Penfold L5 Flashcards
(25 cards)
If we want to describe atoms or molecules what do we need to look at
if you want to describe atoms or molecules you need to look at 3 dimentions
How do we calculate 1/reduced mass
1/μ = 1/me + 1/mN
Where me is the mass of an electron and Mn is the mass of a nucleus
What is the reduced mass
the reduced mass is very similar to the electron mass because the mass of the nucleus is much larger
What is the form of hydrogens wavefunction
𝚿(r, θ,ϕ) = R(r)Y(θ,ϕ)
What is R(r) in hydrogens wavefunction
R(r) is the radial function and describes how far the electron is away from the proton
What is Y(θ,φ) in the wavefunction for hydrogen
Y(θ,φ) Is the spherical harmonic and provide information about where the electron is around the proton
What is spherical harmonics
what the atomic orbitals look like
Describe the energy levels for atomic orbitals of a system with only one electron
if you have a system which involves only 1 electron all of orbitals will be degenerate for the same number of n. So 2s and 2p are degenerate and 3s, 3p and 3d are degenerate
Describe the energy levels for atomic orbitals of a system with more than one electron
If you have more than 1 electron in the system the s,p,d orbitals are no longer degenerate as the electrons interact with one another due to electron-electron repulsion
What is n
principle quantum number - tells us the average relative distance of an electron from the nucleus.
What happen as n increases
as n increase for a given atom so does the average distance of an electron from the nucleus
What is l
Azimuthal quantum number/ angular quantum number - describes the shape of the region of space occupied by the electron
What do the allowed values of l depend on
the allowed values of l depend on the value of n and can range from 0 to n-1
What is ml
Magnetic quantum number - orientation of the region of space occupied by an electron with respect to an applied magnetic field
What is ms
spin quantum number the same- electrons can be either spin up or spin down so m =+/- 1/2
What is the Hamiltonian made up of
kinetic energy of electrons (Te)
Kinetic energy of nuclei (TN)
Electrostatic repulsion between nuclei (VNN)
Electrostatic repulsion between electrons (Vee)
Electrostatic attraction between electrons and nuclei (VeN)
What is the born-Oppenheimer approximation
Because nuclei are much heavier and move much slower than electrons, we can separate their motions when solving quantum problems. We can say the nuclei are static and not moving relative to kinetic energy of electron
What is the hartree approximation
expresses the wavefunction for many electron systems as the product of orbitals occupied by electrons
Ψ = ψ(1)ψ(2)
What do we need to consider when writing a wavefunction for many electron systems
electrons need to be indistinguishable, needs to obey the Pauli exclusion principle, needs to be representative
What is the limitations of the hartree approximation
If we swap the electrons the wavefunction changes and this means that the electrons are not indistinguishable which is not allowed
What is the Pauli exclusion principle
It is impossible for two electrons of the same spin to be at the same point in space. We cannot have two electrons with the same 4 quantum number.
What do we mean when we say the wavefunction needs to be representative
if we implement the wavefunction in a computer we need it to do calculations on lots of different system
What is the slater determinant
mathematically correct way of writing wavefunction for many electron systems it ensure electrons are indistinguishable and the Pauli exclusion principle is obeyed
How do we obey the Pauli-exclusion principle in terms of the wavefunction
We make sure the wavefunction is anti symmetric
