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Problem 64 Hard Difficulty

Suppose the velocity of an electron in an atom is known to an accuracy of $2.0 \times 10^{3} \mathrm{m} / \mathrm{s}$ (reasonably accurate compared with orbital velocities). What is the electron's
minimum uncertainty in position, and how does this compare with the approximate 0.1 -nm size of the atom?

Answer

29.0 $\mathrm{nm}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Farnaz M.

Simon Fraser University

Video Transcript

So in this problem, we know that. Ah, velocity uncertainty off the electron inside to the Adam Ihsaa. Two times sent to the 3rd 2 meters per second. Okay, so Ah, we're going to see that the uncertainty of the mo mentum is delta p equals m times that Evite. Right. So this gives you 1.82 times 10 to the native, 27th kilograms. I need a second. Okay. And according to the has Umberg Uncertainty low. We have that a pete that x a quote h over full pie. Right? So we can see that that axe equal hd by by four pi that a p so this gives you 29 90 meters. All right, so the uncertainty off this election wrong is 29 centimeters, but the size of the the size, so typically the size of the Adam is 0.1 on two meters. So that means that the uncertainty of the electorate is much larger than the size of electron. All right, so let's say this. That exits much larger than the size of the electron that say it's ah, on D uh, Adam. Okay,

Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Farnaz M.

Simon Fraser University