Which of the following functions is an eigenfunction of the operator ?

	a.
	b.
	c.
	d.

.

Which of the following functions is not an eigenfunction of the operator ?

	a.
	b.
	c.
	d.

.

In quantum mechanics, electrons can behave as:

	a. waves.
	b. both waves and particles.
	c. particles.
	d. none of these choices.

.

In quantum mechanics, light can behave as:

	a. waves.
	b. particles.
	c. both waves and particles.
	d. none of these choices.

.

One phenomenon that demonstrates the particle nature of light is:

	a. light diffraction.
	b. the photoelectric effect.
	c. color.
	d. interference effects.

.

One phenomenon that demonstrates the wave nature of light is:

	a. diffraction.
	b. the photoelectric effect.
	c. blackbody radiation.
	d. absorption of light by an electron.

.

Electron (e) has a mass of 9.10938 x 10^(-31) kg, and the mass of proton (p) is 1.67262 x 10^(-27) kg. Assuming both the electron and the proton move at the same speed of 300 m/s, which of the following is a true statement concerning the de Broglie wavelengths?

	a.
	b.
	c.
	d.

.

Electron (e) has a mass of 9.10938 x 10^(-31) kg, and the mass of proton (p) is 1.67262 X 10^(-27) kg. Assuming both the electron and the proton move at the same speed of 500 m/s, which of the following is a true statement concerning the de Broglie wavelengths?

	a.
	b.
	c.
	d.

.

The electronic energy levels of the hydrogen atom are shown in the diagram below. According to the Bohr model of the atom, how many lines will be observed in the atomic emission spectra if the electron is excited to the level with energy of -0.85 eV?

	a. 2
	b. 1
	c. 4
	d. 3

.

The electronic energy levels of the hydrogen atom are shown in the following diagram. According to the Bohr model of the atom, how many lines will be observed in the atomic emission spectra if the electron is excited to the level with an energy of -0.54 eV?

	a. 3
	b. 5
	c. 4
	d. 1

.

A key piece of evidence for the wave-particle duality of electrons is:

	a. that electrons have momentum.
	b. that electrons have mass.
	c. the diffraction of electrons.
	d. that electrons are attracted to the nucleus in an atom.

.

A key piece of evidence for the wave-particle duality of light is:

	a. the wavelength of green light.
	b. the photoelectric effect.
	c. color of light.
	d. intensity of light.

.

Given that a baseball has a mass of 0.14 kg, and the Planck's constant is 6.626 x 10^(-34) J S, what is the de Broglie wavelength (in meters) for the baseball moving at a speed of 40 m/s?

	a. 4.733 x 10^(-33) m
	b. 8.451 x 10^(33) m
	c. 1.183 x 10^(-34) m
	d. 1.657 x 10^(-35) m

.

Given that the mass of an electron is me = 9.11 x 10^(-31) kg, and the Planck's constant is 6.626 x 10^(-34) J S, what is the de Broglie wavelength (in meters) for an electron moving at a speed of 480,000 m/s?

	a. 1.380 x 10^(-39) m
	b. 6.599 x 10^(8) m
	c. 7.273 x 10^(-4) m
	d. 1.515 x 10^(-9) m

.

The atomic emission spectra of the hydrogen atom show a red line at a wavelength of 656 nm. Given that the speed of light is 3.0 x 10^(8) m/s and Planck's constant is 6.626 x 10^(-34) J S, what is the energy possessed by one photon?

	a. 3.300 x 10^(18) J
	b. 3.030 x 10^(-19) J
	c. 1.010 x 10^(-27) J
	d. 4.573 x 10^(14) J

.

The atomic emission spectra of the hydrogen atom show a violet line at a wavelength of 434 nm. Given that the speed of light is 3.0 x 10^(8) m/s and Planck's constant is 6.626 x 10^(-34) J S, what is the energy possessed by one photon?

	a. 6.912 x 10^(14) J
	b. 1.526 x 10^(-27) J
	c. 4.580 x 10^(-19) J
	d. 2.180 x 10^(18) J

.

The time independent form of the Schrödinger equation is given by:

	a.
	b.
	c.
	d.

