon has a wavelength of:A) 5.4 x10-­7mB) 3.0 x10-7mC) 1.7x 10-­7 mD) 1.2x10-­7mE) 1.0x10-­7 m

Q: A particle is trapped in a one-dimensional well with infinite potential energy at the walls. Three possible pairs of energy levels are 1) n= 3 and n= 1 2) n= 3 and n= 2 3) n= 4 and n= 3 Order these pairs according to the difference in energy, least to greatest. A) 1, 2, 3 B) 3, 2, 1 C) 2, 3, 1 D) 1, 3, 2 E) 3, 1, 2

Q: An electron is trapped in a deep well with a width of 0.3 nm. If it is in the state with quantum number n= 3 its kinetic energy is:A) 6.0 x10-28JB) 1.8 x10-27JC) 6.7 x10-19JD) 2.0 x10-18JE) 6.0 x10-18J

Q: Two one-dimensional traps have infinite potential energy at their walls. Trap A has width Land trap B has width 2L. For which value of the quantum number ndoes a particle in trap B have the same energy as a particle in the ground state of trap A? A) n= 1 B) n= 2 C) n= 3 D) n= 4 E) n= 5

Q: The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls: A) is zero B) decreases with temperature C) increases with temperature D) is independent of temperature E) oscillates with time

Q: Four different particles are trapped in one-dimensional wells with infinite potential energy at their walls. The masses of the particles and the width of the wells are 1) mass = 4m0, width = 2L0 2) mass = 2m0, width = 2L0 3) mass = 4m0, width = L0 4) mass = m0, width = 2L0 Rank them according to the kinetic energies of the particles when they are in their ground states, lowest to highest. A) 3 and 4 tied, then 2, then 1 B) 1, 2, then 3 and 4 tied C) 1 and 2 tied, then 3, then 4 D) 4, 3, 2, 1 E) 3, 1, 2, 4

Q: Identical particles are trapped in one-dimensional wells with infinite potential energy at the walls. The widths Lof the traps and the quantum numbers nof the particles are 1) L= 2L0, n= 2 2) L= 2L0, n= 4 3) L= 3L0, n= 3 4) L= 4L0, n= 2 Rank them according to the kinetic energies of the particles, least to greatest. A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1 and 3 tied, then 2, then 4 D) 4, then 1 and 3 tied, then 2 E) 2, then 1 and 3 tied, then 4

Q: An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. The ratio E3/E1of the energy for n= 3 to that for n= 1 is: A) 1/3 B) 1/9 C) 3/1 D) 9/1 E) 1/1

Q: The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is 2.0 eV. If the width of the well is doubled, the ground state energy will be: A) 0.5 eV B) 1.0 eV C) 2.0 eV D) 4.0 eV E) 8.0 eV

Q: The energy of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n= quantum number): A) n B) 1/n C) 1/n2 D) E) n2

Q: The wavelength of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n= quantum number): A) n B) 1/n C) 1/n2 D) E) n2

Q: An electron confined in a one-dimensional infinite potential well has an energy of 180 eV. What is its wavelength? A) 65 pm B) 91 pm C) 130 pm D) 370 pm E) 520 pm

Q: Identical particles, each with energy E, are incident on the following four potential energy barriers: 1) barrier height = 5E, barrier width = 2L 2) barrier height = 10E, barrier width = L 3) barrier height = 17E, barrier width = L/2 4) barrier height = 26E, barrier width = L/3 Rank the barriers in terms of the probability that the particles tunnel through them, from least probability to greatest probability. A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1 and 2 tied, then 3, then4 D) 1, then 2 and 3 tied, then 4 E) 3, 2, 1, 4

Q: An electron with energy Eis incident on a potential energy barrier of height Epotand thickness L. The probability of tunneling increases if: A) Edecreases without any other changes B) Epotincreases without any other changes C) Ldecreases without any other changes D) Eand Epotincrease by the same amount E) Eand Epotdecrease by the same amount

Q: In order to tunnel through a potential barrier a particle must: A) have energy greater than the barrier height B) have spin C) be massive D) have a wavelength longer than the barrier width E) none of the above

