Deck 6: Quantum Mechanics and Molecular Structure

Question 1

In H₂⁺, how many nodes does the 1s_u* orbital have along the internuclear axis?

A) 0
B) 0.5
C) 1
D) 2
E) 3

Answer 1

C

Question 2

If you excited the electron in H₂⁺ from the 1s_g state to the 1s_u* what would expect to happen to the molecule?

A) It would eject an electron to become two H⁺ ions
B) It would vibrate
C) It would contract to a shorter bond length
D) It would dissociate into an H atom and H⁺ ion
E) It would become a Helium atom

Answer 2

D

Question 3

At large internuclear distances the 1p_g orbital in H₂⁺ resembles

A) the sum of two 1s hydrogen orbitals.
B) the difference of two 1s hydrogen orbitals.
C) the sum of two 2p hydrogen orbitals.
D) the difference of two 2p hydrogen orbitals.
E) the sum of a 1s and a 2p hydrogen orbital.

Answer 3

D

Question 4

Which of the following describe the 1s_u* orbital in H₂⁺?

A) this is an antibonding orbital
B) this orbital has a node along the internuclear axis
C) this orbital is odd with respect to inversion
D) a & b
E) all of the above

Question 5

Which will have a longer bond length, H₂ or He₂⁺?

A) H₂
B) He₂⁺
C) They will be exactly the same
D) There is no way to know

Question 6

Which of the following has the highest bond order O₂, O₂⁺, N₂, N₂⁺?

A) O₂
B) O₂⁺
C) N₂
D) N₂⁺
E) N₂⁺ and O₂ are the same and the highest

Question 7

What is the bond order in Cl₂?

A) 0.5
B) 1
C) 1.5
D) 2
E) Cl₂ won't form a bond

Question 8

To be paramagnetic a molecule must have

A) an odd number of electrons.
B) an even number of electrons.
C) have at least one unpaired electron.
D) have at least two unpaired electrons.
E) b & d

Question 9

If you remove one of the electrons from N₂ what will happen to its bond length?

A) the bond length will increase
B) the bond length will decrease
C) the bond length will stay the same
D) there will no longer be a bond in the molecule

Question 10

In the correlation diagram for HF the molecular orbitals are formed by mixing the 1s on the hydrogen with a 2p orbital in fluorine because

A) these orbitals are closest in energy
B) these orbitals have the same symmetry
C) these orbitals have the same angular momentum
D) a & b
E) all of the above

Question 11

In photoelectron spectroscopy if an electron is removed from a bonding orbital the vibrational fine structure will exhibit a

A) higher vibrational frequency than the parent molecule.
B) lower vibrational frequency than the parent molecule.
C) and identical vibrational frequency as the parent molecule.
D) there will be no vibrational fine structure in the spectrum.

Question 12

The orbital energy of core electrons in a molecule are

A) nearly identical to the energy in the unbonded atom.
B) significantly higher than in the unbonded atom.
C) significantly lower than in the unbonded atom.
D) vary depending on the molecule.
E) vary depending on the atom.

Question 13

In a photoelectron spectrum of N₂, you would expect the electrons coming off with the highest kinetic energy to be associated with which MO?

A) 1s N
B) s_g2S
C) p_u2p
D) s_2pz
E) p_g2p^*

Question 14

Why does the VB model predict there will be no bonding in BeH₂?

A) There is no overlap between the atomic orbitals of Be and the H.
B) The orbitals of Be have the wrong symmetry compared to those in H.
C) The energy levels of the Be atomic orbitals are too high to mix with the H.
D) There are no unpaired electrons in the Be atomic orbitals.
E) The Be and H atomic orbitals have the same angular momentum.

Question 15

A simple VB wavefunction for Na₂ would be

A) Y_g = C₁[1s^A (1)1s^B (2) + 1s^A (2)1s^B (1)]
B) Y_g = C₁[1s^A (1)3s^B (2) + 1s^A (2)3s^B (1)]
C) Y_u = C₁[3s^A (1)3s^B (2) - 3s^A (2)3s^B (1)]
D) Y_g = C₁[3s^A (1)3s^B (2) + 3s^A (2)3s^B (1)]
E) Y_g = C₁[1s^A (1)3s^B (2) - 3s^A (2)3s^B (1)]

Question 16

What would the VB model predict for the valency of C without "promotion" or "hybridization"?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 17

What are the VB wavefunctions for the bonds in NH₃?

A) Y_s = C₁[1s^H (1)1s^N (2) + 1s^H (2)1s^N (1)]
B) Y_p = C₁[1s^H (1)2p^N (2) + 1s^H (2)2p^N (1)]
C) Y_s = C₁[1s^H (1)2p^N (2) - 1s^H (2)2p^N (1)]
D) Y_p = C₁[2p^H (1)1s^N (2) + 2p^H (2)1s^N (1)]
E) Y_s = C₁[1s^H (1)2p^N (2) + 1s^H (2)2p^N (1)]

Question 18

What do you predict for the hybridization of the central atom in CCl₃?

