Physics 611
Astrophysics (Stellar Atmospheres)
Problem Assignment #4
Due: Friday, October 13, 2006
THE H-LIKE BOUND-FREE ABSORPTION COEFFICIENT IN A SOLAR ENVIRONMENT
(Böhm-Vitense, Problem 7-3)
The absorption coefficient per hydrogen-like atom in the level with main quantum number n
is given by
an = 64 π4 Z4 me10 / [ 3n5 ν3 ch6 ],
for ν νn0 = 2π2e4m Z2 / h3n2 where
νn0 = threshold frequency for the ionization of a H-like atom in its nth excitation state,
ν = c/λ, c = light velocity = 2.998 × 1010 cm s-1,
m = electron mass = 9.105 × 10-28 g,
h = Planck's constant = 6.626 × 10-27 erg s,
e = electron charge = 4.8024 × 10-10 esu,
Z = nuclear charge + 1 - number of electrons in atom or ion,
Z = 1 for H and He, Z = 2 for He+.
Calculate the hydrogen bound-free absorption coefficient per atom (i.e., NH (n = 1) = 1) for
the levels n 4. Assume T = 5800 K, corresponding to the solar photosphere.
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For purposes of uniformity please calculate the absorption coefficient for at least those
wavelengths necessary to fill in the following table:
The Hydrogen Bound-Free Absorption Coefficient for T = 5800 K
λ [Ǻ]
500
800
911
912
2000
3645
3647
6000
8203
8204
11000
14584
14585
Contributing
Levels, n =
1, 2, 3, 4
4
>4
atotal
log (atotal )
0.000 000
-
(Hints: Your 4th column results should roughly match the curve plotted in Figure 7.3 of BV
for Θ = 1.0. The given λs tightly bracket the Lyman discontinuity, the Balmer discontinuity, the
Paschen discontinuity and the Brackett discontinuity. If you calculate the λs of these
discontinuities your results may lie slightly outside the bracketed ranges, because of the need for
slight corrections. In all cases assume for the close pairs of λs that one lies on each side of the
associated discontinuity.)