330 terms

Question 1

Normalization

Answer 1

Finding A (amplitude) of a soln to the Schrodinger equation since the sum of all the probabilities must be equal to 1

Question 2

Zeeman effect

Answer 2

Describes how the energy of an electron changes in the presence of an electric field

Question 2

What does m quantum number refer to ?

Answer 2

Magentic property

Question 2

Hartree Fock approximation aka orbital approximation

Answer 2

Mathimatically assumes that each electron has its own wavefunction and that the total wavefunction is a seperable product of inidividual wavfunctions

Question 3

Issues with HF approx

Answer 3

HF ALWAYS overestimates energy!

Question 3

Zero point energy

Answer 3

The zero point energy is the ground state energy for the harmonic oscillator E=h(nu). Given the uncertainty principal , if E=0 here, then there would be certain position and certain momentum (since velocity=0).

Question 3

Postulate 1 of Quantum mechanics

Answer 3

All the info ab a quantum mechanical system is contained in the wavefunction
psi is an indepterminate model (psi cannot predict the future)

Question 4

Postulate 2 of Quantum mechanics

Answer 4

Every observable in classical mechanics corresponds with a linear operator
a linear operator is distributive
psi must be single valued,continuous, finite,
(end behavior that gpes to zero)

Question 5

Postulate 3 of Quantum mechanics

Answer 5

Any measurement associated with an observable associated with the operator A, only values that can ever be observed are the eigenvalues from A psi =a psi

Question 6

Postulate 4 of Quantum Mechanics

Answer 6

The average value for any observable is <a>= (integral over all space) psi (complex conj) * Ahat * psi</a>

Question 7

If you constrain a wave you get

Answer 7

Quantized states! can on get interger values of full wavelengths that fit between 2 points.

Question 8

What to orbitals represent?

Answer 8

Probabilites that you find an electronin an area in space

Question 9

A typical molecule has ___ degrees of freedom

Answer 9

3N-6 internal (vibrational degrees of freedom)

Question 10

Anharmonicity

Answer 10

asymetric potential

Question 11

Pauli principal arrise from 2 properties of e-

Answer 11

1) electrons are indistinguisable
2) electrons are

Question 12

Born Oppenhiemer approximation

Answer 12

electrons treat nuclei as frozen and fixed
nuclei see electrons as delocalized
this assumption allows us to multiply electron energy and nuclear energy

Question 13

Define Hermitian

Answer 13

Hermitian means A operator operating on complex conjugate is equal to A operating on the function

Question 14

Eigenfunctions of the Hermitian operator

Answer 14

MUST be real (not imaginary) because all obeservables are observable

Question 14

Commutator

Answer 14

When 2 operators commute they can be simultaneously defined for a system

Question 15

Orthogonal definition

Answer 15

Independent or not overlapping,
can use symmetry argument:

Question 16

Why wavelength and frequency inversely related?

Answer 16

Frequency quantifies the energy per photon
(we could also increase the number of the photons)

Question 17

Photoelectric effect

Answer 17

Ephoton= threshold energy + KE (0.5 mv^2)

Question 18

de Broglie wavelength

Answer 18

=h/p=h/mv
we can determine the wavelength of a piece of matter

Question 19

How does treating matter as wave lead to quantized states ?

Answer 19

Because you contrain a wave such that interger values of the wavelength exist between 2 points

Question 20

Uncertainty for PIB

Answer 20

position momentum

Question 21

Linear operators

Answer 21

Position : x(hat)= x Momentum: p(hat)=-ih(bar) d/dx Kinetic Energy: T(hat)= -h^2/2m d^2/dx^2 Energy: Hamiltonian

Question 22

Resonance criteria

Answer 22

If energy of light wave matches the frequency of chemical processes (spacing of energy levels), then the light can be absorbed

Question 23

Limitation of PIB (from pset)

Answer 23

-the repulsion of other electrons in the system -ignores nuclei -finite walls (molecule can be oxidized)

Question 24

EM spectrum

Answer 24

low E radiowave (excites spin) microwave (excites rotations) IR (excites molecular vibrations and nuclear motions) Vis/Uv (excites electrons) high E

Question 25

Postulate 4 QM

Answer 25

average value is the integral (over all space) of psi* A psi

Question 26

Postulate 5 QM

Answer 26

Time independent Schrodinger equation

Question 27

All Qm operators must be

Answer 27

Hermitian

Question 28

Eigenfunctions of any hermitian operator must be

Answer 28

orthogonal

Question 29

Tunneling region

Answer 29

Intersection of V(x) and the eigenstate, particle can "jump" over an energy barrier

Question 30

Vibrational degrees of freedom

Answer 30

3N-6 for to specify the conformation of bc we subtract away rotations and traslations that don't change bond length

Question 31

Transition states

Answer 31

Most unstable, 3N-7 degees of freedom force constant is negative, and so there is an imaginary frequency meaning that the molecule cannot oscillate, so that it cannot feel a restoring force and so a slight distruption to the bond pushes the molecule to fall to stable product

Question 32

Rigid Rotor

Answer 32

answers following question: what are the likely angular rotations of a diatomic molecule

Question 33

Assumptions of RR model

Answer 33

-Fixed bond length and so as a result mass is constrained to live somewhere on a 2D surface of a sphere -center of mass coordinates

Question 34

order of magnitude for visible light spectrum

Answer 34

400nm-700nm

Question 35

Frequencies of visible light

Answer 35

10^-14 to 10^-15

Question 36

I (moment of inertia)

Answer 36

I= μR^2

Question 37

Reduced mass

Answer 37

m1*m2/(m1+m2)

Question 38

Frank Condon Principal

Answer 38

Over the course of excitation, nuclei do not move

Question 39

Microwave spectrum (rotational energy) features

Answer 39

-regularly spaced CHANGE in energy levels -gap in middle- fundemental frequency -R- branch peaks closer together than P branch (positive delta J) peaks

Question 40

Angular momentum (Lx, Ly, Lz) and L^2)

Answer 40

Can only define one component at a time(carves out curve of uncertainty) ONE exception to this is when L^2 is zero- then each component is zero but for the uncertainty prinicpal to be met ther must be uncertainty in postion (spherical so knoe r but could be anywher on the surface)

Question 41

Only model with regularly spaced energy levels?

Answer 41

The 1D harmonic oscillator

Question 42

Why HF a not great approximation?

Answer 42

e- are moving to the average of the other postion (lots of unceratinty) so HF is always an over approximation

Question 43

Average position of PIB graphically?

Answer 43

Where psi squared is symmetric

Question 44

Can superpostion for H atom have well defined energy?

Answer 44

Yes- in the case of degereracy- ex psi 200 and psi 211 , both have the same energy