Chapter 40: Q. 4 (page 1174)

| FIGURE EX $40.4$ shows the wave function of an electron in a rigid box. The electron energy islocalid="1650137157775" $12.0 e V$ . What is the energy, in localid="1650137162096" $e V$ , of the next higher state?

Short Answer

Expert verified

The energy, in $e V$ is $21.3 e V$ .

Step by step solution

Given Information

We have to given The electron energy is $12 e V$ .

We need to find the energy in $e V$ .

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 two maxima and one minimum, meaning that it has 3 antinodes. Therefore, the wave function shown in the graph corresponds to $n = 3$ The energy of an electron in a rigid box is given by:

$E_{n} = n^{2} E_{1}$

all need to do is to use the given value of $E_{3}$ to calculate $E_{1}$ , then use the equation above to determine the energy of the next state is $E_{4}$ .

$\begin{matrix} E_{3} = 9 E_{1} \\ E_{1} = \frac{E_{3}}{9} = \frac{12 eV}{9} = \frac{4}{3} eV \end{matrix}$

So,

$\begin{matrix} E_{4} = 16 E_{1} = 16 \times \frac{4}{3} eV \\ E_{4} = 21.3 eV \end{matrix}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

| FIGURE EX $40.4$ shows the wave function of an electron in a rigid box. The electron energy islocalid="1650137157775" $12.0 e V$ . What is the energy, in localid="1650137162096" $e V$ , of the next higher state?

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

Fluids

Quantum Physics

Energy Physics

Famous Physicists

Measurements

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

| FIGURE EX40.4 shows the wave function of an electron in a rigid box. The electron energy islocalid="1650137157775" 12.0eV. What is the energy, in localid="1650137162096" eV, of the next higher state?

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

Fluids

Quantum Physics

Energy Physics

Famous Physicists

Measurements

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

| FIGURE EX $40.4$ shows the wave function of an electron in a rigid box. The electron energy islocalid="1650137157775" $12.0 e V$ . What is the energy, in localid="1650137162096" $e V$ , of the next higher state?