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Chapter 40: Q. 3 (page 1174)

| FIGURE EX 40.3shows the wave function of an electron in a rigid box. The electron energy is25eV. How long is the box?

Short Answer

Expert verified

The electron energy is 25eV so the box is0.736nm.

Step by step solution

01

Given Information 

We have to given The electron energy is25eV.

02

Simplify

The graph of 蠄n(x)has n鈭�1nodes, excluding the ends, and nantinodes. In our case, the wave function shown in the graph has three maxima and three minima, meaning that it has six antinodes. Since the wave function is shown in the graph corresponds to the n=6state. The energy of levels of an electron in a rigid box is given by:

En=n2h28mL2

Then,

E6=36h28mL2

the equation to solve the numerical values of the different variables.

L=6h8mE6=66.626脳10鈭�34J鈰�s89.11脳10鈭�31kg25eV脳1.6脳10鈭�19J/eVL=7.36脳10鈭�10m=0.736nm

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