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Chapter 39: Q 10 Exercise (page 1136)

What are the units ofψ(x) ? Explain.

Short Answer

Expert verified

Hence, the unit is m-1/2

Step by step solution

01

Given information

ψ(x)

02

Explanation

We begin by recognising that probability is a dimensionless quantity, and that probability in the context of the wave function is:

P=|ψ(x)|2δx

Because the units of δx are (m), the units of |ψ(x)|2 must be m-1 in order to cancel the units of δx. As a result, ψ units are m-1/2.

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Most popular questions from this chapter

A pulse of light is created by the superposition of many waves that span the frequency range f0-12Δf≤f≤f0+12Δf, wherc f0=c/λis called thc center frequency of thc pulsc. Lascr technology can generate a pulse of light that has a wavelength of 600nmand lasts a mere 6.0fs 1fs=1femtosecond localid="1650804865678" =10-15s.

a. What is the center frequency of this pulse of light?

b. How many cycles, or oscillations, of the light wave are completed during the 6.0fs pulse?

c. What range of frequencies must be superimposed to create this pulse?

d. What is the spatial length of the laser pulse as it travels through space?

e. Draw a snapshot graph of this wave packet.

For the electron wave function shown in FIGURE Q39.3, at what position or positions is the electron most likely to be found? Least likely to be found? Explain.

An electron that is confined to x Ú 0 nm has the normalized wave function c1x2 = b 0 x 6 0 nm 11.414 nm-1/2 2e-x/11.0 nm2 x Ú 0 nm where x is in nm. a. What is the probability of finding the electron in a 0.010-nmwide region at x = 1.0 nm? b. What is the probability of finding the electron in the interval 0.50 nm … x … 1.50 nm?

A small speck of dust with mass 1.0×10-13ghas fallen into the hole shown in FIGURE P39.46 and appears to be at rest. According to the uncertainty principle, could this particle have enough energy to get out of the hole? If not, what is the deepest hole of this width from which it would have a good chance to escape?

The probability density for an electron that has passed through an experimental apparatus. If 1.0×106electrons are used, what is the expected number that will land in alocalid="1649312933417" 0.010mmwide strip atlocalid="1649312941736" (a)x=0.000mmand localid="1649312949893" (b)2.000mm?
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