# Negative energy levels

1. Feb 27, 2012

### quietrain

hi,

why are the energy levels of electrons in say a hydrogen atom -13.6ev, -3.4 eV etc ?

i thought energy is always positive? what does the negative mean?

thanks!

2. Feb 27, 2012

### genericusrnme

Total energy can be negative, it's just kinetic energy that can't be negative
The negative energy comes from the fact that the electrons are in a bound state

If the total energy were zero then the electron would be able to fly off to infinity then turn back.
$E = T + V=\frac{1}{2}m\ v^2 -\frac{e}{r}$

The potential energy due to the nucleus is negative because it causes an attractive force.

So when the electron has negative energy it is bound to a region of certain r, the boundary of which should be when the kinetic energy goes to zero (a turning point)
$E=- \frac{e}{r}$
$r = -\frac{e}{E}$

Since E is a negative quantity this becomes
$r = \frac{e}{|E|}$

If the energy is zero then the turning point happens at
$\frac{e}{r}=0$

So r goes to infinity then turns back.

That's what it means classically and the idea carries over into the quantum world.

3. Feb 27, 2012

### M Quack

It depends on what you define as a reference. If the reference for E=0 is an isolated proton and an isolated electron far away (and both at rest), then the negative energy values can be interpreted as binding energies, i.e. the energy it takes to go back to the reference configuration.

4. Feb 28, 2012

### quietrain

alright thanks!

5. Feb 28, 2012

### cmb

There is no such thing as 'negative energy'. Energy is a description of potential state changes within a system. A system cannot not change in a manner less than if it does nothing!

You may freely define a quantity of 'potential' which may be negative with respect to some other vaule or system. In the case of an atom, the 'ground state' is the state where everything is settled and huncky-dory (that is, nothing is likely to spontaneously change) with all the electrons in their 'rightful place'. It requires energy to pull that electron off the hydrogen atom, leaving behind a 'potential hole' into which an electron will get sucked at the first opportunity so that it can get back to 'ground state'. Therefore it is denoted -ve indicating whether a return to the ground state will require, or release, energy in doing so.

Naturally, your definitions can be your own - if you were to want to define all reactions as 'a release of energy', then those that are endothermic and need energy would be a 'negative energy' process. So it is all in your definition, but the accepted convention is that a +ve ionised atom will carry a 'negative potential'.

6. Feb 29, 2012

### quietrain

so the energy levels are potentials?

7. Feb 29, 2012

### cmb

Energy is a description of potential state changes within a system.

If you want to call energy levels 'potentials', I think that's ok. 'Electrical potential' is, simply, a measure of how many Joules energy would be released per unit of charge as it drops to your 'zero' voltage datum, just as 'gravitational potential' is likewise but for mass dropping through a height to a 'zero' datum.

8. Mar 11, 2012

thanks!