5.2. The Quantum Mechanical Model http://www.ck12.org
FIGURE 5.12
The circumference of the orbit in (A) al-
lows the electron wave to fit perfectly into
the orbit. This is an allowed orbit. In (B),
the electron wave does not fit properly into
the orbit, so this orbit is not allowed.The study of motion in terms of large objects like baseballs and cars is called mechanics, or more specifically,
classical mechanics. Because of the quantum nature of the electron and other tiny particles moving at high speeds,
classical mechanics is inadequate to accurately describe their motion. Quantum mechanicsis the study of the
motion of objects that are atomic or subatomic in size and thus demonstrate wave-particle duality. In classical
mechanics, the size and mass of the objects involved effectively obscures any quantum effects, so such objects
appear to be capable of gaining or losing energy in any amount. Particles whose motion is better described by
quantum mechanics can only gain or lose energy in discrete units called quanta.
Heisenberg Uncertainty Principle
Another feature that is unique to quantum mechanics is the uncertainty principle. TheHeisenberg Uncertainty
Principlestates that it is impossible to determine simultaneously both the position and the velocity of a particle.
The detection of an electron, for example, would be made by way of its interaction with photons of light. Since
photons and electrons have nearly the same energy, any attempt to locate an electron with a photon will knock the
electron off course, resulting in uncertainty about where the electron is headed (Figure5.13). We do not have
to worry about the uncertainty principle with large everyday objects because of their mass. If you are looking for
something with a flashlight, the photons coming from the flashlight are not going to cause the thing you are looking
for to move. This is not the case with atomic-sized particles, so scientists needed a new way to think about how to
envision the location of electrons within atoms.
You can see a funny, animated explanation of Heisenberg’s Uncertainty Principle at http://video.pbs.org/video/18121
247.
Quantum Mechanical Model
In 1926, Austrian physicist Erwin Schrödinger (1887-1961) used the wave-particle duality of the electron to develop
and solve a complex mathematical equation that accurately described the behavior of the electron in a hydrogen atom.
Thequantum mechanical modelof the atom comes from the solution to Schrödinger’s equation.Quantization of
electron energies is a requirement in order to solve the equation. This is unlike the Bohr model, in which quantization
was simply assumed with no mathematical basis.
Recall that in the Bohr model, the exact path of the electron was restricted to very well defined circular orbits around
the nucleus. The quantum mechanical model is a radical departure from that. Solutions to the Schrödinger wave
equation, called wave functions, give only the probability of finding an electron at a given point around the nucleus.