Ch. 30 Test Prep for AP® Courses - College Physics for AP® Courses 2e

30.2 Discovery of the Parts of the Atom: Electrons and Nuclei

In an experiment, three microscopic latex spheres are sprayed into a chamber and become charged with +3e, +5e, and −3e, respectively. Later, all three spheres collide simultaneously and then separate. Which of the following are possible values for the final charges on the spheres? Select two answers.

+4e, −4e, +5e
−4e, +4.5e, +4.5e
+5e, −8e, +7e
+6e, +6e, −7e

In Millikan’s oil drop experiment, he experimented with various voltage differences between two plates to determine what voltage was necessary to hold a drop motionless. He deduced that the charge on the oil drop could be found by setting the gravitational force on the drop (pointing downward) equal to the electric force (pointing upward):

$m_{drop} g = q E$ ,

where $m_{drop}$ is the mass of the oil drop, g is the gravitational acceleration (9.8 m/s²), q is the net charge of the oil drop, and E is the electric field between the plates. Millikan deduced that the charge on an electron, e, is 1.6 × 10⁻¹⁹ C.

For a system of oil drops of equal mass (1.0 × 10⁻¹⁵ kilograms), describe what value or values of the electric field would hold the drops motionless.

30.3 Bohr’s Theory of the Hydrogen Atom

A hypothetical one-electron atom in its highest excited state can only emit photons of energy 2E, 3E, and 5E before reaching the ground state. Which of the following represents the complete set of energy levels for this atom?

0, 3E, 5E
0, 2E, 3E
0, 2E, 3E, 5E
0, 5E, 8E, 10E

The Lyman series of photons each have an energy capable of exciting the electron of a hydrogen atom from the ground state (energy level 1) to energy levels 2, 3, 4, etc. The wavelengths of the first five photons in this series are 121.6 nm, 102.6 nm, 97.3 nm, 95.0 nm, and 93.8 nm. The ground state energy of hydrogen is −13.6 eV. Based on the wavelengths of the Lyman series, calculate the energies of the first five excited states above ground level for a hydrogen atom to the nearest 0.1 eV.

The ground state of a certain type of atom has energy –E₀. What is the wavelength of a photon with enough energy to ionize an atom in the ground state and give the ejected electron a kinetic energy of 2E₀?

$\frac{h c}{3 E_{0}}$
$\frac{h c}{2 E_{0}}$
$\frac{h c}{E_{0}}$
$\frac{2 h c}{E_{0}}$

An electron in a hydrogen atom is initially in energy level 2 (E₂ = -3.4 eV). (a) What frequency of photon must be absorbed by the atom in order for the electron to transition to energy level 3 (E₃ = -1.5 eV)? (b) What frequency of photon must be emitted by the atom in order for the electron to transition to energy level 1 (E₁ = -13.6 eV)?

30.5 Applications of Atomic Excitations and De-Excitations

A sample of hydrogen gas confined to a tube is initially at room temperature. As the gas is heated, the observer notices that the gas begins to glow with a pale pink color. Careful study of the spectrum shows that the light spectrum is not continuous. Instead, the hydrogen gas is only emitting visible wavelength photons of four specific colors, which combine to form the overall color to the human eye. What is the best way to explain this behavior?

As the gas heats up, atoms have more and more collisions and close approaches, so frictional heating causes the gas to glow.
As the gas heats up, the electrons within the hydrogen atoms are excited to high energy levels. As the electrons transition to lower energies, they emit light of specific colors.
As the gas heats up, more and more collisions occur, and the energy lost in these inelastic collisions is converted into light.
As the gas heats up, the turbulence of the gas within the tube causes friction between the gas and the walls of the container, causing the gas to glow.

A rock is illuminated with high energy ultraviolet light. This causes the rock to emit visible light. Explain what is happening in the atomic substructure of the rock that causes this effect, which we call fluorescence.

Which of the following is the best way of explaining why the leaves on a given tree are green?

The molecules in the leaves absorb all visible light but strongly reflect green light.
The molecules in the leaves absorb green light and reflect other visible light.
The molecules are excited by external light sources, and their electrons emit green light when they are de-excited to a lower energy level within the molecules.
The molecules glow with a characteristic green energy in order to balance the absorption of energy due to light and heat from their surroundings.

10.

Explain what phosphorescence is and how it differs from fluorescence. Which process typically takes longer and why?

11.

An electron is excited from the ground state of an atom (energy level 1) into a highly excited state (energy level 8). Which of the following electron behaviors represents the fluorescence effect by the atom?

The electron remains at level 8 for a very long time, then transitions up to level 9.
The electron transitions directly down from level 8 to level 1.
The electron transitions from level 8 to level 1 and then returns quickly to level 8.
The electron transitions from level 8 to level 6, then to level 5, then to level 3, then to level 1.

12.

Describe the process of fluorescence in terms of the emission of photons as electron transitions between energy states. Specifically, explain how this process differs from ordinary atomic emission.

30.6 The Wave Nature of Matter Causes Quantization

13.

Figure 30.61 This figure shows graphical representations of the wave functions of two particles, X and Y, that are moving in the positive x-direction. The maximum amplitude of particle X’s wave function is A₀. Which particle has a greater probability of being located at position x₀ at this instant, and why?

Particle X, because the wave function of particle X spends more time passing through x₀ than the wave function of particle Y.
Particle X, because the wave function of particle X has a longer wavelength than the wave function of particle Y.
Particle Y, because the wave function of particle Y is narrower than the wave function of particle X.
Particle Y, because the wave function of particle Y has a greater amplitude near x₀ than the wave function of particle X.

14.

In Figure 30.61, explain qualitatively the difference in the wave functions of particle X and particle Y. Which particle is more likely to be found at a larger distance from the coordinate x₀ and why? Which particle is more likely be found exactly at x₀ and why?

15.

For an electron with a de Broglie wavelength λ, which of the following orbital circumferences within the atom would be disallowed? Select two answers.

0.5 λ
λ
1.5 λ
2 λ

16.

We have discovered that an electron’s orbit must contain an integer number of de Broglie wavelengths. Explain why, under ordinary conditions, this makes it impossible for electrons to spiral in to merge with the positively charged nucleus.