Environmental Engineering Reference
In-Depth Information
Figure 3.1 Sketch of solar spectrum versus wavelength showing hydrogen n¼2ton¼3
absorption at 656 nm. (Courtesy of M. Medikonda).
The wavelength of the
n¼
2to
n¼
3 absorption given by
l¼D
E
/
hc ¼
1240/
D
E¼
1240/1.888
¼
656 nm is in the red part of the spectrum. As we know, the
composition of the sun is 75%Hby mass, so certainly hydrogen atoms are present in
its atmosphere. The appearance of this sharp dip feature in the spectrum in Fig. 3.1
implies that the suns atmosphere contains some H atoms in the
n¼
2 state, with
excitations
E
of 3/4
13.6 eV
¼
10.2 eV. The probability of such an excitation of the
atom is
P¼
exp(
D
D
E
/
k
B
T
). For
T¼
5973 K, this is
P¼
2.5
10
9
. This suggests that
in the gas of hydrogen atoms above the surface of the sun, about 2.5 per billion will be
able to absorb and contribute to the observed dip.
Note that the reduced mass
m
r
enters the energy formula Equation 3.4, and also
in (3.5). In Chapter 2, we described deuterium as the
first step in the energy releasing
fusion process of the sun. The deuteron D forms a slightly different version of
hydrogen atom, the only difference is the mass of the nucleus, now 2
m
p
for
deuterium. We can
find the small differences
D
in the energy and wavelength values
for D versus H,
n
1
1
n
2
Þ;
D½hn¼D½hc
=l¼D½E
o
ð
1
=
=
ð
3
:
6
Þ
which arise from the small difference in the reduced mass
m
r
m
e
((1
m
e
/
2
m
p
)
(1
m
e
/
m
p
))
¼m
e
(1
þ
1/3670). This makes the energy for D larger by about
2.7
10
4
and correspondingly makes the wavelengths smaller by the same factor.
For the Balmer line, 656.5 nm will be shifted by
0.178 nm to appear at 656.3 nm.
This is observable, because the spectral lines are sharply de
ned, and is the means by
which deuterium was discovered (on the sun). We will see later that in muonic
hydrogen, where the electron is replaced by a
muon
, an electron-like particle whose
mass is 206.8
m
e
, so that the reduced mass with the proton is
m
r
186
m
e
, that the
binding energy is about 186
E
o
2528 eV. If this muonic atom, furthermore, is
made using deuterium, and then a molecule between two such atoms is formed, we
will see later that the deuterons actually come close enough to undergo fusion at a
modest rate.
The Bohr model, which does not incorporate the basic wave-like aspect of
microscopic matter, fails to correctly predict some aspects of the motion and
location of electrons. (It is found that the idea of an electron orbit, in the strict
planetary sense, is no longer correct, in nanophysics. The uncertainty principle
D
