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Chapter 40: Q. 35 (page 1176)

For the quantum-well laser of Figure 40.16, estimate the probability that an electron will be found within one of the GaAlAs layers rather than in the GA As layer. Explain your reasoning.

Short Answer

Expert verified

The probability will be approximately10%.

Step by step solution

01

Given information 

we have given the quantum well laser as shown in above in the figure.

We have to find the probability of electron to found in GaAlAs layer.

02

Simplify

Since we just need to analyses the graph, then using the graph we can say that approximately on an average the probability of electron to being in GA As layer is around 90%.

Then the probability of the electron to being in the outer layer will be around10%.

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Most popular questions from this chapter

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鈮�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=鈭�e2b3蟺蔚0x

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?

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An electron confined in a harmonic potential well emits a 1200nm photon as it undergoes a 3鈫�2quantum jump. What is the spring constant of the potential well?

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.

Consider a quantum harmonic oscillator.

a. What happens to the spacing between the nodes of the wave function as |x| increases? Why?

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c. Sketch a reasonably accurate graph of the n=8 wave function of a quantum harmonic oscillator.

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