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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

The wave function of a particle is

ψx=bπx2+b2

where b is a positive constant. Find the probability that the particle is located in the interval -b≤x ≤b

A particle is described by the wave function c1x2 = b cex/L x … 0 mm ce-x/L x Ú 0 mm where L = 2.0 mm.

a. Sketch graphs of both the wave function and the probability density as functions of x.

b. Determine the normalization constant c.

c. Calculate the probability of finding the particle within 1.0 mm of the origin. d. Interpret your answer to part b by shading the region representing this probability on the appropriate graph in part a

FIGURE Q39.6 shows wave packets for particles 1, 2, and 3. Which particle can have its velocity known most precisely? Explain.

Suppose you draw a card from a regular deck of 52 cards.

a. What is the probability that you draw an ace?

b. What is the probability that you draw a spade?

The wave function of a particle is

ψx=b1+x2-1mm≤x<0mmc1+x20mm≤x≤1mm

and zero elsewhere
See all solutions

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