Orbitals Flashcards
Calculate number of radial nodes
= n-l-1
Orbital Boundary
Where there is a 95% probability of finding the electron inside it
Probability
psi squared
probability of finding the electron at a specific point in space
Radial Distribution Function
4pi r^2 R(r)^2
Probability of finding the electron in a shell, thickness dr, radius r
Useful to find the most probable distance of finding an electron from the nucleus
R(r)
Radial wavefunction, contains information about what happens to the wavefunction as the distance from the nucleus increases
Y(theta, phi)
Angular wavefunction, contains information about the shape of the orbital
Where R(r) = 0, the y = 0
The point where the wavefunction is 0 = Node
in this case, a radial node
s orbitals
Value of l = 0
Spherical in shape
As n increases, sphere radius increases
Larger orbitals are more diffuse
Radial distribution - s orbitals
1s electrons penetrate much closer to the nucleus than 2s or 3s orbitals => much lower energy
p orbitals
Value of l = 1
Have two lobes with a node between them
Three degenerate orbitals: px, py, pz
(degenerate = same energy)
d orbitals
Value of l = 2
dxy, dyz, dxz, dx2-y2, dx2
Numbers of radial or spherical nodes in 3s, 3p, 3d
3s = 2
3p = 1
3d = 0
Energies of orbitals
As number of e-s increases, so does the repulsion between them
- in many -e- atoms, orbitals in the same shell but different subshells (eg. s, p …) are no longer degenerate in energy … E(2s) =/= E(2p)
Coloumb’s Law
Electrostatic interaction:
U = qAqB / 4piE0rAB
qA = Charge on A (nucleus)
qB = Charge on B (electron)
rAB = Distance between A & B
- Bigger charge: greater interaction
- Bigger separation: smaller interaction
Pauli Exclusion Principle:
No 2 electrons in the same atom can have identical sets of quantum numbers
Spin Quantum Number, ms
The spin quantum number, ms, has only 2 allowed values: +1/2(clockwise) and -1/2(anticlockwise)
Stern Gerloch experiment
Single atoms of Silver -> slit -> magnet -> 2 distinct spots on screen => 2 distinct spins
Proved electrons could have spin up and spin down properties
Aufbau Pinciple
Electrons in atoms build up from lowest energy levels
Order of filling up orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, …
Exceptions to Aufbau
Cr: [Ar] 4s1 3d5
Cu: [Ar] 4s1 3d10
due to extra stability associated with half-filled & filled sets of d orbitals
this can occur since the 4s & 3d orbitals are very close in energy
Hund’s Rule
For degenerate orbital, the lowest energy is attained when the number of electrons with parallel spin is maximised.
