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Chapter 39: Q3. (page 1118)

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.

Short Answer

Expert verified

Most likely to be found: x = -2, 0, +2

Least likely to be found x = -4, +4, -1 and +1

Step by step solution

01

Concept used:

p(x)=ψ(x)2

02

Determination of positions where electron would most likely be found.

Now as we know probability will be the square of wave function.
And if we square this wave function, the whole graph will change to positive y axis with squared values.

So the point with highest values will be x = 0, 2nd highest will be at x = -2, +2

Points with minimum values after squaring will be+1, -1, -4 and +4 as function is approaching towards 0 there.

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Most popular questions from this chapter

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?

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?

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?

3 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-wide strip at (a) x = 0.000 mm, (b) x = 0.500 mm, (c) x = 1.000 mm, and (d) x = 2.000 mm?

FIGURE P39.31 shows the wave function of a particle confined

between x = 0 nm and x = 1.0 nm. The wave function is zero

outside this region.

a. Determine the value of the constant c, as defined in the figure.

b. Draw a graph of the probability densityPx=ψx2

c. Draw a dot picture showing where the first 40 or 50 particles

might be found.

d. Calculate the probability of finding the particle in the interval

0nm≤x≤0.25nm.
See all solutions

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