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Chapter 39: Q. 41 (page 1118)

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 10m/s ?

Short Answer

Expert verified

The smallest one-dimensional box is 18.2脳10-6m.

Step by step solution

01

part  (a) step 1: Given information 

Electron's velocity limit: 10m/s

02

part (a) step 2: formulas for solutions

螖x螖p=h2

Whereas, 螖xis the change in position.

螖pis change in momentum.

h is Plank's constant h=6.63脳10-34Js

03

part (b) step 3: calculation

The range of electron's velocity is 10m/sso it can be varied from -10m/stoo +10m/s.

So the change in velocity is 20m/s.

螖pChange in momentum can be given as 螖p=m螖vwhere; mis the mass of electron

螖p=m螖v螖p=9.1脳10-31kg脳20m/s螖p=1.82脳10-29

Here, 螖xis the uncertainty in the position of an electron which is equal to the dimension of the box L

So by using the formula 螖x螖p=h2, we can determine the dimension of the box.

螖x螖p=h2螖x=h2螖p=6.63脳10-3Js2脳1.82脳10-29=18.2脳10-6m

The dimension of the smallest box should be

18.2脳10-6m.

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