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Chapter 40: Q. 3 (page 1174)

A particle in a potential well is in the n=5quantum state. How many peaks are in the probability densityPx=蠄x2 ?

Short Answer

Expert verified

There are five peaks in the probability density Px=蠄x2.

Step by step solution

01

Given Information 

We have to given potential well is in the n=5quantum state, the probability density isPx=蠄x2.

02

Simplify

We know that the particle in a potential well is the n=5quantum state.

Now, find, how many peaks are in the probability density:

Px=蠄x2

therefore, the answer is five.

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Most popular questions from this chapter

The energy of an electron in a 2.00eVdeep potential well is 1.50eV. At what distance into the classically forbidden region has the amplitude of the wave function decreased to 25% of its value at the edge of the potential well?

A typical electron in a piece of metallic sodium has energy-E0compared to a free electron, where E0is the2.7eV work function of sodium.

a. At what distance beyond the surface of the metal is the electron鈥檚 probability density 10%of its value at the surface?

b. How does this distance compare to the size of an atom?

Figure 40.27a modeled a hydrogen atom as a finite potential well with rectangular edges. A more realistic model of a hydrogen atom, although still a one-dimensional model, would be the electron + proton electrostatic potential energy in one dimension:

U(x)=-e24蟺蔚0x

a. Draw a graph of U(x) versus x. Center your graph at x=0.

b. Despite the divergence at x=0, the Schr枚dinger equation can be solved to find energy levels and wave functions for the electron in this potential. Draw a horizontal line across your graph of part a about one-third of the way from the bottom to the top. Label this line E2, then, on this line, sketch a plausible graph of the n=2wave function.

c. Redraw your graph of part a and add a horizontal line about two-thirds of the way from the bottom to the top. Label this line E3, then, on this line, sketch a plausible graph of the n=3 wave function.

Even the smoothest mirror finishes are 鈥渞ough鈥� when viewed at a scale of 100nm. When two very smooth metals are placed in contact with each other, the actual distance between the surfaces varies from0nmat a few points of real contact to 鈮�100nm. The average distance between the surfaces is鈮�50nm. The work function of aluminum is 4.3eV. What is the probability that an electron will tunnel between two pieces of aluminum that are 50nmapart? Give your answer as a power of10rather than a power ofe.

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