In the quantum mechanical model of the atom, the electron is mathematically modeled as a standing wave around the nucleus in the Schrödinger equation. Solutions to the Schrödinger equation are expressed as wave functions, which relate to the probability of finding an electron in a particular space around the nucleus. Based on each of the solutions to the Schrödinger equation, we can create an orbital, which is the volume that encompasses 90% of the probability of finding an electron. Each orbital is designated by three quantum numbers: the principal quantum number, angular momentum quantum number, and magnetic quantum number. A fourth quantum number, the spin quantum number, designates an electron within the orbital. Our principal quantum number, n, determines the size and energy of an orbital. The possible values are integers: 1, 2, 3, 4, etc. As the value of n increases, the orbital has a higher energy and the electrons within the orbital are generally farther away from the nucleus. For the hydrogen atom, we can calculate the energy of each orbital based on the equation: energy equals -2.18 times 10 to the -18 power times the quantity 1 divided by n squared. With multi-electron atoms, the calculation becomes more complicated. The angular momentum quantum number, l, determines the shape of an orbital. The possible values are integers from 0 to n-1. So if n=1, the only possible value of l is 0. If n=2, the possible values are 0 or 1. If n=3, the possible values are 0, 1, or 2. And if n=4, the possible values are 0, 1, 2, or 3. There are also letter designations for each value of l. l=0 is also called "s" and it corresponds to the shape of the sphere shown in blue. l=1 is "p" and corresponds to the red dual teardrop shape. l=2 is "d" and l=3 is "f". The magnetic quantum number, ml, determines the orientation of the orbital. Possible values of ml are integers from -l to +l, including zero. So if l=0, the only possible value of ml is 0. This means there's only one orientation for the "s" shape. If l=1, the possible values of ml are -1, 0, and +1. These three possible orientations of the "p" shape are centered on the X, Y, and Z axes. When l=2, there are 5 possible orientations for the "d" shape responding to the numbers -2 through +2. And when l=3, there are seven possible orientations for the "f" shape. The spin quantum number determines the spin of the electron within the orbital. The possible values are +½ and -½, so each orbital can hold two electrons. Orbitals with the same value of n are said to be in the same shell or principle level. Orbitals with the same value of n and l are said to be in the same subshell or sub-level. And the first 3 quantum numbers specify a single orbital within the atom. We can apply our possible values for quantum numbers to an atom. When n=1, the only possible value of l is 0; this corresponds to the "s" shape. When l=0, the only value of ml is 0, so there's only one orbital in the 1s subshell. When n=2, the possible values of l are 0 or 1. We have one orbital in the 2s subshell, but we have 3 orbitals in the 2p subshell, which corresponds to the three possible values of ml when l equals 1. When n=3, we add the "d" subshell, which has 5 orbitals. So the third shell holds a total of 9 orbitals or 18 electrons.