What is the kinetic energy of the electron?

Click For 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
Messages
4
Reaction score
0

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...
 
Physics news on Phys.org
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.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Purcell 1.77 Electron jelly
  • · Replies 2 ·
Replies
2
Views
964
Working out the kinetic energy of a body due to a gravitational field
  • · Replies 3 ·
Replies
3
Views
1K
Using energy considerations to analyse particle motion
  • · Replies 3 ·
Replies
3
Views
963
Find at what rate the orbit radius will grow
  • · Replies 30 ·
2
Replies
30
Views
2K
Expression for magnitude of the constant friction force
  • · Replies 7 ·
Replies
7
Views
1K
How to Correctly Solve for the Minimum Distance Between Two Electrons?
  • · Replies 5 ·
Replies
5
Views
1K
Finding kinetic energy and initial velocity of a cart over time
  • · Replies 6 ·
Replies
6
Views
2K
What is the Minimum Distance of Masses After a Split in a Satellite System?
  • · Replies 8 ·
Replies
8
Views
2K
Potential Energy and raising a satellite from Earth into a Circular Orbit
  • · Replies 5 ·
Replies
5
Views
3K
Kinetic Energy of Colliding Protons
  • · Replies 54 ·
2
Replies
54
Views
11K