Because Calculus/Quantum Mechanics

Uncertainty

Basic laws of quantum mechanics state that the exact location of an electron in its orbit can not be accurately determined. Only a range can be determined. The following levels and sub levels will show the calculated possible position of each electron.

S Sublevel

The S-Sublevel is found in all of the energy level. It takes the shape of a sphere. Each S sublevel can hold 2 electrons

P Sublevel

The P sublevel is found in every energy level that is greater than 2. There are three different of p orbitals, They all look like 2 balloons stuck together on opposite ends, and line up. However, the direction the different orbital is pointing in is in a different direction from the others. Each P sublevel can hold 2 electrons.

D Sublevel

The D sublevel is found in every energy level that is greater than three. There are 5 types of D orbitals. 4 of them look like a 4 leaf clover, except they are oriented on the axis differently. The last one looks like a P orbital with a ring in between the middle. Each D sublevel can hold 2 electrons

F Sublevel

The F sublevel is currently only found on the 4th energy level. There are 7 types of F orbitals. 4 of them look like 2 four leave clovers back to back. The difference between these four is their orientation on their specific axis. 2 orbitals look like a 6 petal flower with different axis orientation as well. The last type of F orbital looks like a P orbital with 2 rings around the middle of the orbital. Each F level can hold 2 electrons.

G sublevel

As of right now, the g sublevel does not exist. But with a bit of extrapolation, it can be hypothesized that there will be 9 different types of orbitals, since the difference between the previeos number of types of orbitals from S-P, P-D, D-F is 2. Thus by adding two to the types of F orbitals, we can deduce that there should be 9 different orbitals. Also each G sublevel should 2 electrons, since all the other sublevels only hold two

Levels

In Level 1, there is only 1 S orbital which means that Level 1 can have a maximum 2 electrons.

In Level 2, there is 1 S orbital and 3 P orbitals. This means Level 2 can contain a maximum of 8 electrons.

In Level 3, there is 1 S Orbital, 3 P orbitals, and 5 D orbitals. This means Level 3 can have a maximum of 18 electrons.

In Level 4, there is 1 S orbital, 3 P orbitals, 5 D orbitals, and 7 F orbitals. This means that Level 4 can have a maximum of 32 electrons.

Following the pattern, Level 5 should have 1 S orbital, 3 P orbitals, 5 D orbitals, 7 F orbitals, and 9 G orbitals. This means that Level 5 should have a maximum of 50 electrons.