It is a particle with wave-like properties. Remember, however, that the electron is not just a wave. Thus, one has two options for a 4s electron. Since this orbital is filled already, there is not just one choice. In summary, you can think of electron orbitals as standing waves of the electron wave function when it is bound to a postively charged nucleus. Every electron can have either spin-up 1/2 or spin-down 1/2 for the value of ms. Any more would violate Pauli's Principle. Since there are only two values of m s, then any orbital can only hold two electrons with opposite vales of m s. Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers n, ℓ, m ℓ, m s. The electron spin is very important in understanding the electronic structure of atoms containing many electrons (not just one like Hydrogen) because of the Pauli Exclusion Principle. The spin quantum number shows up when the wave function of quantum mechanics is modified to include the effects of relativity.

This property is called spin because if electrons were balls of charge spinning about their own axes, they would behave in this way in a magnetic field.

As n increases, the electron orbital becomes larger and the electron spends more time farther from the nucleus.Ĭlearly the three quantum numbers, n, ℓ, m ℓ, are not enough to completely describe the state of the H-atom, Another quantum number is required to describe whether it goes up or down in a spatially varying magnetic field. The principal quantum number has integral values of n = 1, 2, 3. For an electron trapped by its electrostatic attraction to positively charged nucleus we use the three following quantum numbers to describe the electron state (orbital). Let's look at the quantum numbers needed to label the possible standing waves or states of an electron trapped by its electrostatic attraction to a positively charged nucleus. Normally we operate in 4 dimensions (3 space and 1 time dimension), so in general we will need 4 quantum numbers to fully specify an electron state ( i.e., standing wave). It is always a positive integer, that is n 1, 2, 3. PRINCIPAL QUANTUM NUMBER (n) - Represents the main energy level, or shell, occupied by an electron. Now it turns out that if you consider an electron trapped inside a sphere (instead of in a one-dimensional box) it will have standing waves that are very similar to an electron bound to a positively charged nucleus by electrostatic attraction. The quantum numbers are parameters that describe the distribution of electrons in the atom, and therefore its fundamental nature. Quantum Numbers - Specifying the electron state

Quantum numbers