g/The spectrum of the light
from the star Sirius.
quantum physics, these wave patterns are referred to as “states” of
the particle-in-the-box system.
The following seemingly innocuous observations about the par-
ticle in the box lead us directly to the solutions to some of the most
vexing failures of classical physics:
The particle’s energy is quantized (can only have certain values).
Each wavelength corresponds to a certain momentum, and a given
momentum implies a definite kinetic energy,E=p^2 / 2 m. (This is
the second type of energy quantization we have encountered. The
type we studied previously had to do with restricting the number
of particles to a whole number, while assuming some specific wave-
length and energy for each particle. This type of quantization refers
to the energies that a single particle can have. Both photons and
matter particles demonstrate both types of quantization under the
appropriate circumstances.)
The particle has a minimum kinetic energy.Long wavelengths cor-
respond to low momenta and low energies. There can be no state
with an energy lower than that of then= 1 state, called the ground
state.
The smaller the space in which the particle is confined, the higher
its kinetic energy must be.Again, this is because long wavelengths
give lower energies.Spectra of thin gases example 13
A fact that was inexplicable by classical physics was that thin
gases absorb and emit light only at certain wavelengths. This
was observed both in earthbound laboratories and in the spectra
of stars. The figure on the left shows the example of the spec-
trum of the star Sirius, in which there are “gap teeth” at certain
wavelengths. Taking this spectrum as an example, we can give a
straightforward explanation using quantum physics.
Energy is released in the dense interior of the star, but the outer
layers of the star are thin, so the atoms are far apart and electrons
are confined within individual atoms. Although their standing-
wave patterns are not as simple as those of the particle in the
box, their energies are quantized.
When a photon is on its way out through the outer layers, it can be
absorbed by an electron in an atom, but only if the amount of en-
ergy it carries happens to be the right amount to kick the electron
from one of the allowed energy levels to one of the higher lev-
els. The photon energies that are missing from the spectrum are
the ones that equal the difference in energy between two elec-
tron energy levels. (The most prominent of the absorption lines in
Sirius’s spectrum are absorption lines of the hydrogen atom.)
The stability of atoms example 14898 Chapter 13 Quantum Physics