.

The time independent form of the Schrödinger equation is given by:

	a.
	b.
	c.
	d.

.

For a one-dimensional system, the potential energy function is described by . The Schrödinger equation for the system is:

	a.
	b.
	c.
	d.

.

For a one-dimensional system, the potential energy function is described by . The Schrödinger equation for the system is

	a.
	b.
	c.
	d.

.

According to the Heisenberg's uncertainty principle:

	a.
	b.
	c.
	d.

.

Which of the following equations does NOT violate the Heisenberg's uncertainty principle?

	a.
	b.
	c.
	d.

.

Which of the following is an acceptable wave function?

	a.
	b.
	c.
	d.

.

Which of the following is an unacceptable wave function?

	a.
	b.
	c.
	d.

.

For a given system, the wavefunction is given by is:

	a.
	b.
	c.
	d.

.

For a given system, the wavefunction is given by . The probability density for finding the particle is:

	a.
	b.
	c.
	d.

.

For a given system, the wavefunction is given by is:

	a. 1
	b.
	c.
	d.

.

For a given system, the wavefunction is given by is:

	a.
	b.
	c.
	d.

.

The energy operator in quantum mechanics, , is called the:

	a. momentum.
	b. Laplacian.
	c. Hamiltonian.
	d. Hermitian.

.

The kinetic energy operator for a one-dimensional system is:

	a.
	b.
	c.
	d.

.

The expectation value for a physical observable represented by a Hermitian operator is:

	a.
	b.
	c.
	d.

.

The expectation value for the linear momentum at a given quantum mechanical state is:

	a.
	b.
	c.
	d.

.

Acceptable wave functions must satisfy which of the following requirements?

	a. Single valued
	b. Finite
	c. Continuous
	d. All of these choices

.

A physical requirement on an acceptable wave function is that it must be:

	a. positive everywhere.
	b. normalizable.
	c. reliable.
	d. none of these choices.

.

The postulate that is:

	a. Einstein’s hypothesis.
	b. De Broglie’s hypothesis.
	c. Born’s postulate.
	d. Schrödinger’s idea.

.

In the probabilistic interpretation of wave function is:

	a. a probability.
	b. a probability density.
	c. always negative.
	d. none of these choices.

.

In solving the Schrödinger equation for the particle in a box system, satisfying the boundary conditions imposes:

	a. the Heisenberg uncertainty principle.
	b. zero-point energy.
	c. quantization of energy.
	d. all of these choices.

.

In solving the Schrödinger equation for the harmonic oscillator, satisfying the boundary conditions imposes:

	a. quantization of energy.
	b. the Heisenberg uncertainty principle.
	c. zero-point energy.
	d. all of these choices.

.

The phenomenon that wave functions can extend into the classically forbidden region, i.e., the region where a classical particle would have negative kinetic energy, is termed:

	a. quantization.
	b. quantum mechanical tunneling.
	c. normalization.
	d. zero-point energy.

.

Which of the following is TRUE about tunneling?

	a. It occurs in the harmonic oscillator system.
	b. It is the phenomenon that wave functions can extend into the classically forbidden region, i.e., the region where a classical particle would have negative kinetic energy.
	c. It becomes less as the mass of particle increases.
	d. All of these choices

.

The vibrational frequency for the hydrogen chloride molecule HCl is 2886 cm^(-1). Assuming the diatomic vibration can be treated as a harmonic oscillator, calculate the zero-point energy for HCl:

	a. 2.87 x 10^(-22) J
	b. 5.74 x 10^(-20) J
	c. 0
	d. 2.87 x 10^(-20) J

.

The vibrational frequency for the hydrogen bromide molecule (HBr) is 2558 cm^(-1). Assuming the diatomic vibration can be treated as a harmonic oscillator, calculate the zero-point energy for HBr.

	a. 0
	b. 5.08 x 10^(-20) J
	c. 2.54 x 10^(-20) J
	d. 1.27 x 10^(-20) J

.

