What is the kinetic energy of the electron?

AI Thread Summary
In the Bohr Model of a hydrogen atom, the kinetic energy (KE) of the electron is expressed as KE = ke^2/2r, where k is Coulomb's constant and e is the charge of the electron. The electrical potential energy (U) is given by U = kqq/r. The discussion highlights the relationship between kinetic energy and potential energy, noting that KE = -1/2U, which leads to the conclusion that KE = kqq/2r. Participants clarify that gravitational forces are negligible at the atomic scale, emphasizing the dominance of electromagnetic interactions. The thread concludes with a request for further assistance on related topics in electric fields.
jamespetrovitch
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Homework Statement


In the Bohr Model of a hydrogen atom, a single electron revolves around a single proton in a circle of radius r. Assume that the proton remains at rest.
(a) what is the kinetic energy of the electron?
(b) what is the electrical potential energy?
(c) show that the electron's kinetic energy is equal to half of the electric potential energy.
(give answers in terms of e, Me, Mp, and r)

Homework Equations


KE = 1/2mv^2
F = Ma(centripetal accel.)
a(centripetal accel.) = v^2/r
F = (mv)^2/r = (kqq)/r^2

KE = -1/2U
U = GMm/r^2 = (kqq)/r
v(orbit) = \sqrt{}GM/r
1/2mv^2 = GMm/2r
F = q|E|
|E| = F/q = kq/r^2


The Attempt at a Solution


a)KE = ke^2/2r

b) I am having trouble finding a way to say that KE = -1/2U because I keep getting that...
KE = ke^2/2r
and that
U = GMm/2r even though U should be equal to something like...
U = -GMm/4r

c)cannot find a way to relate them...
 
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jamespetrovitch said:

The Attempt at a Solution


a)KE = ke^2/2r
Correct
jamespetrovitch said:
b) I am having trouble finding a way to say that KE = -1/2U because I keep getting that...
KE = ke^2/2r
and that
U = GMm/2r even though U should be equal to something like...
U = -GMm/4r
Look up the equation for electic potentional energy :wink:
 
ah, so for ...
b) U=kqq/r

and

c) KE = ke^2/2r
(1/2)(kqq/r) = KE = kee/2r

do I need to relate
KE = GMm/2r = kqq/2r any further or do the constants pretty much switch out since it is dealing with electric potential and not gravitation?
 
jamespetrovitch said:
ah, so for ...
b) U=kqq/r

and

c) KE = ke^2/2r
(1/2)(kqq/r) = KE = kee/2r

do I need to relate
KE = GMm/2r = kqq/2r any further or do the constants pretty much switch out since it is dealing with electric potential and not gravitation?
The gravitational field is negligable on the atomic scale, you only need to consider the electromagnetic field.
 

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