Chapter 40: Q. 3 (page 1174)

| FIGURE EX $40.3$ shows the wave function of an electron in a rigid box. The electron energy is $25 e V$ . How long is the box?

Short Answer

Expert verified

The electron energy is $25 e V$ so the box is $0.736 n m$ .

Step by step solution

Given Information

We have to given The electron energy is $25 e V$ .

Simplify

The graph of $ψ_{n} (x)$ has $(n - 1)$ nodes, excluding the ends, and $(n)$ antinodes. 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 $n = 6$ state. The energy of levels of an electron in a rigid box is given by:

$E_{n} = n^{2} \frac{h^{2}}{8 m L^{2}}$

Then,

$E_{6} = \frac{36 h^{2}}{8 m L^{2}}$

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

$L = \frac{6 h}{\sqrt{8 m E_{6}}} = \frac{6 (6.626 \times 10^{- 34} J \cdot s)}{\sqrt{8 (9.11 \times 10^{- 31} kg) (25 eV \times 1.6 \times 10^{- 19} J / eV)}} L = 7.36 \times 10^{- 10} m = 0.736 nm$

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| FIGURE EX $40.3$ shows the wave function of an electron in a rigid box. The electron energy is $25 e V$ . How long is the box?

Short Answer

Step by step solution

Given Information

Simplify

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| 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

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Work Energy and Power

Particle Model of Matter

Circular Motion and Gravitation

Electric Charge Field and Potential

Electrostatics

Study anywhere. Anytime. Across all devices.

| FIGURE EX $40.3$ shows the wave function of an electron in a rigid box. The electron energy is $25 e V$ . How long is the box?