In three dimensions, the solutions of the SchrГ¶dinger equation provided a set of three additional quantum numbers that could be used to describe electron behavior even in more complicated many-electron atoms. There was an appreciation that the energy level of an electron was related to the principal quantum number n, however there was no numerical means of classifying additional aspects of an electronвЂ™s motion in space, such as its orientation or direction.

While the work of Bohr and de Broglie clearly established that electrons take on different discrete energy levels that are related to the atomic radius, their model was a relatively simplistic spherical view.

quantum numberOne of certain integers or half-integers that specify the state of a quantum mechanical system (such as an electron in an atom).

quantumThe smallest possible, and therefore indivisible, unit of a given quantity or quantifiable phenomenon.

angular momentumThe vector product that describes the rotary inertia of a system about an axis.

The dynamics of any quantum system are described by a quantum Hamiltonian (H).

The value of n ranges from 1 to the shell containing the outermost electron of that atom.

The first quantum number describes the electron shell, or energy level, of an atom.

To completely describe an electron in an atom, four quantum numbers are needed: energy ( n), angular momentum (в„“), magnetic moment (m в„“), and spin (m s).

The wave function squared gives the probability of finding the electron at any particular position. It is a particle with wave-like properties. Remember, however, that the electron is not just a wave. 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. 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, в„“, m в„“, 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.Д¬learly the three quantum numbers, n, в„“, m в„“, 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). 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. Quantum Numbers - Specifying the electron state

How do quantum numbers help chemists