The energy gap between two adjacent quantum states for the rigid rotor system:

	a. is a constant.
	b. increases as the quantum number becomes larger.
	c. decrease as the quantum number becomes larger.
	d. none of these choices.

.

The energy gap between two adjacent quantum states for the harmonic oscillator system:

	a. decreases as the quantum number becomes larger.
	b. increases as the quantum number becomes larger.
	c. is a constant.
	d. equals .

.

The ground state wavefunction for the one-dimensional particle in a box system is given by ?

	a. -1/2
	b. 1
	c. 1/4
	d. 1/2

.

The state wavefunction for the one-dimensional particle in a box system is given by ?

	a. -1/2
	b. 1/4
	c. 1/2
	d. 1

.

For the three-dimensional particle in a box system, the Hamiltonian is separable, i.e., . The total energy of the system can be expressed as:

	a.
	b.
	c.
	d. none of these choices.

.

For the three-dimensional particle in a box system, the Hamiltonian is separable, i.e., . The total wave function of the system can be expressed as:

	a.
	b.
	c.
	d.

.

The Schrödinger equation for the rigid rotor system must be solved with the spherical coordinate system. Giving component of the angular momentum, the correct expression for cal7culating the average value of Lx is:

	a.
	b.
	c.
	d.

.

The Schrödinger equation for the rigid rotor system must be solved with the spherical coordinate system. Giving is:

	a.
	b.
	c.
	d.

.

The solution of the Schrödinger equation for the rigid rotor system resulted in degenerated states for a nonzero angular momentum quantum number . For the energy level, the degeneracy is:

	a. 5.
	b. 2.
	c. 3.
	d. 1.

.

The solution of the Schrödinger equation for the rigid rotor system results in degenerated states for a nonzero angular momentum quantum number energy level, the degeneracy is:

	a. 5.
	b. 2.
	c. 3.
	d. 1.

.

The solution of the Schrödinger equation for the particle on a ring system resulted in the normalized wave function ?

	a. 1
	b. 1/4
	c. 1/2
	d. 0

.

The solution of the Schrödinger equation for the particle on a ring system resulted in the normalized wave function ?

	a. 1/8
	b. 1/4
	c. 1/2
	d. 1

.

Wave functions for the hydrogen atom contain nodes. The 4d orbital possesses:

	a. three angular nodes and one radial node.
	b. four angular nodes and two radial nodes.
	c. four angular nodes and one radial node.
	d. two angular nodes and one radial node.

.

Wave functions for the hydrogen atom can contain nodes. The 5p orbital possesses:

	a. two angular nodes and two radial nodes.
	b. one angular nodes and three radial nodes.
	c. five angular nodes and three radial nodes.
	d. one angular node and five radial nodes.

.

The solution of the Schrödinger equation for the hydrogen atom resulted in degenerated states for the principal energy levels characterized by the principal quantum number n. For the ) are:

	a. (2, 2, 1), (2, 1, -1), (2, 1, 0), (2, 1, 1), and (2, 0, 0).
	b. (2, 1, -1), (2, 1, 0), (2, 1, 1), and (2, 0, 0).
	c. (2, 1, -1), (2, 1, 0), (2, 1, 1), (2, 0, -1), (2, 0, 0), and (2, 0, 1).
	d. (2, 2, -1), (2, 1, -1), (2, 1, 0), and (2, 1, 1).

.

The solution of the Schrödinger equation for the hydrogen atom results in degenerated states for the principal energy levels characterized by the principal quantum number is the angular momentum quantum number, and ml is the magnetic quantum number)?

	a.
	b.
	c.
	d.

.

The solution of the Schrödinger equation for the hydrogen atom resulted in degenerated states for the principal energy levels characterized by the principal quantum number energy level, the degeneracy is:

	a. 3.
	b. 6.
	c. 4.
	d. 9.

.

The solution of the Schrödinger equation for the hydrogen atom results in degenerated states for the principal energy levels characterized by the principal quantum number energy level, the degeneracy is:

	a. 3.
	b. 6.
	c. 4.
	d. 9.

.

Which of the following orbitals can be represented by the set of quantum numbers ?

	a. 4d
	b. 4p
	c. 4s
	d. 1s

.

