h/Two hydrogen atoms bond
to form an H 2 molecule. In the
molecule, the two electrons’ wave
patterns overlap , and are about
twice as wide.In many Star Trek episodes the Enterprise, in orbit around a planet,
suddenly lost engine power and began spiraling down toward the
planet’s surface. This was utter nonsense, of course, due to con-
servation of energy: the ship had no way of getting rid of energy,
so it did not need the engines to replenish it.
Consider, however, the electron in an atom as it orbits the nu-
cleus. The electrondoeshave a way to release energy: it has an
acceleration due to its continuously changing direction of motion,
and according to classical physics, any accelerating charged par-
ticle emits electromagnetic waves. According to classical physics,
atoms should collapse!
The solution lies in the observation that a bound state has a min-
imum energy. An electron in one of the higher-energy atomic
states can and does emit photons and hop down step by step in
energy. But once it is in the ground state, it cannot emit a photon
because there is no lower-energy state for it to go to.Chemical bonds example 15
I began this section with a classical argument that chemical
bonds, as in an H 2 molecule, should not exist. Quantum physics
explains why this type of bonding does in fact occur. When the
atoms are next to each other, the electrons are shared between
them. The “box” is about twice as wide, and a larger box allows
a smaller energy. Energy is required in order to separate the
atoms. (A qualitatively different type of bonding is discussed on
page 939. Example 24 on page 932 revisits the H 2 bond in more
detail.)Discussion Questions
A Neutrons attract each other via the strong nuclear force, so according
to classical physics it should be possible to form nuclei out of clusters of
two or more neutrons, with no protons at all. Experimental searches,
however, have failed to turn up evidence of a stable two-neutron system
(dineutron) or larger stable clusters. These systems are apparently not
just unstable in the sense of being able to beta decay but unstable in
the sense that they don’t hold together at all. Explain based on quantum
physics why a dineutron might spontaneously fly apart.
B The following table shows the energy gap between the ground state
and the first excited state for four nuclei, in units of picojoules. (The nuclei
were chosen to be ones that have similar structures, e.g., they are all
spherical in shape.)
nucleus energy gap (picojoules)(^4) He 3.234
(^16) O 0.968
(^40) Ca 0.536
(^208) Pb 0.418
Explain the trend in the data.
Section 13.3 Matter as a wave 899