Chapter 39: Q5. (page 1136)
What is the value of the constant a in FIGURE Q39.5?

Short Answer
a = 2mm-1
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Chapter 39: Q5. (page 1136)
What is the value of the constant a in FIGURE Q39.5?

a = 2mm-1
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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?
An experiment has four possible outcomes, labeled A to D. The probability of A is PA= 40% and of B is PB = 30%. Outcome C is twice as probable as outcome D. What are the probabilities PCand PD?
Soot particles, from incomplete combustion in diesel engines, are typically in diameter and have a density of . FIGURE P39.45 shows soot particles released from rest, in vacuum, just above a thin plate with a -diameter holeroughly the wavelength of visible light. After passing through the hole, the particles fall distance and land on a detector. If soot particles were purely classical, they would fall straight down and, ideally, all land in a -diameter circle. Allowing for some experimental imperfections, any quantum effects would be noticeable if the circle diameter were . How far would the particles have to fall to fill a circle of this diameter?

The probability density for an electron that has passed through an experimental apparatus. If electrons are used, what is the expected number that will land in alocalid="1649312933417" wide strip atlocalid="1649312941736" and localid="1649312949893" ?

Consider the electron wave function
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?
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