Q: An electron with energy Eis incident upon a potential energy barrier of height Epot<Eand thickness L. If the reflection coefficient R= 0.05, A) the electron has a 0.05% chance of being reflected B) the electron has a 5% chance of being reflected C) the electron has a 95% chance of being reflected D) the electron will be partially reflected and partially transmitted E) the electron has no chance of being reflected

Q: An electron with energy Eis incident upon a potential energy barrier of height Epot<Eand thickness L. The reflection coefficient R:A) is always equal to zeroB) is always equal to 1C) does not depend on E- EpotD) is, in general, not equal to zeroE) is equal to T+ 1 where Tis the transmission coefficient

Q: An electron with energy Eis incident upon a potential energy barrier of height Epot>Eand thickness L. The transmission coefficient T: A) is zero B) decreases exponentially with L C) is proportional to 1/L D) is proportional to 1/L2 E) is non-zero and independent of L

Q: The reflection coefficient Rfor a certain barrier tunneling problem is 0.80. The corresponding transmission coefficient T is: A) 0.80 B) 0.60 C) 0.50 D) 0.20 E) 0

Q: The uncertainty in position of an electron in a certain state is 5 x10-10m. The uncertainty in its momentum could beA) 5.0x10-24kg.m/sB) 4.0 x10-24kg.m/sC) 3.0 x10-24 kg.m/sD) any of the aboveE) none of the above

Q: A free electron in motion along the xaxis has a localized wave function. The uncertainty in its momentum is decreased if: A) the wave function is made more narrow B) the wave function is made less narrow C) the wave function remains the same but the energy of the electron is increased D) the wave function remains the same but the energy of the electron is decreased E) none of the above

Q: A free electron in motion along the xaxis has a localized wave function. If it enters a region of space where its potential energy increases, A) its total energy will decrease. B) its momentum will increase. C) its wave number will increase. D) its wavelength will increase. E) its kinetic energy will increase.

Q: Maxwell's equations are to electric and magnetic fields as __________ equation is to the wave function of the particle. A) Einstein's B) Fermi's C) Newton's D) Schrdinger's E) Bohr's

Q: The significance of is:A) probabilityB) energyC) probability densityD) energy densityE) wavelength

Q: is the wave function for a particle moving along the xaxis. The probability that the particle is in the interval from x= ato x= bis given by:

Q: The probability that a particle is in a given small region of space is proportional to: A) its energy B) its momentum C) the magnitude of its wave function D) the wavelength of its wave function E) the square of the magnitude of its wave function

Q: A free electron and a free proton have the same speed. This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has: A) a shorter wavelength and a greater frequency B) a longer wavelength and a greater frequency C) a shorter wavelength and a smaller frequency D) the same wavelength and a greater frequency E) a longer wavelength and a smaller frequency

Q: A free electron and a free proton have the same momentum. This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has: A) a shorter wavelength and a greater frequency B) a longer wavelength and a greater frequency C) the same wavelength and the same frequency D) the same wavelength and a greater frequency E) the same wavelength and a smaller frequency

Q: A free electron and a free proton have the same kinetic energy. This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has: A) a shorter wavelength and a greater frequency B) a longer wavelength and a greater frequency C) a shorter wavelength and the same frequency D) a longer wavelength and the same frequency E) a shorter wavelength and a smaller frequency

Q: A non-relativistic free electron has kinetic energy K. If its wavelength doubles, its kinetic energy is: A) 4 K B) 2 K C) K D) K/2 E) K/4

Q: If the kinetic energy of a non-relativistic free electron doubles, the frequency of its wave function changes by the factor: A) 1/ B) 1/2 C) 1/4 D) E) 2

Q: The frequency and wavelength of the matter wave associated with a 10-eV free electron are:A) 1.5 x1034Hz, 3.9x10-10mB) 1.5 x1034Hz, 1.3 x10-34mC) 2.4 x1015Hz, 1.2 x10-9mD) 2.4 x1015Hz, 3.9 x10-10mE) 4.8 x1015Hz, 1.9 x10-10m

Q: A free electron has a momentum of 5.0 x10-24kg .m/s. Its wavelength,as given by its wave function, is:A) 1.3 x10-8 mB) 1.3 x10-10 mC) 2.3 x10-11 mD) 2.3 x10-13 mE) none of these

