wavefunctions of the hydrogen atom

radial wavefunction

dependent on n and l

angular wavefunction

dependent on l and m_l

hydrogen atom wavefunction in spherical polar coordinates + what the terms are

wavefunction = radical wavefunction x angular wavefunction

bohr radius

• symbol

• equation

wavefunction of the 1s orbital

radial nodes for spdf

diagrams for 1s → 3d

when/why do radial nodes occur?

s = (n - 1) nodes

p = (n - 2) nodes

d = (n - 3) nodes

f = (n - 4) nodes

radial nodes occur at R(r) = 0 ie ψ = 0 - the electron cannot exist at this point

radial distribution function

• diagram

• equation

radial distribution function = 4πr²R²_n,l(r)

radial distribution function plots for n=1 to n=3

what does the peak represent

shape and wavefunction (phases) for s orbitals

shape and diagrams including wavefunction phases for p orbitals

nodes for p orbitals

at the nodal plane, ψ = 0. since this nodal plane arises from the angular wavefunction it is called an angular node

shapes of d orbitals

nodal planes for d_x²-y² and d_z²

how is the problem of schrodinger only being solvable for two-body problems resolved

using the orbital approximation in which ψ is approximated by the product of N single-electron wavefunctions

m_s quantum number

• name

• values

• diagram

aufbau principle, degeneracy and what is different about hydrogen

• lowest energy levels are filled first

• energy levels are degenerate for different values of l and m_l for any given value of n

• but for hydrogen energy levels only depend on n

pauli exclusion principle

• principle

• what it means for electrons in an orbital

• other intermolecular effects

• graph?

• principle: no two electrons in the same region of space can have the same set of four quantum numbers

• so we can have two electrons per orbital with different m_s values (±1/2)

• this also gives rise to short-range steric repulsion between atoms/molecules - when electrons overlap, electrons in different atoms with the same quantum numbers repel