[rivercitybruin]

ORIGINALLY POSTED BY ME IN AN MCAT FORUM

hi, hoping people can help. this is really basic, but seems potentially confusing. and glossed over in all but most detailed textbook

part 1:

the further away an electron from the nucleus, the more energy it has...

BUT.... the equation for energy of an electron has "radii squared" in the denominator.... therefore, as partial derivative, energy should go down

FURTHER, at infinite distance, the energy of the election is zero.

i don't understand this.. doesn't make sense to me.. i understand it's only a partial derivative. so bigger atoms have more charge and therefore the electrons have more energy.

but the basic concept seems backwards to me.. or at least poor explained. and i know it's something that bothered me in the past.

part 2 (various questions):

is there negative and positive energy values? i.e. attractive vs. repulsive force? or it is just an absolute number?

does the electron have energy or potential energy? or is that the same thing?.. is a barrell of oil have energy or potential energy? same with a giant boulder hanging off a large cliff?

lastly, what is the nature of the electron's energy (potential) energy? it's movement. it's attraction to protons.

thx in advance . i might need a 1200 page chemistry textbook vs. the various study guides i have handy

[Corribus]

First, it's important to distinguish what kind of energy you are talking about. In this case, it seems we are talking about potential energy. In the case of charges, the potential energy is a way of describing the force acting upon the charges due to mutual attraction or repulsion.

Generally, potential energy is a relative scale, i.e., it is only defined relative to a point of reference, which is assigned a value of zero. For point charges, that frame of reference is when they are infinitely separate. Therefore when the distance separating two point charges is infinitely large, they have a potential energy of zero.

In, say, a hydrogen atom, as the electron gets closer to the proton nucleus, the potential energy is smaller. This is consistent with the fact that the charges are attractive because they are opposite. A system moves toward lower potential energy if possible. Note that lower potential energy does NOT mean closer to zero!  It means more negative.

This is not in disagreement with the coulomb potential equation, because recall that the equation includes the electric charges. So, as r gets smaller, the magnitude of the potential gets larger, but the sign is negative (positive nucleus * negative electron = negative value), so the potential energy gets more negative, i.e., smaller. If r = 0, the potential energy is undefined, negative infinity.

One of the peculiarities of quantum mechanics is, of course, that the electron does not fall into the nucleus, even though classically it should (like an asteroid falls to the earth). Only certain values of r are allowed, determined by the quantization of the energy eigenvalue.