Q: Consider the following three particles: 1) a free electron with kinetic energy K0 2) a free proton with kinetic energy K0 3) a free proton with kinetic energy 2K0 Rank them according to the wavelengths of their waves, least to greatest. A) 1, 2, 3 B) 3, 2, 1 C) 2, 3, 1 D) 1, 3, 2 E) 1, then 2 and 3 tied

Q: Consider the following three particles: 1) a free electron with speed v0 2) a free proton with speed v0 3) a free proton with speed 2v0 Rank them according to the wavelengths of their matter waves, least to greatest. A) 1, 2, 3 B) 3, 2, 1 C) 2, 3, 1 D) 1, 3, 2 E) 1, then 2 and 3 tied

Q: Of the following which is the best evidence for the wave nature of matter? A) The photoelectric effect B) The Compton effect C) The spectral radiancy of cavity radiation D) The relationship between momentum and energy for an electron E) The reflection of electrons by crystals

Q: Which of the following is NOT evidence for the wave nature of matter? A) The photoelectric effect B) The diffraction pattern obtained when electrons pass through a slit C) Electron tunneling D) The validity of the Heisenberg uncertainty principle E) The interference pattern obtained when electrons pass through a two-slit system

Q: Evidence for the wave nature of matter is: A) electron diffraction experiments of Davisson and Germer B) Thompson's measurement of e/m C) Young's double slit experiment D) the Compton effect E) Lenz's law

Q: Monoenergetic electrons are incident on a single slit barrier. If the energy of each incident electron is increased the central maximum of the diffraction pattern: A) widens B) narrows C) stays the same width D) widens for slow electrons and narrows for fast electrons E) narrows for slow electrons and widens for fast electrons

Q: What is the temperature of a burner on an electric stove when its glow is barely visible, at a wavelength of 700 nm? Assume the burner radiates as an ideal blackbody and that 700 nm represents the peak of its emission spectrum. A) 41 K B) 240 K C) 410 K D) 2400 K E) 4100 K

Q: The surface of the Sun is at a temperature of approximately 5800 K, and radiates a peak wavelength of 500 nm. According to the Planck radiation law, what is its emitted intensity per unit wavelength at the peak? A) 8.4 W/cm2nm B) 42 W/cm2nm C) 84 W/cm2nm D) 8.4 x 103 W/cm2nm E) 4.2 x 107 W/cm2nm

Q: The main problem that physicists had in understanding blackbody radiation before Planck's work was: A) Blackbody radiation came from objects that were not actually black. B) The classically predicted frequency spectrum showed an infinitely large peak at low frequencies. C) The classically predicted frequency spectrum showed an infinitely large peak at high frequencies. D) The classically predicted frequency spectrum had a minimum intensity rather than a maximum as observed. E) The classically predicted frequency spectrum had a maximum intensity that decreased with temperature, rather than increasing as observed.

Q: Consider the following: I. A photoelectric process in which all emitted electrons have energy less than hf,wheref is the frequency of the incident light. II. A photoelectric process in which some emitted electrons have kinetic energy greater than hf. III. Compton scattering from stationary electrons for which the emitted light has a frequency that is greater than that of the incident light. IV. Compton scattering from stationary electrons for which the emitted light has a frequency that is less than that of the incident light. The only possible processes are: A) I B) III C) I and III D) I and IV E) II and IV

Q: Electromagnetic radiation with a wavelength of 3.5 x10-12m is scattered from stationary electrons, and photons that have been scattered through 50°are detected. After a scattering event the magnitude of the photon's momentum is:A) 0 kg.m/sB) 8.7 x10-23kg.m/sC) 1.5 x10-22kg.m/sD) 2.0 x10-22kg.m/sE) 2.2 x10-22kg.m/s

Q: Electromagnetic radiation with a wavelength of 3.5 x10-12m is scattered from stationary electrons and photons that have been scattered through 50°are detected. An electron from which one of these photons was scattered receives an energy of:A) 0 JB) 1.1 x10-14JC) 1.9 x10-14JD) 2.3 x10-14JE) 1.3 x10-13J

Q: Electromagnetic radiation with a wavelength of 5.7 x10-12m is incident on stationary electrons. Radiation that has a wavelength of 6.6x10-12m is detected at a scattering angle of:A) 10°B) 40°C) 50°D) 69°E) 111°

