Which of the following functions is an eigenfunction of the operator

Choose one answer.

	a.
	b.
	c.
	d.

Question 2

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 3

In quantum mechanics, electrons can behave as:

Choose one answer.

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

Question 4

In quantum mechanics, light can behave as:

Choose one answer.

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

Question 5

One phenomenon that demonstrates the particle nature of light is:

Choose one answer.

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

Question 6

One phenomenon that demonstrates the wave nature of light is:

Choose one answer.

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

Question 7

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?

Choose one answer.

	a.
	b.
	c.
	d.

Question 8

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?

Choose one answer.

	a.
	b.
	c.
	d.

Question 9

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?

Choose one answer.

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

Question 10

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?

Choose one answer.

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

Question 11

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

Choose one answer.

	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.

Question 12

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

Choose one answer.

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

Question 13

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?

Choose one answer.

	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

Question 14

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?

Choose one answer.

	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

Question 15

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?

Choose one answer.

	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

Question 16

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?

Choose one answer.

	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

Question 17

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 18

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 19

For a one-dimensional system, the potential energy function is described by

. The Schrödinger equation for the system is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 20

For a one-dimensional system, the potential energy function is described by

. The Schrödinger equation for the system is

Choose one answer.

	a.
	b.
	c.
	d.

Question 21

According to the Heisenberg's uncertainty principle:

Choose one answer.

	a.
	b.
	c.
	d.

Question 22

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 23

Which of the following is an acceptable wave function?

Choose one answer.

	a.
	b.
	c.
	d.

Question 24

Which of the following is an unacceptable wave function?

Choose one answer.

	a.
	b.
	c.
	d.

Question 25

For a given system, the wavefunction is given by

is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 26

For a given system, the wavefunction is given by

. The probability density for finding the particle is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 27

For a given system, the wavefunction is given by

is:

Choose one answer.

	a. 1
	b.
	c.
	d.

Question 28

For a given system, the wavefunction is given by

is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 29

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

Choose one answer.

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

Question 30

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 31

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

is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 32

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

is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 33

Acceptable wave functions must satisfy which of the following requirements?

Choose one answer.

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

Question 34

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

Choose one answer.

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

Question 35

The postulate that

is:

Choose one answer.

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

Question 36

In the probabilistic interpretation of wave function

is:

Choose one answer.

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

Question 37

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

Choose one answer.

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

Question 38

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

Choose one answer.

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

Question 39

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:

Choose one answer.

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

Question 40

Which of the following is TRUE about tunneling?

Choose one answer.

	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

Question 41

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:

Choose one answer.

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

Question 42

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.

Choose one answer.

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

Question 43

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

Choose one answer.

	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.

Question 44

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

Choose one answer.

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

Question 45

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

Choose one answer.

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

Question 46

The

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

Choose one answer.

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

Question 47

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:

Choose one answer.

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

Question 48

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:

Choose one answer.

	a.
	b.
	c.
	d.

Question 49

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:

Choose one answer.

	a.
	b.
	c.
	d.

Question 50

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

is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 51

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:

Choose one answer.

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

Question 52

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:

Choose one answer.

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

Question 53

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

Choose one answer.

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

Question 54

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

Choose one answer.

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

Question 55

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

Choose one answer.

	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.

Question 56

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

Choose one answer.

	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.

Question 57

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:

Choose one answer.

	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).

Question 58

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)?

Choose one answer.

	a.
	b.
	c.
	d.

Question 59

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:

Choose one answer.

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

Question 60

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:

Choose one answer.

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

Question 61

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

Choose one answer.

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

Question 62

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

Choose one answer.

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

Question 63

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.

Choose one answer.

	a.
	b.
	c.
	d.

Question 64

What is the total number of microstates in a

term of the ground state iron atom?

Choose one answer.

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

Question 65

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 66

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 67

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

Choose one answer.

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

Question 68

According to the molecular orbital theory, the bonding order for the

ion is:

Choose one answer.

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

Question 69

Which of the following statements is FALSE?

Choose one answer.

	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. .

Question 70

Which of the following statements is FALSE?

Choose one answer.

	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. .

Question 71

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 72

Based on the Hückel molecular orbital theory, the conjugated

is:

Choose one answer.

	a.
	b.
	c.
	d.

Question 73

Identify all symmetry elements in the ammonia molecule

, and assign a point group.

Choose one answer.

	a.
	b.
	c.
	d.

Question 74

Identify all symmetry elements in the trigonal planar

molecule.

Choose one answer.

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

Question 75

The symmetry operation

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

Choose one answer.

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

Question 76

The symmetry operation

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

Choose one answer.

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

Question 77

Using the character table for the

group given below, what is the number of one-dimensional irreducible representations?

Choose one answer.

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

Question 78

The character table for the

group is given below. How many three-dimensional irreducible representations are there?

Choose one answer.

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

Question 79

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.

Choose one answer.

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

Question 80

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.

Choose one answer.

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

Question 81

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

Choose one answer.

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

Question 82

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?

Choose one answer.

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

Question 83

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 84

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 85

The carbon dioxide molecule

will be both RAMAN and IR active?

Choose one answer.

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

Question 86

Which of the following vibrational modes of the carbon dioxide molecule

will be IR active?

Choose one answer.

	a.
	b.
	c.
	d. None

Question 87

How many normal modes of vibration occur in a nonlinear molecule

Choose one answer.

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

Question 88

How many normal modes of vibration occur in the benzene molecule

Choose one answer.

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

Question 89

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?

Choose one answer.

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

Question 90

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?

Choose one answer.

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

Question 91

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?

Choose one answer.

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

Question 92

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

Choose one answer.

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

Question 93

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?

Choose one answer.

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

Question 94

The chlorophyll molecule possesses a singlet ground state

. Which of the following is true?

Choose one answer.

	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.

Question 95

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?

Choose one answer.

	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.

Question 96

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?

Choose one answer.

	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.

Question 97

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

Choose one answer.

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

Question 98

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

Choose one answer.

	a.
	b.
	c.
	d.

Question 99

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

Choose one answer.

	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.

Question 100

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?

Choose one answer.

	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.