Chem 110A
Homework
7:
Due MONDAY, November 23
Chemistry 110A —
2009
Professor McCurdy
1.
Atomic units:
(a)
Using atomic units, for the quantities in the general formula for the energy levels of a
one electron atom,
E
n
=
!
Z
2
2
n
2
me
4
16
"
2
#
0
2
!
2
$
%
&
’
(
)
, show that the energy of the
helium
ion in its
ground state in atomic units is 2.
These energy units are hartrees.
What is that energy in
electron volts?
(b)
The “fine structure” constant is a
unitless
constant defined in terms of other
elementary physical constants as:
!
=
e
2
!
c
4
"#
0
=
1
137.035999
(to 9 significant digits).
Using this definition, express the
quantities in the fine structure constant in atomic units, and thus show that in atomic units
the speed of light is c = 137.0 (to 4 figures).
The units are a
0
/(atomic time units).
(c)
Since the speed of light has to have units of length/time, use the fact that the Bohr
radius a
0
= 5.2918 x 10
11
m and the value of c in SI units (2.9979 x 10
10
m/sec)
to
express the atomic unit of time in seconds.
The period of the first Bohr orbit is
2
in atomic units.
If you did part (c) correctly you
should find that
2
times the atomic unit time in seconds is about 150 attoseconds = 150
x 10
18
s.
It is now possible to make pulses of ultraviolet light that last only 250
attoseconds.
It’s instructive to read this
short abstract of an article
in Nature in 2004 (volume
427, page 817) reporting
the results of the first
experiments with 250
attosecond pulses.
This
work is what a Nobel
prize looks like before it is
won.
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 Fall '09
 Mccurdy
 Electron, Photon, Slater, 1s, Atomic Units

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