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Atomic Spectra and the hydrogen atom
 1
1 
 R 2  2 
n

ni 
 f
1
E2  E1  h f
h
2
L  mvr 
En  
E1
n2
rn  r1 n 2
E1  13.6 eV
r1  5.29  1011 m
Mathematical models (empirical) of the hydrogen atom spectrum were developed by Balmer
and Rydberg
Rydberg equation

R
ni
nf
nf = 2
 1
1 
 R 2  2 
n

ni 
 f
1
1
wavelength of emitted electromagnetic radiation
0.9
Rydberg constant
R = 1.097107 m-1
quantum number
for initial state ( integer ni = 3, 4, 5, … )
0.8
quantum number for final state ( ni > nf )
0.7
 Balmer series
0.6
short wavelength limit
0.5
0.4
0.3
0.2
0.1
0
350
Equation Mindmap eq24
400
450
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500
550
wavelength (nm)
600
650
700
1
Bohr or Bohr-Rutherford Model of the hydrogen atom: mixture of classical physics &
quantum physics ideas introduced by Planck (quantization of energy) & Einstein (photon E =
hf ) .
Electron exist in certain stable circular orbits around a positive nucleus – a non-classical
physics argument
According to
electromagnetic theory, an
accelerating charge losses
energy by emitting
radiation, hence, electrons
in atoms should spiral
towards the nucleus.
Equation Mindmap eq24
electron (-)
negative electron
attracted towards
positive nucleus
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+
spiral path of
electron towards
positive nucleus
2
Quantum hypothesis: the angular momentum L of the electron is quantized
L  mv r  n
h
2
quantum number n = 1, 2, 3, …
 stable orbits for a discrete set of radii rn  n2
 total energy of electron in system quantised En  -1/n2
 atom emits or absorbs energy only when electron moves from one stable orbit to
another
E  E f  E i  h f
Bohr model  derivation of Rydberg equation, hence some theoretical justification of the
equation.
n
Balmer Series of hydrogen
6
5
H
656.3
H
486.1
H
434.1
4
H
410.2 nm
nf  2
Equation Mindmap eq24
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3
H
H
H
H
2
3
Pfund series
IR
0
-2
energy (eV)
5
4
3
Brackett
series IR
2
Balmer series
visible
-4
6
-6
n
-8
-10
Lymann series
UV
-12
-14
0
0.2
0.4
0.6
0.8
1
1
Bohr theory could not explain the spectra of multi-electron atoms and the characteristics of
spectral lines for example:
ZEEMAN EFFECT
spectral lines vary in intensity
HYPERFINE SPLITTING
no magnetic field
greatly magnified
external
magnetic field
Equation Mindmap eq24
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4