The equation, lmatter = h/mv, is due to deBroglie and expresses the fact that particles
can have wave-like properties. Here lmatter is the wavelength (in meters) of the matter-wave where
Planck's constant, h = 6.626x10-34 J-s ; m is the mass of the particle (in kg) ;
and v is the velocity (in m/s).
Regular objects (like a baseball) have masses of the order of 1 kilogram so that their lmatter is much
smaller than the size of the object itselft. Thus we don't notice the wave-like properties of ordinary
matter. For very small objects like electrons or protons whose masses are more like 10-30 kg, we can
get lmatter of the order of the "size" of the electron itself and so this wave-like property becomes
very noticeable and important.
Now recall Figure 6.18 on page 216 of Brown-Lemay Bursten which shows the electron density of
the 1s, 2s, and 3s orbitals of the hydrogen atom. To see animation of these orbitals go to Radial Density Movie
This is the picture of the 3s wavefunction vs r with its two nodes
If we square the above we get the electron density which is always non-negative:
We can think of this wave function as a standing matter wave by analogy to a light wave.
Recall that a light wave is cosine function that looks like the following:
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