Introduction to SAT II Physics - FreeExamPapers

Because the electron can only make certain jumps in its energy level, it can only emit
photons of certain frequencies. Because it makes these jumps, and does not emit a steady
flow of energy, the electron will never spiral into the proton, as Rutherford’s model
suggests.
Also, because an atom can only emit photons of certain frequencies, a spectroscopic
image of the light emanating from a particular element will only carry the frequencies of
photon that element can emit. For instance, the sun is mostly made of hydrogen, so most
of the light we see coming from the sun is in one of the allowed frequencies for energy
jumps in hydrogen atoms.
Analogies with the Planetary Model
Because the electron of a hydrogen atom orbits the proton, there are some analogies
between the nature of this orbit and the nature of planetary orbits. The first is that the
centripetal force in both cases is
. That means that the centripetal force on the
electron is directly proportional to its mass and to the square of its orbital velocity and is
inversely proportional to the radius of its orbit.
The second is that this centripetal force is related to the electric force in the same way
that the centripetal force on planets is related to the gravitational force:
where e is the electric charge of the electron, and Ze is the electric charge of the nucleus.
Z is a variable for the number of protons in the nucleus, so in the hydrogen atom, Z = 1.
The third analogy is that of potential energy. If we recall, the gravitational potential
energy of a body in orbit is
. Analogously, the potential energy of an
electron in orbit is:
Differences from the Planetary Model
However, the planetary model places no restriction on the radius at which planets may
orbit the sun. One of Bohr’s fundamental insights was that the angular momentum of the
electron, L, must be an integer multiple of . The constant is so common in
quantum physics that it has its own symbol,
. If we take n to be an integer, we get:
Consequently,
. By equating the formula for centripetal force and the formula
for electric force, we can now solve for r:
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