Q: In Compton scattering from stationary electrons the largest change in wavelength that can occur is:A) 2.43 x10-15mB) 2.43 x10-12mC) 2.43 x10-9mD) dependent on the frequency of the incident lightE) dependent on the work function

Q: In Compton scattering from stationary electrons the frequency of the emitted light is independent of: A) the frequency of the incident light B) the recoil speed of the electron C) the scattering angle D) the electron recoil energy E) none of the above

Q: Of the following, Compton scattering from electrons is most easily observed for: A) microwaves B) infrared light C) visible light D) ultraviolet light E) x rays

Q: In Compton scattering from stationary particles the maximum change in wavelength can be made smaller by using: A) higher frequency radiation B) lower frequency radiation C) more massive particles D) less massive particles E) particles with greater charge

Q: Separate Compton effect experiments are carried out using visible light and x rays. The scattered radiation is observed at the same scattering angle. For these experiments: A) the x rays have the greater shift in wavelength and the greater change in photon energy B) the two radiations have the same shift in wavelength and the x rays have the greater change in photon energy C) the two radiations have the same shift in wavelength and the visible light has the greater change in photon energy D) the two radiations have the same shift in wavelength and the same change in photon energy E) the visible light has the greater shift in wavelength and the greater shift in photon energy

Q: In Compton scattering from stationary electrons the largest change in wavelength occurs when the photon is scattered through:A) 0°B) 22.5°C) 45°D) 90°E) 180°

Q: A photon in light beam A has twice the energy of a photon in light beam B. The ratio pA/pBof their momenta is: A) 1/2 B) 1/4 C) 1 D) 2 E) 4

Q: Which of the following electromagnetic radiations has photons with the greatest momentum? A) blue light B) yellow light C) xrays D) radio waves E) microwaves

Q: The diagram shows the graphs of the stopping potential as a function of the frequency of the incident light for photoelectric experiments performed on three different materials. Rank the materials according to the values of their work functions, from least to greatest. A) 1, 2, 3 B) 3, 2, 1 C) 2, 3, 1 D) 2, 1, 3 E) 1, 3, 2

Q: The stopping potential for electrons ejected by 6.8 x1014-Hz electromagnetic radiation incident on a certain sample is 1.8 V. The kinetic energy of the most energetic electrons ejected and the work function of the sample, respectively, are:A) 1.8 eV, 2.8 eVB) 1.8 eV, 1.0 eVC) 1.8 eV, 4.6 eVD) 2.8 eV, 1.0 eVE) 1.0 eV, 4.6 eV

Q: The work function for a certain sample is 2.3 eV. The stopping potential for electrons ejected from the sample by 7.0x1014-Hz electromagnetic radiation is:A) 0 VB) 0.60 VC) 2.3 VD) 2.9 VE) 5.2 V

Q: In a photoelectric effect experiment no electrons are ejected if the frequency of the incident light is less than A/h, where his the Planck constant and Ais: A) the maximum energy needed to eject the least energetic electron B) the minimum energy needed to eject the least energetic electron C) the maximum energy needed to eject the most energetic electron D) the minimum energy needed to eject the most energetic electron E) the intensity of the incident light

Q: In a photoelectric effect experiment at a frequency above cut off, the stopping potential is proportional to: A) the energy of the least energetic electron before it is ejected B) the energy of the least energetic electron after it is ejected C) the energy of the most energetic electron before it is ejected D) the energy of the most energetic electron after it is ejected E) the electron potential energy at the surface of the sample

Q: In a photoelectric effect experiment the stopping potential is: A) the energy required to remove an electron from the sample B) the kinetic energy of the most energetic electron ejected C) the potential energy of the most energetic electron ejected D) the photon energy E) the electric potential that causes the electron current to vanish

Q: The main problem physicists had with understanding the photoelectric effect before Einstein explained it in terms of photons was: A) the intensity of emitted electrons did not depend on the intensity of the source. B) the maximum energy of the emitted electrons did not depend on the frequency of the source. C) the maximum energy of the emitted electrons did not depend on the intensity of the source. D) the cutoff frequency depended on the material used as a target. E) the cutoff frequency did not depend on the material used as a target.

Q: In a photoelectric effect experiment at a frequency above cut off, the number of electrons ejected is proportional to: A) their kinetic energy B) their potential energy C) the work function D) the frequency of the incident light E) the number of photons that hit the sample