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T (transmittance)
I/I_{0}

Absorbance (Trans deffinition)
A=log(T)

Absorption (lambert beer)


Rotational Constant (B)
 Formual that relates I to Energy


Increase in energy between levels for Rotatational Transition
2(J+1)Bh

Values of rotational quantum nubmer (J)
Integers greater than 0

Relation between wavenumber and wavelength v

What does spectroscopy measure
Changes in Energy!!!

What is energy spacing in change beteen levels for sepctroscopy?
2 Bh

Pauli Exclusion Principle
No two electrons cannot share the same set of quantum numbers within the same system. Therefore, there is room for only two electrons in each spatial orbital. One of these electrons must have (for some chosen direction z), , and the other must have .

Hunds law
Favored configuration normally invovles maximum unpaired spin.

Perturbation theory for hamiltonian
 \
 This implies that
 \

Energies relation to basic wave data
E

Wavelength to frequency relation
cv

What happens when light is absorbed
Nothing visually, but atom is excited to higher energy level.

What happens when atom moves to lower energy level?
Atom relaxes to lower energy level and releases light.

What type of energy change shown by spectrograph lines?
Electronic Energy!

Which region of energy spectrum does rotational energy correspond to?
Microwave

Which region of energyspectrum does electronic energy correspond tro?
Visible

Which energy region does vibrational energy correspond to?
Infared

Where is rigid rotor model important?
In rotating atoms

What is classical momentum modelled after (P)
mass* velocity

What is rotational momentum (p) modelled after?
Moment of inertia* rotational velocity = Iw

What is formula and deffinition of reduced mass (\ )?
\

What are two quantum numbers associated with rigid rotor wave functions adn what are their possible values?
 l=angular momentum quantum number = integer 0 or greater
 m_{i} =magnetic number =integer beteen l (angular moment) and l(angular moment)

Which quantum number does the energy of rigid momentum depend on?
l (angular)

What is degeneracy of rigid momentum energy levels depend on?
2 (angularm momentum)+ 1

Quantum energy for harmonic oscilator?
At E _{0} it simplifies to )

What are allowable energy levels (v) for the harmonic oscilator function_)
integers of 0 or greater

What is order of energy needed for transitions of different tyeps
Rotational<Vibrational<Electronic

Hunds Rules (Spin)
For a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to 2S +1 , where S is the total spin angular momentum for all electrons. The term with lowest energy is also the term with maximum S.

Hunds Rule (angular momentum)
For a given multiplicity, the term with the largest value of the total orbital angular momentum number L has the lowest energy.

Hunds rule (orbital Momentum)
For a given term, in an atom with outermost subshell halffilled or less, the level with the lowest value of the total angular momentum quantum number J (for the operator J = L+S ) lies lowest in energy. If the outermost shell is more than halffilled, the level with the highest value of is lowest in energy.

Where does hunds rule work best?
Hund's rules work best for the determination of the ground state of an atom or molecule. May also be used for first level of excitation

What is J?
 Total angular momentum quantum number S+L
 Spin + orbital Angular Momentum combines both the spin and orbital angular momentum of a particle or system

What is L?
 Orbital angular momentum L is mathematically defined as the cross product of a wave function's position operator (r) and momentum operator (p):
 Orbital Angular momentum

What is m?
M is the third of a set of quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter m. The magnetic quantum number denotes the energy levels available within a subshell.

What is S?
In atomic physics, the spin quantum number is a quantum number that parameterizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle.

Angular Momentum Eigenformula

Spherical Harmonics Theta
Angle from z

Spherical coordinates phi
Angle from x

Spherical harmonics
the angular portion of a set of solutions to Laplace's equation. Represented in a system of spherical coordinates, Laplace's spherical harmonics are a specific set of spherical harmonics that forms anorthogonal system

