What's the difference between an orbital and an energy level? Are they the same thing?

Question

In chemistry, you're likely to learn that each atom has a given number of orbitals, or electron shells, where the first orbital contains two electrons, the next contains eight electrons, and so on. In physics, you're likely to learn about electron excitation (electrons going from a lower energy level to a higher one) and photon emission (electrons returning from higher energy levels to lower energy levels). The concepts of orbitals and energy levels are clearly related - with each atom having a predetermined number of each - but the number of orbitals of an atom doesn't always (or ever, I'm not sure) equal the number of energy levels of that same atom.

For example; hydrogen has one orbital (containing one electron) but has 5 discrete energy levels at which the electron can exist.

If anyone could clear up my confusion it would be much appreciated. Thanks in advance!

Answer 1

For each system you look at (e.g. atoms or molecules) there is a whole spectrum of a infinite number of orbitals and energy levels. From a theoreticians point of view, you can put in the electrons into these orbitals as you like to get a specific state of the system. With each occupied orbital you occupy the corresponding energy level. But of course you cannot occupy all oritals/levels due to the limited number of electron in a system. So to be precise:

• each (physical) system has an infinity number of energy levels
• each orbital has a energy level
• there are occupied and unoccupied orbitals
• the layout (which orbitals are occupied by electrons) determines the state of the system
• the hydrogen atom has a infinite number of "occupieable" orbitals, but only one is occupied.

The chemists calssify the orbitals of single ions by labeling 1s 2s 2p ... 3d .... But these are classes of orbitals not the orbitals itself. For example in the class of the 3d orbitals every orbitals has a angular momentum quantum number l=2 and thus the class yields orbitals with angular-z-momentum m=-2,-1,0,1,2 and electrons of spin up and down, thus 10 orbitals.

But be aware that the thinking of orbitals and energy levels in just an approximation. The true quantum mechanical state of a system is given by its wave function, which is far more complex and yield much more physical effects that can be described by a simple orbital picture.