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Problem 36 Medium Difficulty

An electron is moving in the $+x$ -direction with speed measured at
$50 \mathrm{Mm} / \mathrm{s},$ accurate to $\pm 10 \% .$ What's the minimum uncertainty in its position?

Answer

$1.16 \times 10^{-11} \mathrm{~m}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Meghan M.

McMaster University

Video Transcript

before, considering an electron that's moving at a speed via 50 mega meters per second, which is 50 times center, the six meters per second. But we know it's accuracy down to 10%. We confined the uncertainty in that speed the Delta V by taking, uh the value 50 times 10 of the six meters percent getting multiplying it by 60.1. That's our uncertainty in that value. Um so did this comes out. You know, if you multiply that value by 0.1, this comes out to be 50 times 10 to the fifth meters per second. So now that we know the uncertainty in V, we confined the uncertainty in the position X from the uncertainty principle. Delta X Delta P is greater than equal to Planck's constant H divided by four pi. Because Delta P is equal to the mass times Delta V just coming straight from our relationship for momentum. So if we go ahead and sulfur Delta X, we find that Delta X is approximately equal to Plank's constant H, which we're gonna be using S I units here. So this is 6.63 times 10 to the minus 34 Jewell second, divided by four times pi. And it's also divided by the mo mentum Delta P or the Moment of Uncertainty Delta P, which is the mass m here. We're using the mass of the electron because it's a moving electrons. This is 9.1 times 10 to the minus, uh, 31 times Delta V, which is the value that we found above 50 times 10 to the fifth meters per second plugging these values. And we find that this comes out to approximately be 1.16 times 10 to the minus 11 meters weaken boxes and is the solution to our question.

University of Kansas
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Meghan M.

McMaster University