Electron Motion Near Nucleus: Calculating Period and Velocity

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SUMMARY

The discussion focuses on calculating the period and velocity of an electron in motion near a radon nucleus, specifically at a distance of 5.00 × 10-10 m. The electric field at this distance is established at 4.95 × 1011 N/C, while the force on the electron is calculated to be 7.94 × 10-8 N. The participant attempts to derive the angular frequency (ω) using the force, radius, and mass of the radon nucleus but encounters difficulties in calculating both the period (T) and velocity (v) of the electron's motion.

PREREQUISITES
  • Understanding of classical mechanics, specifically circular motion.
  • Familiarity with the equations of motion: T = 2π/ω, a = v²/r, and f = mω².
  • Knowledge of electric fields and forces acting on charged particles.
  • Basic understanding of atomic structure and electron behavior around nuclei.
NEXT STEPS
  • Review the derivation of angular frequency (ω) in circular motion scenarios.
  • Learn how to apply Newton's second law to circular motion to find velocity (v).
  • Study the relationship between electric fields and forces on charged particles in atomic physics.
  • Explore advanced topics in quantum mechanics for a deeper understanding of electron behavior.
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Students studying physics, particularly those focusing on atomic physics and classical mechanics, as well as educators seeking to clarify concepts related to electron motion and forces in electric fields.

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Homework Statement


What is the magnitude of the electric field at a distance of 5.00 ×10−10 m from a radon nucleus?
=4.95×1011 N/C
What is the magnitude of the force on an electron at that distance?
=7.94×10-8 N
Now here is where I am getting stuck..
Treating the electron classically, that is, as a point object that can move around the nucleus at reasonably slow speeds, what is the period of the electron's motion? &
Again treating the electron classically, how fast it it moving?


Homework Equations


T=2Pi/omega
a=v^2/r
f=mr omega^2


The Attempt at a Solution



i tried solving for omega by plugging in the force, radius and mass of radon. then square rooting the answer. so ill have omega and then i take 2 pi over it right? for the period.. that's not working.
then i tried solving for the velocity by taking the force * radius / mass then square rooting that as well to find the velocity and that is wrong...

i don't know where i am going wrong.. any help would be great.

thanks!
 
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