What is Coulomb potential and energy?

[quietrain]

is it just potential and potential energy?

but if so, why is it given as

V(r) = - Ze² / 4πεr ?
and
E = Z²e² / 4πεr

i am having trouble understanding how come for potential V, Q = Ze²

while

for E, Q² = Z²e²

thanks!

 

[chrisbaird]

If E is meant to denote the classical electrostatic field and V the classical electrostatic potential, then your equations look all wrong. Where did you get them?

The term "Coulomb potential" is essentially used to mean the potential that gives rise to a classical electrostatic force (quantum effects can be neglected). Van der Waals force potentials, covalent bond potentials, quantum wells, etc. are all electromagnetic potentials but are quantum in nature.

 

[quietrain]

i got them off my notes, but they may be wrong

so is it right that charge Q = Ze?

so electric potential energy = kQQ/R = k(Ze)²/R ?

Ze is bascially the charge of the nucleus right? number of proton mulitply by electron charge e?

also, so the term "coulomb" refers to classical electrodynamics mainly?

 

[chrisbaird]

i got them off my notes, but they may be wrong

so is it right that charge Q = Ze?

Yes, if you are neglecting screening and quantum effects, then the total charge of a mass it the number of elementary charges (protons) times the charge of one element.

so electric potential energy = kQQ/R = k(Ze)²/R ?

I think I see the problem. Coulomb Potential energy U = kQ₁Q₂/R where Q₁ is the charge of the one particle and Q₂ is the charge of the other. If you are treating a one-electron atom classically, then for the electron Q₁ = -e and for the protons, Q₂ = +Ze so that:

U = k(-e)(Ze)/R = - k Ze²/R

Ze is bascially the charge of the nucleus right? number of proton mulitply by electron charge e?

Yes

also, so the term "coulomb" refers to classical electrodynamics mainly?

Yes

 

[quietrain]

If you are treating a one-electron atom classically, then for the electron Q₁ = -e and for the protons, Q₂ = +Ze so that:

U = k(-e)(Ze)/R = - k Ze²/R

ah i see... but why is an atom "one-electron" classically?

 

[chrisbaird]

ah i see... but why is an atom "one-electron" classically?

When you have an atom with more than one electron, the quantum effects become so strong that using a classical approach is rendered essentially useless. If you are going to use Coulomb's law to describe an atom (already a shaky proposition), it's best to keep to one-electron atoms. Even with the help of quantum theory, deriving the potential of a multi-electron atom is nontrivial. Sadly, most of the atoms we encounter in every day life are multi-electron, so the clean one-electron pictures are not entirely useful.

 

[quietrain]

i see thank you very much