Q13 (3.3)

The selection rule for transitions in the R branch of an infra-red absorption spectrum is

delta_vee = +1, delta_J = +1

In a series of measurements of the quantity A, if the particle's state is NOT an eigenfunction of the operator A, the outcome will be:

each individual observation yields one of the eigenvalues, and the probability of getting that eigenvalue is the square of the coefficient of that eigenstate in an expansion of the wavefunction in terms of eigenstates

"Space quantization" refers to the fact that in quantum mechanics

a rotating body can only rotate about certain axes

The energy levels of an anharmonic oscillator

converge

The most strongly metallic elements are found

to the bottom left of the Periodic Table

The vibrational energy levels for a harmonic oscillator are

(vee + 1/2) h_nu

Molecular vibrational transitions are in what region of the spectrum?

infra-red

Which of the following molecules can show a pure rotational spectrum? Check all that apply.

• CO

• HCl

What vibrational transitions are typically observed at room temperature in the infra-red spectrum of a diatomic molecule?

only the v = 0 to v = 1 transition, and possibly a very weak v = 0 to v = 2 overtone

The gross selection rule for pure rotational spectroscopy is that

the dipole moment of the molecule must change during rotation, which is only possible if the molecule has a permanent dipole moment

The vibration frequency of a diatomic molecule is lowest for

weak bonds and heavy atoms

The gross selection rule for infra-red spectroscopy of diatomic molecules is that

the dipole moment must change during vibration, which for diatomics means having a permanent dipole moment, i.e. only heteronuclear diatomics can show an infra-red spectrum

The first R branch line corresponds to the transition

v = 0, J = 0 to v = 1, J = 1

"Classical", massive particles have de Broglie wavelengths that are

so short that the wave character of the particle is undetectable: the undulations are on too small a scale

The greater the kinetic energy of a particle

the greater the curvature of the wavefunction and the larger the wavefunction's second derivative

Which vibrational energy levels are likely to be populated at room temperature?

only the v = 0 energy level

The wavefunctions of the particle in a 1-D box are

sine functions

In the O₂ molecule, which lies lower in energy, the 2p sigma bonding orbital or the 2p pi bonding orbital?

the 2p sigma bonding orbital: the "normal" ordering returns at O₂

In calculating the black body radiation curve, Rayleigh's mistake was

using the equipartition principle for the average energy of an oscillator

The third P branch line in an infra-red absorption spectrum corresponds to the transition

v = 0, J = 3 to v = 1, J = 2