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22 Cards in this Set

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De Broglie waves:


(1) are a form of electromagnetic radiation.


(2) are a basic property of all particles, whether at rest or in motion.


(3) travel at the speed of light.


(4) describe the wave-type behavior of moving particles.

4

The deBroglie wave of a particle can best be described as:


(1) a form of electromagnetic wave.


(2) a characteristic of the oscillation of the particle.


(3) a probability wave.


(4) none of the above.

3

Which of the following is NOT true about the deBroglie wavelength?


(1) It is larger for an electron than for a baseball moving at the same speed.


(2) It applies only to charged particles.


(3) It describes the wave properties of particles such as electrons.


(4) It is a property of waves of probability.

2

The uncertainty relationships:


(1) apply to all types of waves.


(2) apply only to de Broglie waves.


(3) apply only to classical waves.


(4) apply only to light waves.

1

In the following situations, choose which particle has the larger de Broglie wavelength:


(1) the electron


(2) the proton


(3) they are both the same


(a) An electron and a proton moving with the same momentum.


(b) An electron and a proton moving at the same speed.


(c) An electron and a proton with the same nonrelativistic kinetic energy.


(d) An electron and a proton with the same kinetic energy, in both cases much larger than the rest energy

(a) 3 (b) 1 (c) 1 (d) 3

Why is it not possible to observe double-slit interference with baseballs?


(1) The de Broglie wavelength of a baseball is too large.


(2) The de Broglie wavelength of a baseball is too small.


(3) Baseballs are too large to fit through a double-slit apparatus.


(4) Baseballs can't be accelerated to the speed of light.

3

A beam of electrons moving with speed v passes through a single slit and strikes a screen, where it forms a diffraction pattern with a bright central maximum and some less intense maxima on either side of center.


(a) If the speed of the electrons is increased to 2v, what happens to the width of the central maximum?


(1) Increases (2) Decreases (3) Remains the same


(b) If the beam of electrons is replaced with a beam of protons moving with speed v, what happens to the width of the central maximum compared with that of electrons moving with the same speed?


(1) Increases (2) Decreases (3) Remains the same

(a) 2 (b) 2
Suppose an electron is moving at speed v. In terms of v, what would be the speed of a baseball with the same deBroglie wavelength as the electron? (1) v(2) 10^10v(3) 10^−10v (4) 10^−20v(5) 10^−30v
5

A beam of monoenergetic electrons is incident on a mask that contains a single narrow slit. A pattern of diffraction maxima and minima appears on the screen.


(a) If the slit width is halved, the diffraction minima on the screen would then be:


(1) closer together (2) farther apart (3) unchanged


(b) If the kinetic energy of the electrons in the original experiment is halved, the diffraction minima on the screen would be:


(1) closer together (2) farther apart (3) unchanged


(c) Suppose the beam of electrons were replaced with a beam of particles of greater mass, such that the resultant diffraction pattern was exactly the same as that in the original experiment. To accomplish this, the kinetic energy of the new particles would be:


(1) greater than that of the original electrons (2) less than that of the original electrons (3) equal to that of the original electrons

(a) 2 (b) 2 (c) 2

(a) A packet of water waves of width Δ x contains a range of wavelengths Δλ about a central wavelength λ; that is, the range of wavelengths is from about λ - Δλ/2 to λ + Δλ/2. If the packet were made half as wide, what would be the new range of wavelengths?


(1) 2Δλ (2) Δλ/2 (3) Δλ (4) None of these


(b) A whistle blast lasts for a time interval Δt . It consists of a central frequency ν with a range Δν. If the blast were made twice as long, what would be the new range of frequencies? (1) 2Δν (2) Δν/2 (3) Δν (4) None of these


(c) A beam of electrons of momentum p x moving in the x direction passes through a slit of width Δ y = a. The beam diffracts through the slit so that the range in its y momentum is Δ p y, that is, from -Δ p y/2 to + Δ p y/2. What is the new range in the y momentum if the slit is made half as wide?


