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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

a. Sketch graphs of the probability density ψx2for the four states in the finite potential well of Figure 40.14a. Stack them vertically, similar to the Figure 40.14a graph of ψx.

b. What is the probability that a particle in then=2 state of the finite potential well will be found at the center of the well? Explain.

c. Is your answer to part b consistent with what you know about standing waves? Explain.

An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is600nm. How long is the box?

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?

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.

Show that the penetration distance ηhas units of m.
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