Which of the following orbitals can be represented by the set of quantum numbers ?

	a. 2d
	b. 4p
	c. 5s
	d. 5d

.

The following term symbols correspond to the ground electronic state of atomic carbon, C. Use Hund's rule to predict which of these levels is lowest in energy.

	a.
	b.
	c.
	d.

.

What is the total number of microstates in a term of the ground state iron atom?

	a. 12
	b. 25
	c. 15
	d. 10

.

What kind of molecular orbital forms when the two atomic orbitals shown below interact in the manner indicated?

	a.
	b.
	c.
	d.

.

What kind of molecular orbital forms when the two atomic orbitals shown below interact in the manner indicated?

	a.
	b.
	c.
	d.

.

According to the molecular orbital theory, the bonding order for the carbon monoxide molecule CO is:

	a. 3.
	b. 3.5.
	c. 2.
	d. 2.5.

.

According to the molecular orbital theory, the bonding order for the ion is:

	a. 3.
	b. 2.
	c. 1.
	d. 2.5.

.

Which of the following statements is FALSE?

	a. Molecular orbitals are often expressed as sums and differences of atomic orbitals that are based on H-atom orbitals.
	b. Bonding orbitals result from in-phase superposition of atomic orbitals.
	c. Even with the application of the Born-Oppenheimer approximation, the Schrödinger equation for the ion is still analytically unsolvable.
	d. .

.

Which of the following statements is FALSE?

	a. A molecular orbital extends over more than two atoms and can hold more than two electrons.
	b. The Hartree-Fock method requires the Born-Oppenheimer approximation.
	c. .

.

Based on the Hückel molecular orbital theory, the highest occupied molecular orbital (HOMO) for the benzene molecule has an energy of:

	a.
	b.
	c.
	d.

.

Based on the Hückel molecular orbital theory, the conjugated is:

	a.
	b.
	c.
	d.

.

Identify all symmetry elements in the ammonia molecule , and assign a point group.

	a.
	b.
	c.
	d.

.

Identify all symmetry elements in the trigonal planar molecule.

	a.
	b.
	c.
	d. None of these choices

.

The symmetry operation group can be represented as a three-dimensional matrix by:

	a.
	b.
	c.
	d. none of these choices.

.

The symmetry operation group can be represented as a three-dimensional matrix by:

	a.
	b.
	c.
	d. none of these choices.

.

Using the character table for the group given below, what is the number of one-dimensional irreducible representations?

	a. 6
	b. 5
	c. 3
	d. 4

.

The character table for the group is given below. How many three-dimensional irreducible representations are there?

	a. 6
	b. 0
	c. 2
	d. 4

.

The IR spectra for the hydrogen chloride molecule (HCl) display a peak at 2886 cm^(-1). Assuming the diatomic vibration can be treated as a harmonic oscillator, calculate the energy for the first vibrational excited state of HCl.

	a. 8.63 kcal/mol
	b. 43.17 kcal/mol
	c. 25.90 kcal/mol
	d. 17.27 kcal/mol

.

The IR spectra for the hydrogen bromide molecule (HBr) display a peak at 2558 cm^(-1). Assuming the diatomic vibration can be treated as a harmonic oscillator, calculate the energy for the first vibrational excited state of HBr.

	a. 7.65 kcal/mol
	b. 22.96 kcal/mol
	c. 15.30 kcal/mol
	d. 38.26 kcal/mol

.

An absorption spectrum for the diatomic molecule hydrogen iodide (HI) appeared in the microwave region. The most likely origin for the observed spectra is:

	a. pure rotational transition.
	b. pure vibrational transition.
	c. electronic transition.
	d. none of these choices.

.

An absorption spectrum for the diatomic molecule hydrogen bromide HBr appeared at the IR region as shown below. Which of the following is the most likely origin for the observed spectrum?

	a. Pure rotational transition
	b. Pure vibrational transition
	c. Electronic transition
	d. Ro-vibrational transition

.

Which of the following molecules will NOT exhibit a microwave rotational absorption spectrum?

	a.
	b.
	c.
	d.

