Electron in orbit of around a single proton

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Discussion Overview

The discussion revolves around the calculation of the kinetic energy of an electron in orbit around a proton in a hydrogen atom. Participants explore the application of Newton's laws and the implications of the signs in the equations used to describe the forces and energies involved.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant outlines a method for calculating the kinetic energy of an electron using Newton's second law and Coulomb's law, noting that the kinetic energy appears negative.
  • Another participant questions the direction of the electrostatic force (FE) acting on the electron.
  • A subsequent reply clarifies that the electrostatic force points towards the nucleus, suggesting it provides the necessary centripetal force for the electron's motion.
  • It is noted that the centripetal force expression also points towards the center, implying that a negative sign may be needed in the energy equation as well.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the interpretation of the negative kinetic energy result, and there are differing views on the implications of the signs in the equations presented.

Contextual Notes

The discussion does not resolve the assumptions regarding the definitions of forces and energies, nor does it clarify the conditions under which the equations are applied.

Ian Baughman
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Today I was doing some reading and I came across this topic. If we have a stationary hydrogen atom with a single electron in orbit around the nucleus and want to calculate the kinetic energy of the electron we would take the following approach.

1) Using Newton's second law:
F = ma ⇒ FE = mac ⇒ k(q1q2)/r2 = mv2/r​
2) We know:
charge of the electron = -e = -1.602×10-19 and the charge of the proton = +e = 1.602×10-19
​
3) Now using equation in step 1:
-k(e2)/r = mv2 ⇒ -k(e2)/(2r)=(1/2)mv2​

We know kinetic energy is suppose to be positive so why is it that it comes out negative in this case?
 
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Towards the nucleus of the atom.
 
So FE provides the centripetal force. It's the only force around. ##mv^2\over r## also points towards the center, so it needs a minus sign too.
 
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