Energy of an Electron

[Joe Rich 1D]

Why is the energy of an electron negative for any given energy level (according to the equation E=-hR/(n^2))? What does the energy for an electron at a given energy level correspond to (for instance, does a higher energy of an electron change its velocity or wavelength)?

[Kyle Sheu 1C]

As the e- is totally gone (i.e. when n approaches infinity), the e- has 0 energy.
As the e- falls in energy levels, it gives off/loses energy through photons; so from our perspective, the energy becomes negative.

An analog to this would be the equation for gravitational potential energy, where 0 potential energy is defined as at a point infinitely far away.

[RuchaDeshpande1L]

We are using E = 0 as a reference point in this case to represent the farthest an electron can be from its ground state. The negative sign basically means that an atomically bound electron has less energy than a free electron.

Just remember that electrons in an atom do not ACTUALLY have negative energies. It is just negative relative to our initial reference point.