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Chapter 39: Q.29 (page 1138)

Consider a single-slit diffraction experiment using electrons. Using Figure 39.5 as a model, draw

a. A dot picture showing the arrival positions of the first 40or 50electrons.

b. A graph of ψx2for the electrons on the detection screen.

c. A graph of ψxfor the electrons. Keep in mind that ψ, as a wave-like function, oscillates between positive and negative.

Short Answer

Expert verified

Explanation with diagram of electron arrival positions om detector, Interference fringes and electron wave function.

Step by step solution

01

Explanation with diagram:

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Most popular questions from this chapter


FIGURE P39.32 shows |ψ(x)|2for the electrons in an experiment.

a. Is the electron wave function normalized? Explain.

b. Draw a graph of ψ(x)over this same interval. Provide a numerical scale on both axes. (There may be more than one acceptable answer.)

c. What is the probability that an electron will be detected in a 0.0010-cm-wide region at x=0.00cm? At x=0.50cm? At x=0.999cm?

d. If 104electrons are detected, how many are expected to land in the interval -0.30cm≤x≤0.30cm?

FIGURE P39.32 shows |ψ(x)|2for the electrons in an experiment.

a. Is the electron wave function normalized? Explain.

b. Draw a graph of ψ(x)over this same interval. Provide a numerical scale on both axes. (There may be more than one acceptable answer.)

c. What is the probability that an electron will be detected in a 0.0010-cm-wide region atx=0.00cm? At x=0.50cm? At x=0.999cm?

d. If 104electrons are detected, how many are expected to land in the interval -0.30cm≤x≤0.30cm?

The probability density of finding a particle somewhere along thex-axisis0forx61mm.Atx=1mm,the probability density is c. ForxU1mm, the probability density decreases by a factor of 8each time the distance from the origin is doubled. What is the probability that the particle will be found in the interval 2mm...x...4mm?

In one experiment, 2000 photons are detected in a 0.10-mm- wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm- wide strip where the amplitude is 30 V/m?

shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-widestripatax=0.000mm,bx=0.500mm,cx=1.000mm,anddx=2.000mm?xmm-3-2-101230.50px=0cx02mm-1
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