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Chapter 39: Q4. (page 1136)

FIGURE Q39.4 shows the dot pattern of electrons landing on a screen. a. At what value or values of x is the electron probability density at maximum? Explain. b. Can you tell at what value or values of x the electron wave function c1x2 is most positive? If so, where? If not, why not?

Short Answer

Expert verified

a: x = -2, +2

b: x = -2, +2

Step by step solution

01

Concept used:

Wave function of electron gives the value of its probability density in a certain region.

02

Part a:

At x = -2, +2

Because as it can be seen in the given image, most number of electrons hit the screen at these locations so these are the regions where electron probability density will be maximum.

03

Part b:

The wave function will also be most positive at x = -2, +2 because wave function tells about distribution of probability density of electron.

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Most popular questions from this chapter

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

The wave function of a particle is

ψx=b1+x2-1mm≤x<0mmc1+x20mm≤x≤1mm

and zero elsewhere

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?

FIGURE P39.46

Heavy nuclei often undergo alpha decay in which they emit an alpha particle (i.e., a helium nucleus). Alpha particles are so tightly bound together that it's reasonable to think of an alpha particle as a single unit within the nucleus from which it is emitted.

a. AU238nucleus, which decays by alpha emission, is 15fm in diameter. Model an alpha particle within a U238nucleus as being in a one-dimensional box. What is the maximum speed an alpha particle is likely to have?

b. The probability that a nucleus will undergo alpha decay is proportional to the frequency with which the alpha particle reflects from the walls of the nucleus. What is that frequency (reflections/s) for a maximum-speed alpha particle within a U238nucleus?

Consider the electron wave function

ψX=0x<0nm1.414nm-12e-x1.0nmx≥0nm

where x is in cm.

a. Determine the normalization constant c.

b. Draw a graph of c1x2 over the interval -2 cm ≤x ≤2 cm. Provide numerical scales on both axes.

c. Draw a graph of 0 c1x2 0 2 over the interval -2 cm ≤x ≤2 cm. Provide numerical scales.

d. If 104 electrons are detected, how many will be in the interval 0.00 cm ≤x ≤0.50 cm?
See all solutions

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