Atomic and
Molecular Physics FYSC11
HT 2015
Orbital angular momentum
Consider a state of the hydrogen atom with orbital angular
momentum quantum number l=5. How many different
possible values of the quantum number ml does this imply?
A. 5
B. 6
C. 7
D. 8
E. 9
F. 10
G. 11
H. 12
Orbital angular momentum
i.
The vector L precesses around the z-axis.
ii.
One component of L can be determined together with
the length of L, while the other two components remain
undetermined.
iii. For a given state, L can only have one orientation.
A. i+ii+iii
B. ii
C. iii
D. i + iii
E. ii + iii
Radial wave functions of the hydrogen atom
From: Demtröder,
Atoms, Molecules and Photons
From: Thorne, Litzén, Johansson, Spectrophysics
Hydrogen atom, radial probability densities
From: Thorne, Litzén, Johansson, Spectrophysics
From: Atom- och molekylfysik, kompendium Uppsala universitet
Hydrogen atom, density distributions
From: Haken and Wolf, The Physics of Atoms and Quanta
Measuring emission and absorption spectra
Emission
measurement
Emission spectrum of iron
Absorption
measurement
Absorption spectrum
of sodium
Images taken from W. Demtröder, Atoms, Molecules and Photons, Springer, Berlin, Heidelberg 2006
Hydrogen spectra: Balmer series
Hd
He Hg
Hb
Ha
From http://www.astronomyknowhow.com/hydrogen-alpha.htm
Emission/absorption series in atomic hydrogen
Image taken from W. Demtröder, Atoms, Molecules and Photons, Springer, Berlin, Heidelberg 2006
The first spectral series of hydrogen
www.daviddarling.info
Paschen
Balmer
Lyman
Wavenumbers (cm-1)
Wavelength (nm)
Frequency (Hz)
Energy (eV)
n’=4
5.3 x 103
1875
1.6 x 1014
0.66
n’=∞
1.2 x 104
820
3.7 x 1014
1.51
n’=3
1.5 x 104
656
4.6 x 1014
1.89
n’=∞
2.7 x 104
365
8.2 x 1014
3.40
n’=2
8.2 x 104
122
2.5 x 1015
10.20
n’=∞
1.1 x 105
91
3.3 x 1015
13.60
The hydrogen spectrum
The hydrogen spectrum