Energy of Atomic Electrons
Name: Christopher S.
I really do not understand how energy values were
assigned to atoms. As I understand it, the ground state is assigned the
lowest *negative* number, in either eV or Joules, and at ionization, n =
infinity, it is zero Joules. Am I right in thinking that the energy of
the atom is thought to be zero when an electron is lost because the
energy of the atom comes from the energy of its electrons? Therefore, if
ionization equals the zero energy level of the atom, the ground state
*must* be the lowest negative number which increases to zero -
arithmetically, it is the only way to handle it. Likewise, if the
electron absorbs energy to more than ionize it, the extra energy shows up
as a positive number of Joules which is the kinetic energy of the
electron. Is it fair to say that the negative numbers for the energy
reflect the state of the atom only and the positive numbers reflect the
state of the electron only, when signs change it reflects a shift in
frame of reference from atom to electron? A related question - how is it
that the energy of an atom could be zero after one of its electrons
ionizes if that atom has more than one electron? Thanks for all your help.
Chris "confused but trudging on"
Whoa!! Let us step back from this a minute, I think you have gotten yourself in
a tangle, making something that is not too hard seem hopelessly complex.
Only DIFFERENCES in energy can be measured, unless you want to say that the
absolute zero of energy is determined by Einstein's equation: E = m*c^2
relating mass and energy. But on this scale, most all other energies are
exceedingly and uselessly small. So, since it is DIFFERENCES that we are
measuring we are permitted to select whatever zero that is convenient.
When considering atoms theoretically and computationally, it is convenient
to choose the zero of energy to be the electron(or electrons) and the
nucleus (or nucleii) to be the particles an infinite distance apart
(although this too cannot be strictly true). This choice is useful in atomic
and molecular calculations because if a calculated energy comes out less
than zero the system, whatever we happen to be talking about is some sort of
bound condition, and if the energy comes out greater than zero, whatever the
system we happen to be talking about is in some sort of unbound state. That
is the particles have sufficient kinetic energy so that the particles can
possibly escape one another.
Scientists who study vibrational spectroscopy do not find this selection of
a zero convenient, and they often choose the minimum in the potential energy
of a molecule to be the zero of energy. This includes the "zero point
energy" that the Heisenberg Uncertainty Principle requires.
Scientists who carry out thermodynamic calculations usually could care less
"zero point energy" because it cannot be convert heat into work or work into
heat. So they choose the lowest electronic/vibrational/rotational state to
be the zero of energy.
Scientists who study electronic spectra switch back and forth. There may be
excited electronic states that are bound, that is the electron(s) are in a
higher energy state, but are still bound to the nuclear frame, which
generally will be different than the structure of the ground electronic
state, but bound none the less. Depending upon what is useful for them they
may choose the zero or energy to be the electron in the excited electronic
state with the electron and the nuclear frame by an infinite distance -- or
the electron /
nuclear frame of the ground state separated by an infinite distance.
The point of these examples, probably overkill, for 99.999% of scientific
applications we are free to choose the energy zero anywhere that is
convenient for our purposes.
The 0.001% of cases where things need to be treated more cautiously is in
arcane high energy relativistic physics and cosmological -- the world of
virtual particles, negative kinetic energies. But we will leave the
Hawking's, the Wheeler's, and the other cosmologists to worry about that --
we do not have to.
The energy values assigned to electrons are potential energies. As a
result, the only important factor is change in value as an electron passes
from state to state. With gravitational potential energy, zero energy can
be assigned to any height, so long as the potential energy values of all
other heights are scaled correctly. For atoms, the one state that is the
same for all electrons is being free of the atom. So as to keep that one
common state at the same energy level for all atoms, the choice was to make
being free have zero potential energy. All electrons contained within atoms
are at less than free levels: energy must be added to free the electron.
If an atom has a positive energy, it is free. Assuming it is not under the
influence of other objects any more, the positive energy equals the kinetic
energy. Other than convenience, there is no special reason to make complete
freedom correspond to zero potential energy.
Dr. Ken Mellendorf
Illinois Central College
The properties of an atom are determined only by the relative positions and
relative velocities of its electron and nuclear components. The "zero
energy" state is when the electrons and nucleus have no relative kinetic
energy and are infinitely separated from each other. To go from this state
to a "bound" state, they have to lose energy. Likewise, to go from a
"bound" state to the separated state, energy has to be added. If the
electron and nucleus are dissociated AND have kinetic energy, then the total
energy of the system is the kinetic energy. When they are bound, their
potential energy is negative.
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
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Update: June 2012