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Chapter 40: Q. 4 (page 1174)

What is the quantum number of the particle in FIGURE Q40.4? How can you tell?

Short Answer

Expert verified

The quantum number of the particle is6.

Step by step solution

01

Given Information

We need to find the quantum number of the particle.

02

Simplify

Now, find the quantum number of the particle on the picture.

therefore, n=6because there are six peaks.

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Most popular questions from this chapter

A 2.0μmdiameter water droplet is moving with a speed of 1.0mm/sin a 20μmlong box.

a. Estimate the particle’s quantum number.

b. Use the correspondence principle to determine whether quantum mechanics is needed to understand the particle’s motion or if it is “safe” to use classical physics.

Consider a particle in a rigid box of length L. For each of the states n=1,n=2,and n=3:

a. Sketch graphs of ψ(x)2. Label the points x=0and x=L.

b. Where, in terms of L, are the positions at which the particle is most likely to be found?

c. Where, in terms of L, are the positions at which the particle is least likely to be found?

d. Determine, by examining your ψ(x)2graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 13. Explain your reasoning.

e. Calculate the probability that the particle will be found in the left one-third of the box

FIGURE Q40.7shows two possible wave functions for an electron in a linear triatomic molecule. Which of these is a bonding orbital and which is an antibonding orbital? Explain how you can distinguish them.

In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. FIGURE CP40.47is a one-dimensional model of a crystal lattice. The ions have mass m, charge eand an equilibrium separation b.

a. Suppose the middle charge is displaced a very small distance x≪bfrom its equilibrium position while the outer charges remain fixed. Show that the net electric force on the middle charge is given approximately by

F=−e2b3πε0x

In other words, the charge experiences a linear restoring force.

b. Suppose this crystal consists of aluminum ions with an equilibrium spacing of 0.30nm. What are the energies of the four lowest vibrational states of these ions?

c. What wavelength photons are emitted during quantum jumps between adjacent energy levels? Is this wavelength in the infrared, visible, or ultraviolet portion of the spectrum?

Use the data from Figure 40.24 to calculate the first three vibrational energy levels of a C=Ocarbon-oxygen double bond.
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