Quantum Mechanics and Spectroscopy

Flashcards covering key concepts from the Quantum Mechanics and Spectroscopy lecture notes.

What is the Franck-Condon Principle?

A rule in spectroscopy/quantum chemistry that explains the intensity of vibronic transitions.

What phenomena can be explained with the Franck-Condon Principle?

Stokes shift and Bond structure in Electronic Spectra

List some photophysical processes.

Absorption from S0 to S1, fluorescence S1 to S0, internal conversion, intersystem crossing, phosphorescence.

Name the Nobel Prize winners mentioned and their contributions.

1921 (Photoelectric effect), 1929 (Wave nature of electron), 1922 (Wave nature of electron), 1954 (Interpretation of wave eq.), 1918 (Discovery of energy quanta).

What is black body radiation?

Radiation emitted from a body material when it is heated.

Give two examples of black body radiators.

Sun and incandescent light bulb

What does Wien's displacement law state?

The wavelength of maximum spectral energy density emitted from a black body is inversely proportional to its temperature.

What is an application of Wien's displacement law?

Temperature of sun and stars (surface).

What are standing waves?

A wave that remains stationary due to the interference of two waves traveling in opposite directions with the same frequency and amplitude.

Give examples of standing waves.

Guitar strings, sound, pressure, gravitational, and electromagnetic waves.

What is the Broglie wavelength?

λ = h / (m*v), where h is Planck's constant, m is mass, and v is velocity.

Describe the photoelectric effect.

Light shines on a metal, and if the intensity of light is strong enough, photoelectrons will gain enough kinetic energy to leave the metal.

Give an example of a phenomenon that demonstrated that electrons behave like waves.

Electron diffraction/X-ray.

What instrument is used to image nanoscale structures?

Transmission Electron Microscope (TEM).

How does a TEM work, and what concept does it utilize?

Electrons beams hit a specimen and create an image; TEM measures the de Broglie waves of samples as the electrons are transmitted.

What are Bohr's two main assumptions?

Electrons exist in stationary orbits and the Broglie wave must match and be in phase.

Why are stable orbitals for electrons classically forbidden?

Electrons moving in a circular orbit around the nucleus will emit electromagnetic radiation and lose energy, eventually hitting the nucleus.

What is the Heisenberg Uncertainty Principle?

It is impossible to predict simultaneously the exact position and exact momentum of a particle.

List the historical models of the atom in chronological order with their key scientists and years.

Solid sphere model (John Dalton, 1803), Plum pudding model (J.J. Thomson, 1904), Nuclear model (Ernest Rutherford, 1911), Planetary model (Niels Bohr, 1913), Quantum model (Schrödinger, 1926).

What is the definition of an 'operator' in quantum mechanics?

A symbol that tells you to do something to whatever follows the symbol.

What are eigenfunctions?

Special wave functions that represent a defined state of a quantum system.

How do you calculate the average value of an observable in quantum mechanics?

The average value of an observable corresponding to operator  is given by ∫Ψ* Â Ψ dx.

What is the equation for orthonormality?

∫Ψm*(x) Ψn(x) dx = δmn

Why is a particle in a box considered a free particle?

There is no force acting on the particle in the box; it is confined, so it moves inside where V(x) = 0.

What information does the wavefunction provide?

All possible information about the system can be derived from Ψ(x).

How do you determine if an operator is Hermitian?

δ/δx ∫Ψ(δΨ/δx) dx = ∫(δΨ/δx) Ψ dx. If this is true, the operator is Hermitian.

What is the mnemonic for remembering the diatomic molecules?

Have No Fear Of Ice Cold Beer.

What model is used to approximate the rotational motion of a diatomic molecule?

Rigid Rotor model.

What is the key assumption of the Rigid Rotor model?

Bond length is fixed, assuming no vibrational effect.

What model can be used to describe the infrared spectrum of a diatomic molecule?

Harmonic Oscillator model.

What are the selection rules and assumptions of the Harmonic Oscillator model?

Transitions with Δv = ±1 are allowed. HOOKS Law (-kx).

Why is the separation between lines in the microwave spectrum of a diatomic molecule not exactly constant?

As molecules rotate faster, centrifugal distortion causes the bond to stretch.

What quantum mechanical operators have spherical harmonics as eigenfunctions?

Angular momentum squared (L^2) and the Z component of angular momentum (Lz).

What is a limitation regarding the components of angular momentum?

You cannot simultaneously know the values of all 3 components.

What is the Hamiltonian operator for the Hydrogen atom?

Ĥ = -ħ^2/(2me) ∇^2 - e^2/(4πε0r)

Define a vibronic transition.

Vibronic transitions involve a simultaneous change in electronic and vibrational energy levels.

What can be learned from microwave spectra (e.g., rotation of Chloroferecene)?

Learn about dipole moment orientation and rotational constant B.

What molecular processes can be studied by Spectroscopy?

Rotational (Microwave spectroscopy), Vibrational (IR spectroscopy), Electronic (UV-Vis spectroscopy).

State the Born-Oppenheimer approximation.

The motion of atomic nuclei and electrons in a molecule can be separated; ΨTotal = Ψelectronic * Ψnuclear.