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Spectra
Continuous spectrum
Emission spectrum
Prism or diffraction grating
emitted
light
low pressure gas
MM 2006 AH
Emission spectrum of neon
, nm
650
600
550
500
MM 2006 AH
Emission spectrum of hydrogen
The Balmer series
, nm
E = Lh
656
c = 
486
434
410
E= Lhc

• energy emitted when excited electrons fall back to a lower energy level
• frequency of line due to difference in energy between 2 electron energy levels
MM 2006 AH
Energy levels
E3
E3
E2
DEb = E3 - E2 = hb
E1
+
E2
DEa = E3 - E1 = ha
E1
• frequency of lines in emission spectrum fixed
• energy between levels fixed
• energy of electrons fixed
- quantised
- photon emitted when electron moves to lower energy level
MM 2006 AH
Full emission spectrum of hydrogen
Series
Energy level excited electron falls to
Part of electromagnetic spectrum
Lyman
n=1
Ultra-violet
Balmer
n=2
Visible
Paschen
n=3
Infra-red
Brackett
n=4
Infra-red
Pfund
n=5
Infra-red
P7 & 8 LTS
MM 2006 AH
The Lyman series
, nm
121.6
102.6
97.3
91.2
convergence limit
p9 LTS Q
MM 2006 AH
Bohr’s theory
• the hydrogen atom’s electron exists only in certain definite energy levels
• the electron changes energy levels when a photon is absorbed or emitted
• the energy of the photon equals the difference between the two energy levels
DE = h.
Quanta - fixed quantities of energy possessed by electrons
MM 2006 AH
Quantum mechanics
electrons - wave-particle duality
4 quantum numbers define energy of an electron
electrons arranged in shells
shells described by principal quantum number, n
n = 1, closest to nucleus; second shell n = 2
the higher n, the higher the potential energy associated the shell
and the further from the nucleus the electron likely to be found
Spectra show doublets and triplets suggesting subshells
s, p, d, f
MM 2006 AH
Shells and subshells
Shell
Subshells
1
1s
2
2s, 2p
3
3s, 3p, 3d
4
4s, 4p, 4d, 4f
subshells have different energies s < p < d < f
MM 2006 AH
Second quantum number
each subshell contains one or more energy levels or orbitals
orbitals defined by angular momentum quantum number, l
l related to shape of orbital
l value 0, 1, 2 …… (n -1)
Heisenberg’s uncertainty principle governs behaviour of electrons
impossible to define a point in space where electron certain to be found
regions in space where probability of finding an electron high atomic orbitals
n defines orbital size
l defines shape of orbital
MM 2006 AH
s orbitals
1s
2s
3s
MM 2006 AH
Third quantum number
defines p, d, f orbitals
m1 magnetic quantum number
gives number of orbitals and spatial orientation
m1 any integer between -l and +l
MM 2006 AH
p orbitals
l=1
3 possible values of m1, -1, 0, +1
3 orbitals of equal energy - degenerate
arranged along 3 axes x, y, z
e.g. 2px, 2py, 2pz
MM 2006 AH
d orbitals
l=2
m1 = -2, -1, 0, +1, +2
hence 5 d orbitals
f orbitals
l=3
m1 = -3, -2, -1, 0, +1, +2, |+3
hence 7 f orbitals
MM 2006 AH
Fourth quantum number
electrons spin
spin quantum number, ms
+1/2 and -1/2
MM 2006 AH