(1) 2Δ p y (2) Δ p y/2 (3) Δ p y (4) None of these

(a) 1 (b) 2 (c) 1

Consider the following three experiments:


(a) The x component of the position of an electron is measured to within ±Δ x, and simultaneously the x component of its momentum is measured to within ±Δ p x.


(b) The x component of the position of an electron is measured to within ±Δ x, and then later the x component of its momentum is measured to within ±Δ p x.


(c) The x component of the position of an electron is measured to within ±Δ x, and simultaneously the y component of its momentum is measured to within ±Δ p y. In which of these cases does the uncertainty principle NOT impose a limitation on the outcome of the experiment?


(1) a only (2) b only (3) c only (4) a and b only (5) a and c only (6) b and c only (7) a, b, and c

6
A sodium atom, a neutron, a proton, and an electron all have the same nonrelativistic kinetic energy. Which has the smallest de Broglie wavelength? (a) sodium atom (b) neutron (c) proton (d) electron
a
Which of the following does NOT provide evidence for the wave nature of matter? (a) the photoelectric effect (b) neutron diffraction (c) the Heisenberg relationships (d) electron diffraction
a

The probability density for a particle in the ground state of a one-dimensional infinite potential energy well:


(1) has a single maximum at the center of the well.


(2) has a minimum at the center of the well and maxima at the sides of the well.


(3) has several maxima and minima in the well. (4) is constant throughout the well.

1

In the one-dimensional infinite well, how does the energy spacing between the excited states change as the energy of the states increases?


(1) The spacing is constant.


(2) The spacing decreases.


(3) The spacing increases.


(4) The spacing changes randomly.

3

A beam of particles is incident from the negative x axis onto a positive potential energy step located at x = 0. The kinetic energy of the particles is less than the potential energy of the step. Which is the best description of the behavior of the particles?


(1) All particles are reflected precisely at x = 0. (2) Some particles are reflected at the step and some are transmitted into the x > 0 region.


(3) Some particles are reflected and some are absorbed.


(4) All particles are reflected, but they can penetrate a short distance into the x > 0 region.


(5) All particles are absorbed at the step.

4

The probability to find a particle at any specific location in space:


(1) is directly proportional to the amplitude of the wave function.


(2) can never be zero.


(3) depends on the squared amplitude of the wave function.


(4) can sometimes be infinite.

3

The Schrödinger equation is (a) a second-order differential equation. (b) an equation based on conservation of energy. (c) an equation whose solution gives the wave function that describes a particle. How many of the above statements are true?


(1) Zero (2) One (3) Two (4) All three

4
Which of the following is NOT a characteristic of the Bohr model of the structure of the atom? (1) Electrons move in circular orbits about the nucleus. (2) Photons are emitted when an electron jumps from one circular orbit to a lower-energy orbit. (3) The circular motion of the electron is consistent with the uncertainty principle. (4) The angular momentum of each orbit can take only values that are integer multiples of the smallest value.
3
In the Bohr model: (1) Electrons move in circular orbits of definite radius. (2) Electrons move in elliptical orbits. (3) Electrons moving in the same orbit can have different energies. (4) Electrons can never jump from one orbit to another.
1
Which of the following is NOT used in the Bohr model of the atom? (1) Quantization of energy. (2) Relativistic energy and momentum. (3) Coulomb’s law for electrostatic forces. (4) Quantization of angular momentum.
2
In a Rutherford scattering experiment: (1) most of the particles are not scattered at all or scattered only at small angles, but a few are scattered at large angles. (2) the experimental results verify that the positive charge of the atom is spread throughout the volume of the atom. (3) most particles are scattered only once, but the ones that are scattered at large angles are scattered many times. (4) scattering by the negatively charged electrons can cancel scattering by the positively charged nucleus.
1