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.
Most likely to be found: x = -2, 0, +2
Least likely to be found x = -4, +4, -1 and +1
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.
Consider the electron wave function
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?
A small speck of dust with mass has 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?
A -mm-diameter sphere bounces back and forth between two walls at and . The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is
a. At exactly ?
b. Between and ?
c. At ?
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