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Chapter |
The simplest helium atom consists of two protons and two
electrons.
The helium atom’s electric charge and magnetic charge density distribution is:
(19.1)
Helium’s magnetic charge density distribution is:
(19.2)
The helium atom’s electric
charge distribution equation is:
(19.3)
Helium’s magnetic
charge distribution equation is:
(19.4)
Helium’s electric
field equation is:
(19.5)
The helium atom’s magnetic
field equation is:
(19.6)
Thus:
(19.7)
As we know from (6.3), thus:
(19.8)
Thus:
(19.9)
For the cylindrical
coordinates (
, 
, z), which has the following relationship with the spherical
coordinate (r, 
, 
):
We can separate the angular momentum density into
‘z’ component and ‘
’ component,
The
‘z’ component of angular momentum density is:
(19.10)
The ‘
’ component of angular momentum density is:
(19.11)
As
we know, the volume element is:
For
the ‘
’ component of angular
momentum density, because:
Thus, we can get
the ‘
’ component of angular
momentum:
(19.12)
For
the ‘z’ component of electron angular momentum, we have:
(19.13)
Thus:
(19.14)
Thus:
(19.15)
Thus:
(19.16)
When 
, thus the z component of angular momentum is:
(19.17)
When 
, thus:
(19.18)
In which
(19.19)
(19.20)
As we know, eg=h
Thus:
(19.21)
As we know:
(19.22)
And
(19.23)
Thus:
(19.24)
The helium atom’s spin (angular momentum) is almost zero.
|
What
is the electron spin?
ISBN 0-9743974-9-0 Copyright © 2003 Gengyun Li All rights reserved http://www.electronspin.org |