# The quantum mechanical states

Each state of a nuclear particle- system is described by four quantum numbers clearly.

The four quantum numbers are:

** Principal quantum number n Angular momentum quantum number l Magnetic quantum number m Spin quantum number sPrincipal quantum number n**The principal quantum number n runs through all natural numbers from 1 to N, in the case of the periodic table a principal quantum number is allocated to each shell, it is the numbers 1 up to 7

**The angular momentum quantum number l**

The angular momentum quantum number l is able to reach integral values from 0 to n-1 for each n. For example: for n = 1, it can only reach the value 0. The angular momentum quantum number defines the lower bowls of each shell.

**The magnetic quantum number m**

The magnetic quantum number m can reach integral values from –I up to +l for each l, Regarding the principal quantum number n = 1, l reaches the value 0 and m also reaches value 0. m defines the number of states per sub shell.

**The Spin quantum number s**

The spin quantum number takes reaches the values +1/2 or -1/2 for each state s. This means that each state of a nuclear particle system is filled twice; which means for the state of the the quantum numbers n = 1, l = 0 and m = 0, this means that it is also filled twice.

**The Pauli principle**

Regarding the Pauli – principle (which only applies to fermions), the states in each quantum mechanical model has to differ in at least one of the four quantum numbers. The atomic components, neutrons, protons and electrons are fermions. It was not possible to explain the Mendelejewsche organizing principle before using the Pauli principle. Each sub shell contains odd number of states that can be doubled by the Pauli principle only so that an explanation of an even number of states was possible from that moment on.

Representation of the possible quantum states of the first seven principal quantum numbers:

By definition of the quantum numbers, there may be n Z_n=2n^2 states per principal number. Please find a comparison of the oretical and measured as follows: