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Q. 41

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1118

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Short Answer

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

See the step by step solution

Step by Step Solution

part  (a) step 1: Given information 

Electron's velocity limit:

part (a) step 2: formulas for solutions

Whereas, is the change in position.

is change in momentum.

h is Plank's constant

part (b) step 3: calculation

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

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