Q. 41

Expert-verifiedFound in: Page 1118

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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

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