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 ?
The smallest one-dimensional box is
Electron's velocity limit:
Whereas, is the change in position.
is change in momentum.
h is Plank's constant
The range of electron's velocity is so it can be varied from too
So the change in velocity is
Change in momentum can be given as where; is the mass of electron
Here, is the uncertainty in the position of an electron which is equal to the dimension of the box L
So by using the formula , we can determine the dimension of the box.
The dimension of the smallest box should be
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?
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