.

Which of the following molecules will not exhibit a microwave rotational absorption spectrum?

	a.
	b.
	c.
	d.

.

The carbon dioxide molecule will be both RAMAN and IR active?

	a. 1
	b. 2
	c. 0
	d. 3

.

Which of the following vibrational modes of the carbon dioxide molecule will be IR active?

	a.
	b.
	c.
	d. None

.

How many normal modes of vibration occur in a nonlinear molecule ?

	a. 8
	b. 15
	c. 16
	d. 18

.

How many normal modes of vibration occur in the benzene molecule ?

	a. 12
	b. 36
	c. 30
	d. 6

.

In a typical ro-vibrational absorption spectrum with a v = 0 to v = 1 transition, which of the following lines occurs at the lowest frequency?

	a. J = 4 to J = 3
	b. J = 1 to J = 0
	c. J = 3 to J = 4
	d. J = 0 to J = 1

.

In a typical ro-vibrational absorption spectrum with a v = 0 to v = 1 transition, which of the following lines occurs at the highest frequency?

	a. J = 4 to J = 3
	b. J = 0 to J = 1
	c. J = 3 to J = 4
	d. J = 4 to J = 5

.

For which of the following transitions does the frequency of light absorption occur in the UV-V is region for a heteronuclear diatomic molecule like HBr?

	a. Electronic transition
	b. Rotational transition
	c. Vibrational transition
	d. Translational transition

.

For which of the following transitions is the frequency of light absorption the highest for a heteronuclear diatomic molecule like HBr?

	a. Rotational transition
	b. Ro-vibrational transition
	c. Vibrational transition
	d. Electronic transition

.

As an electron is excited from a singlet ground state to a singlet excited state of the chlorophyll molecule, what is a possible fate of the electronic excited state?

	a. Fluorescence
	b. Phosphorescence
	c. Transference of energy to a nearby receptor molecule
	d. All of these choices

.

The chlorophyll molecule possesses a singlet ground state . Which of the following is true?

	a. Fluorescence occurs as a result of transition.
	b. Phosphorescence is a spin-forbidden transition.
	c. Phosphorescence occurs at the same time scale as fluorescence.
	d. Emission of light does not obey the Franck-Condon principle.

.

For a certain molecule, the fluorescence spectrum can be a mirror image of the absorption spectrum. Which of the following is NOT a likely contributing factor for the occurrence of the mirror image?

	a. Absorption of light by the vibrational transition obeys the Franck-Condon principle.
	b. The ground electronic state has very similar vibrational states as the first electronic excited state.
	c. The emission of light by vibrational transition obeys the Franck-Condon principle.
	d. Both absorption and emission of light are measured by the same instrument.

.

For a certain molecule, the fluorescence spectrum can be a mirror image of the absorption spectrum. Which of the following is not a likely contributing factor for the occurrence of the mirror image?

	a. Absorption of light from the ground electronic state starts at the ground vibrational state.
	b. Both absorption and emission of light are directly proportional to concentration of the molecule
	c. Emission of light from the electronically excited state starts at the ground vibrational state.
	d. The Franck-Condon principle governs both absorption and emission of light by the molecule.

.

Which list below contains only spin active nuclei in the NMR spectroscopy?

	a.
	b.
	c. 2H, 12C, 31P
	d. 1H, 13C, 31P

.

Which list below contains only spin-active nuclei in the NMR spectroscopy?

	a.
	b.
	c.
	d.

.

In a NMR experiment, an external magnetic field is applied to the sample. What happens to the protons in a sample?

	a. All protons align opposite to the field.
	b. Some protons align with the field and some align opposite to it.
	c. All protons align with the field.
	d. All protons assume a random orientation.

.

In a NMR experiment, a radio frequency (RF) signal is applied to the sample, in addition to the magnetic field. What happens to the spins of the sample?

	a. The RF will force all spins to align opposite to the magnetic field.
	b. The RF will force all spins to assume a random orientation.
	c. The RF will force all spins to align with the magnetic field.
	d. The RF will flip the spin so as to prompt a spin transition to a slightly higher energy state.

.