Quantum numbers (4)
1. Principal quantum number, n
2. Angular momentum quantum number, l
3. Magnetic quantum number, ml
4. Spin quantum number, ms
Principal quantum number
n
Indicates the orbital (Bohr's energy level)
*As n gets larger, amount of energy between orbitals gets smaller
Equation for energy of a hydrogen electron
En = -RH (1/n2)
RH is Rydberg constant for hydrogen
RH = 2.18 × 10-18 J
Angular momentum quantum number
l
Angular momentum = what kind of/angle of orbit
l = 0, 1,... n-1
l = 0 → s
l = 1 → p
l = 2 → d
l = 3 → f
e.g.
n = 2
l = [0, 1]
Magnetic quantum number
ml
ml = [-l, l]
e.g.
n = 2
l = [0, 2] → d orbital
ml = [-2, 2] → 5 d orbitals
Spin quantum number
ms
Specifies the orientation of the spin of the electron
Value is either:
+1/2 (spins up)
or
-1/2 (spins down)
Describing an orbital (3)
1. n, l, ml describes one orbital
2. Orbitals with same n value = same principal energy level (shell)
3. Orbitals with the same values of n & l = same sublevel (subshell)
Equation for energy transition in hydrogen
ΔE = Efinal - Einitial
ΔEH atom = -2.18 × 10-18 J (1/n2final - 1/n2initial)
Energy emitted by electron is carried away by the releated photon, thus:
Ephoton = -ΔE
Probability density
The probability of finding an electron at a particular point in space
Probability decreases as distance from nucleus increases
Radial distribution function
Total probability of finding an electron at a certain distance r from the nucleus
Volume of shell also increases with distance from nucleus
Nodes
Where the probability drops to zero, for both probabilities
s orbital
l = 0
spherical shape
1 s orbital
p orbital
l = 1
shaped like two balloons
-1, 0, 1
3 p orbitals
d orbital
l = 2
shaped like four balloons
-2, -1, 0, 1, 2
5 d orbitals
f orbital
l = 3
shaped like eight balloons
-3, -2, -1, 0, 1, 2, 3
7 f orbitals