A) not hybridized
B) sp³
C) sp²
D) sp
E) sp³d²

Question 19

In the molecule, H-CºN, the VB model would describe the sigma bond between the C and the N as a combination of

A) 2p orbital on the C and a 2p orbital on the N.
B) 2p orbital on the C and a 2s orbital on the N.
C) 2s orbital on the C and a 2p orbital on the N.
D) a sp hybridized orbital on the C and a 2p orbital on the N.
E) a sp³ hybridized orbital on the C and a 2p orbital on the N.

Question 20

In the molecule, H-CºN, the VB model would predict how many s and p bonds?

A) 1s and 2p
B) 2s and 2p
C) 2s and 1p
D) 1s and 1p
E) 1s and 3p

Question 21

In the LCAO wavefunction for H₂ given below, the second term can be described as "ionic" because = [1s^A (1)1s^B (2) + 1s^A (2)1s^B (1)] + [1s^A (1)1s^A (2) + 1s^B (1)1s^B (2)]

A) it describes the excited state of each orbital.
B) it has both electrons centered on one nucleus or the other.
C) it has both electrons equally shared between the two nuclei.
D) it is a wavefunction that describes two electrons.
E) the second term is not an "ionic" term.

Question 22

A Lewis dot structure for benzene, C₆H₆ would give two equivalent resonance structures for this cyclic molecule with alternating single and double bonds A combined LCAO and MO picture for the bonding of the carbon atoms in benzene would be

A) 3s(C2p-C2p) bonds between each C atom
B) 2s(Csp³-Csp³) bonds between each C atom, and 1p MO delocalized over the C's
C) 1s(Csp³-Csp³) bonds between each C atom, and 1p MO delocalized over the C's
D) 1s(Csp²-Csp²) bonds between each C atom, and 2p MO delocalized over the C's
E) 1s(Csp²-Csp²) bonds between each C atom, and 3p MO delocalized over the C's

Question 23

VB theory is poorly suited to polar molecules such as HCl because

A) VB theory is a localized bonding model
B) VB theory assumes bonds form only between unpaired electrons in atomic orbitals
C) VB theory can't predict p bonds
D) VB wavefunctions always have even parity with respect to inversion
E) VB wavefunctions do not contain any ionic states

Question 24

The Born Openheimer approximation assumes that the electrons move much faster than the nuclei. This lets us assume the wavefunctions for the electrons in the molecule

A) are independent of the position of the nuclei.
B) depend only on the positions of the nuclei.
C) are the same as the wavefunctions for the nuclei.
D) the product of one electron wavefunctions.
E) always even with regard to inversion symmetry.

Question 25

The lowest energy antibonding orbital in H₂⁺

A) has a node along the internuclear axis
B) has an energy that is higher than H + H⁺
C) is antisymmetric with respect to inversion
D) a & b
E) all of the above

Question 26

The ionization energy of H₂^- would be expected to be

A) higher than that of H₂
B) higher than that of H
C) lower than that of H₂
D) lower than that of H
E) a & b
F) c & d

Question 27

A MO orbital for a heteronuclear diatomic is given by If A is more electronegative than B then you would predict that

A) C_A > C_B
B) C_A = C_B
C) C_A < C_B
D) C_A = -C_B
E) you would not expect any relation between these coefficients and the electronegativity of the elements A & B

Question 28

The molecule HeH⁺ has an antibonding MO of the form For this you would expect

A) C₁ > C₂
B) C₂ < C₂
C) C₁ = C₂

Question 29

VB theory and MO theory both predict that N₂ has a bond order of three, one sigma bond and two pi bonds. What is the difference between these two models?

A) The wavefunctions for the electrons are different
B) The energies predicted would be different
C) both a & b
D) There are no differences between VB and MO for N₂

Question 30

In CO₂ the hybridization of the C atom is

A) not hybridized
B) sp
C) sp²
D) sp³
E) sp³d²

Question 31

Of the following homonuclear diatomic molecules, which is paramagnetic?

A) B₂
B) C₂
C) N₂
D) F₂
E) None of the above

Question 32

Oxygen is paramagnetic and has a bond order of two. Which of the following represents the ground electronic state for oxygen?

A)

B)

C)

D) A and C are equally probable
E) None of the above

Question 33

Which of the following combinations of atomic orbitals will result in a bonding molecular orbital for a homonuclear diatomic molecule when the z-axis is aligned with the nuclei of the bonded atom?

A)

B)

C)

D)

E) A, B, and D