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Problem 15 Easy Difficulty

In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is $5.29 \times 10^{-11} \mathrm{m} .$ (a) Find the magnitude of the electric force exerted on each particle. (b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?

Answer

a) $8.23 \times 10^{-8} \mathrm{N}$
b) $2.19 \times 10^{6} \mathrm{m} / \mathrm{s}$

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Video Transcript

Okay, so question a the force which is the natural forces, equals Okay, times queues grow of r squared. OK, the reason why it's accused where he's because hydrogen only have one Protais will charge on Proton is 1.6 times 10 to apartment 19 groups. Okay. And okay, then are here is the distance between the hydrogen atom and the proton, which is the radius off the circular motion. Okay, which is equal to 5.29 times 10 to the power off on every level meter in case the Quillin constant which is 9.0, it has tension are up. Nine Newtown has meter, square foot go on square, therefore have force half. He's equal to now. I'm going over tens since about NYU Utah task meter, square vocal on square and sometimes 1.6 times tens of pollinating 19 Cool into a power square over 5.29 times tend to apartment every 11 meter s square and it will give us the that. The larger force is about a point two or three times. Tend to apartment eight Newtok Newton. OK, so this is the, uh, lateral force extra exerted on each particle. Okay for question be was asking us the speed or the velocity off the natural? We know. So this is a circular motion in a question and the only force there was exerted on each particle is that's workforce. So therefore, these centrifugal force is equal to relax to force, which would give us half MV squared over r it reduced on a ranch. Mahir will eventually have we which is a spiel without trying to see what the f are aware. So the force is we just figure out last pressure, which is a point to three times 10 to apartment a new tops and our, which is the Regis, is given 5.29 hands. Attention public 11 meter and a massive villa Choice is a 9.11 That's potential power. Next 31 kilograms, therefore, can determine the speed of the truck which is equal to the square root, a 0.23 times potential opponent, a new top and then tires 5.29 times essentially pollinate negative 11 meter over 9.11 times 10 to a prominent 31 kilograms, and this will give us the speed of the that trance about to a boy. One i times tends to about a six meter per second. And these are the answers for this question. Thank you.

Georgia State University
Top Physics 102 Electricity and Magnetism Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp