Question

I'm taking a look at energy levels in the Bohr model for hydrogen. In the derivation I've got a positive kinetic energy term and a negative potential energy term. Why is the potential energy term negative?

Answer 1

Potential energy: \[kq1q2/r\]. Let q1 be the charge of the nucleus, and q2 the charge of the electron. Electrons have a negative charge, and nuclei positive charges. Thus, the potential energy is negative. This is referring to the fact that positive charges attract negative charges, and so the electron will be attracted to the nucleus.

Answer 2

How much do you know of calculus?

Answer 3

Up to differential equations and multivariable. Why you ask?

Answer 4

Not you, @cndetriot for a possible explaination about energy in general.

Answer 5

OOps sorry i didn't see on my notice tab about who posted last.

Answer 6

Energy is an odd quantity, because we cannot measure it directly. There is no such thing as an energy meter. What we can measure are forces, velocities and displacements. Once we have a theory of kinetic energy, measurement of the velocity allows us to measure absolute kinetic energy (at least within a given reference frame), because Ek = 0 when v = 0.

However, for potential energy we cannot even in principle measure absolute potential energy. All we can do is measure the work required to displace a system, so we can measure the differences in potential energy between one place (or state) and another. In order to come up with a number, we have to simply define one place (or state) in which potential energy is DEFINED to be zero, and then measure all other potential energy relative to that point. (It's very similar to measuring voltage -- we have to define zero volts somewhere, and measure with respect to that point.)

In electrostatics, by tradition we define U = 0 to be when all the charges are infinitely far apart, and exerting no force on each other. Necessarily, then, the potential energy of charges that repel will be higher than 0, and the potential energy of charges that attract will be lower than 0 (you have to put energy in to pull them apart, and get them to U = 0).

Could we define the zero of electrostatic potential energy in such a way that U was always positive, as we do for kinetic energy? Not easily. We'd have to know the position and location of all the charged particles in the Universe when the attractive particles were as close as possible, and the repelling particles as far apart as possible. That's the minimum potential energy situation. If we knew it, we could measure U from there, and it would always be positive. But you can see the practical difficulty. By contrast, it's very easy to define the state where all the particles in the Universe (or in some system) are infinitely far apart and exerting no force on each other.

Answer 7

work done is nothing but the exchange of energy which u have to do in a force region to change the configuray=tion...