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Chapter 40: Q. 5 (page 1175)

FIGURE EX 40.5is the probability density for an electron in a rigid box. What is the electron鈥檚 energy, in eV?

Short Answer

Expert verified

The electron鈥檚 energy, in eV is16.9eV.

Step by step solution

01

Given Information

We need to find the electron鈥檚 energy, ineV.

02

Simplify

The given graph of the probability density has three antinodes, which means that the wave function also has three antinodes. And we know that the graph of 蠄nxhas nantinodes .). So, the wave function shown in the graph corresponds to the n=3state. But the energy of an electron in a rigid box is given by:

En=n2h28mL2

Notice that L is given to be0.45nm from the graph, which is the maximum value of x

substitute the numerical values for the quantities in the equation above to find E3

E3=9脳6.626脳10鈭�34J鈰�s28脳9.11脳10鈭�31kg脳0.45脳10鈭�9m2=2.7脳10鈭�18J

or in electronvolt

E3=2.7脳10鈭�18J脳1eV1.6脳10鈭�19JE3=16.9eV

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