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Chapter 39: Q. 6 (page 1136)

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

Short Answer

Expert verified

The velocity of particle 1 is the most exact.

Step by step solution

01

Given information

Given: Graphs for wave functions of each particle.

02

Which particle has most precise wavelength.

When compared to particle 1, the wave functions of particles 2 and 3 are less spatially stretched. The more specific the position is known, the less precise the momentum is known, according to Heisenberg's Uncertainty Principle. Particles 2 and 3 have more exact position because their wave functions are less spatially stretched, but they have less precise momentum.

The most exact momentum belongs to particle 1.

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Most popular questions from this chapter

The probability density for finding a particle at position x is P1x2 = • a 11 - x2 -1 mm … x 6 0 mm b11 - x2 0 mm … x … 1 mm and zero elsewhere. a. You will learn in Chapter 40 that the wave function must be a continuous function. Assuming that to be the case, what can you conclude about the relationship between a and b? b. Determine values for a and b. c. Draw a graph of the probability density over the interval -2 mm … x … 2 mm. d. What is the probability that the particle will be found to the left of the origin?

1.0x 1010 photons pass through an experimental apparatus. How many of them land in a 0.10-mm-wide strip where the probability density is 20 m-1?

Consider the electron wave function

ψx=cxx≤1nmcxx≤1nm

where x is in nm. a. Determine the normalization constant c.

b. Draw a graph of c1x2 over the interval -5 nm … x … 5 nm. Provide numerical scales on both axes.

c. Draw a graph of 0 c1x2 0 2 over the interval -5 nm … x … 5 nm. Provide numerical scales.

d. If 106 electrons are detected, how many will be in the interval -1.0 nm … x … 1.0 nm?

What is the smallest one-dimensional box in which you can confine an electron if you want to know for certain that the electron’s speed is no more than 10 m/s?

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
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