topic 6 Flashcards
(23 cards)
l
is the orbital angular momentum quantum number
- take any integer (n-1)
- vector quantity
- equation angular momentum = position vector x momentum vector
- only magnitude and one spatial component can be predicted simultaneously due to Heisenberg uncertainty principle
- describes the shape
ml
magnetic quantum number
- can be any number ranging from -l to l
- describes orientation of atomic orbitals
angular momentum
- ## vector quantity
how to calculate the magnitude for orbital angular momentum
- square root ( (l(l+1) x reduced planks constant)
- l = orbital angular momentum principle number
how to calculate the orientation in orbital angular momentum
- lz = ml x reduced planks constant
- ml = magnetic quantum number
to completely describe state of an electron in atom we must
specify wavenumber mlml and its spin state -
spin angular momentum
- spin angular momentum quantum number, s = 1/2
- spin magnetic quantum number ms = +/- 1/2
quantises the magnitude of the spin angular momentum
- (square root (3))/2 reduced planks constant
ms quantises its projections along z giving rise to
spin up and spin down states
sz = +/- 1/2 reduced planks constant
solving the SE for the equation for H atom means
- a quantum of a description of the atom
what describes the size, shape and orientation of an orbital
- size = principle quantum number n
- shape = angular momentum quantum number l
- orientation = magnetic quantum number ml
radial distribution functions
- gives probability of finding an electron within a spherical shell at thickness dr at a distance of r from the nucleus of the atom though born approximation
- r = 0, zero probability
- radial nodes = values of r where there is zero probability of finding an electron
angular wave functions
- angular component of wavefunction determines the shape of the orbitals
- for s orbitals l=0, there is no angular dependence of the wavfunction and the orbitals are spherically symmetrical
- therefore no angular nodes
- psotivie and negative wave function are separated by the radial nodes (wave function =0)
angular nodes
- nodal planes where wave function = 0
- s orbitals have no angular nodes
- p orbitals have one angular node
- number of angular nodes = l
radial nodes
- nodal surfaces where wavefucntion = 0
- s orbitals have max in wave function at nucleus
- other orbitals wave function = 0 at nucleus
- all orbitals decay exponentially as r tends to infinity
- number radial nodes = n-l-1
- occur at p(r) = 0
total number of nodes
(angular + radial)
= n-1
ionisation energy
- energy required to move one electron of atom from ground state to infinite distance from the nucleus
expect hydrogenic ions to have ionisation energjes and spectral lines to have …
wavenumbers that are Z^2 larger than hydrogen
- use equation for ionisation energy x (z^2/n^2)
- reality not always true, some assumptions become less valid for heavier atoms
population factors rules effecting appearance of atomic spectrum
- absoprtion and emission between two states can only occur if sufficient number of atoms in initial state
- intensity of spectral lines associated with transition is proportional to ni/N
- Given by Boltzmann distribution
- greater population = more light absorbed
selection rules for transitions
- stem from conservation of angular momentum
- electron angula momentum and magnetic quantum number need to change to compensate for loss or creation of angular momentum of a photon
- change n no restrictions
- change in l = +/- l
- change in ml = 0, +/- 1
- energy and mass conserved
atomic spectrum of hydrogen
- grotrian diagram
- shows absoprtion transition from np level are allowed by selection rule l = +/- 1
- only see Lyman series in absorption due to low Boltzmann population factor of n = 2
- uv and em spectrum
- allowed transitions for hydrogen with n = 2 as lower energy state can be observed in grotrian diagram in emission
stern - gerlach experiment
- diffraction expected one dot
- observed appearance of 2 clear atom trajectories in applied field means must be another angular momentum with a quantum number 1/2
key effect causing the deviation from the prediction of the SE
- spin - orbital coupling
- stems from fact electron posses own intrinsic angular momentum (spin)
- discovered from Stern - Gerlach experiment
