http://www.ck12.org Chapter 24. Atomic Physics
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/112738De Broglie suggested that electrons orbiting around the nucleus could be acting as waves, forming circular standing
waves based on the size of the orbit. Just as a string which could only support a discrete set of wavelengths between
its fixed nodes, an integer number of electron waves would have to fit within an orbital. SeeFigure24.8.
With de Broglie’s hypothesis confirmed by the work of C.J Davisson and L.H. Germer, Bohr’s atomic theory finally
had a physical explanation to support it.
FIGURE 24.8
Electron orbits as standing waves around
the nucleus.This neatly connected the wave-particle duality and the observation that electrons would only occupy distinct
orbits. However, it was still unclear what matter or energy really was –waves or particles.
The Heisenberg Uncertainty Principle
German physicist Werner Heisenberg (1901-1976) suggested an approach that treated matter as particles, but the
exact position and speed of the particle was fundamentally fuzzy and uncertain. This uncertainty around the particle
is continuous and results in wave-like properties. Take the case of light passing through a single narrow slit. In
classical physical optics, we would treat this as a wave.
In Heisenberg’s formulation, though, we can look at the light as a set of particles –photons –that are flying at the
slit. As the photons reach the slit, their position is precisely determined. Those that get through have a well-defined
position. TheUncertainty Principlesays that the more narrowly we define the position∆x, thelesswell defined
we know the momentum,∆p.
In principle, we could use very small-wavelength electromagnetic energy, say, gamma rays, and very accurately
locate the electron by detecting where the collision between the photon and the electron took place. But any hope
of determining the momentum of the electron at the time of the interaction is gone. It would be like slamming a
fast-moving bowling ball into a Ping-Pong ball in an attempt to determine how fast the Ping-Pong ball was traveling
before the collision.
We call this the Heisenberg uncertainty principle. It should not be thought of as an uncertainty due to the lacking
effectiveness of the measuring tool used. Rather, it is a fundamental constraint, upon any such set of measurements,
made with any tool. Heisenberg stated the uncertainty principle in mathematical terms. We will briefly explain his
thinking.
Heisenberg reasoned that the location of an object could be no more accurate than the wavelength of the light used
to detect the object. Thus, if light of wavelengthλis used to detect the object, its location in space would have an
uncertainty of
∆x=λ