Question

What is the meaning of electron density? Explain with an example.

Answer 1

Answer on Question #53289 – Chemistry – Inorganic Chemistry

Question:

What is the meaning of electron density? Explain with an example.

Answer:

If $P(x, y, z) \, \mathrm{d}x \, \mathrm{d}y \, \mathrm{d}z$ is the probability of finding an electron in the volume element $\mathrm{d}x \, \mathrm{d}y \, \mathrm{d}z$ at the point of a molecular entity with coordinates $x, y, z$, then $P(x, y, z)$ is the electron density $(\rho)$ at this point.

An example

The following picture is a graph of the electron density in a water molecule. The graph consists of two surfaces, a "solid" inner surface and a "mesh" outer surface. Each surface is constructed so that $\rho$ (rho) has the same value at every point on the surface.

This particular graph is constructed so that $\rho$ is 10 times larger on the solid surface than on the mesh surface. In other words, if we randomly select one point (rsolid) on the solid surface and one point (rmesh) on the mesh surface, the value of $\rho$ at rsolid is 10 times larger than the value at rmesh. Of course, this also means that it is 10 times more likely that an electron will be at rsolid than at rmesh.

We can also compare the probabilities of finding electrons anywhere on each surface. The probability of finding an electron anywhere on a surface is proportional to $\rho \times A$, the electron density multiplied by the area of the surface. It so happens that the area of the solid surface is about 2.5 times smaller than the area of the mesh surface. Therefore, it is only about 4 times more likely that an electron will be somewhere on the solid surface ($4 = 10/2.5$).

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