What is the correct order of subshell energies? [duplicate]

I was taught in high school that the order is given by the Aufbau Principle: 1s>2s>2p>3s>3p>4s>3d>4p>5s>4d>5p>6s>4f>5d>6p...

Why is the 3d subshell higher in energy than the 4s subshell if it is in a lower shell? Why not call it the 4d shell?

My current understanding is that the shell number indicates distance from the nucleus, while energy can be affected by other factors, such as subshell type.

Using the element bromine (e- config [Ar]4s2 3d10 4p5) as an example, there are three reasons why I think this is the case:

1. The 4s subshell would fill with electrons before the 3d subshell since it is lower in energy for some reason.
2. The 4p subshell would fill with electrons after the 3d subshell since it is higher in energy for some reason.
3. The valence subshells for Br are the 4s and 4p despite 3d being higher in energy than 4s because 4s and 4p are farther from the nucleus distancewise.
• The shell number comes from certain mathematical procedure; it may be somewhat related to the distance from the nucleus, but does not indicate the said distance, nor can it be ascribed arbitrarily. So the 3d subshell is indeed 3 and not 4. – Ivan Neretin Feb 24 '16 at 19:38
• Have a look here, especially at the part "Why do states with the same n but lower ℓ values have lower energy eigenvalues?". – Philipp Feb 24 '16 at 19:43
• – Mithoron Feb 24 '16 at 19:52
• Thanks for your help. I will research more thoroughly next time. – Alex Smith Feb 24 '16 at 21:17