Principal quantum number

Principal quantum number

In atomic physics, the principal quantum number symbolized as "n" is the first of a set of quantum numbers (which includes: the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) of an atomic orbital. The quantum number n labels the energy levels of hydrogenic atoms. It is the first in a set of numbers that show the unique quantum state of an electron. Labeling follows spectroscopic notation.

Derivation

There are a set of quantum numbers associated with the energy states of the atom. The four quantum numbers "n", "l", "m", and "s" specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital. No two electrons belonging to the same atom can have the same four quantum numbers which is shown in the Pauli exclusion principle. The wavefunction of the Schrödinger wave equation reduces to the three equations that when solved lead to the first three quantum numbers. Therefore, the equations for the first three quantum numbers are all interrelated. The principal quantum number arose in the solution of the radial part of the wave equation as shown below.

The Schrödinger wave equation describes energy eigenstates having corresponding real numbers "En" with a definite total energy which the value of "En" defines. The bound state energies of the electron in the hydrogen atom are given by:

: E_n = frac {E_1}{n^2} = frac {-13.6eV}{n^2}, n=1,2,3...

The parameter n can take only positive integer values. This idea of energy levels and notation was borrowed from the earlier Bohr model of the atom and expanded in Schrödinger's equation from the flat two-dimensional Bohr atom to the three-dimensional wavefunction model of the atom.

The allowed orbits depend on quantized (discrete) values of orbital angular momentum, "L" according to the equation:: mathbf{L} = n cdot hbar = n cdot {h over 2pi}

: Where "n" = 1,2,3,… and is called the principal quantum number, and "h" is Planck's constant.

The energy of any wave is the frequency multiplied by Planck's constant. This causes the wave to display particle-like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck's reduced constant which only allows particular or discrete or quantized energy levels.

The principal quantum number n represents the relative overall energy of each orbital and the energy of each orbital increases as the distance from the nucleus increases. The sets of orbitals with the same "n"-value are often referred to as electron shells or energy levels.

In the notation of the periodic table, the main shells of electrons are labeled:

K(n=1), L(n=2), M(n=3), etc.

based on the principal quantum number.

The principal quantum number is related to the radial quantum number, n_r , by:

n = n_r + l + 1

where "l" is the azimuthal quantum number and n_r is equal to the number of nodes in the radial wavefunction.

* Quantum number
** Azimuthal quantum number
** Magnetic quantum number
** Spin quantum number
** Total angular momentum quantum number
* Basic quantum mechanics
* Schrödinger equation

External references

* [http://www.colorado.edu/physics/2000/applets/a2.html Periodic Table Applet: showing principal and azimuthal quantum number for each element]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • principal quantum number — pagrindinis kvantinis skaičius statusas T sritis Standartizacija ir metrologija apibrėžtis Sveikasis skaičius, apibūdinantis elektrono energiją atitinkamoje orbitalėje. atitikmenys: angl. first quantum number; main quantum number; principal… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • principal quantum number — pagrindinis kvantinis skaičius statusas T sritis fizika atitikmenys: angl. first quantum number; main quantum number; principal quantum number vok. Hauptquantenzahl, f rus. главное квантовое число, n pranc. nombre quantique principal, m …   Fizikos terminų žodynas

  • principal quantum number — pagrindinis kvantinis skaičius statusas T sritis chemija apibrėžtis Sveikasis skaičius, nusakantis elektrono energiją atitinkamoje orbitalėje ir tos orbitalės dydį. santrumpa( os) n atitikmenys: angl. first quantum number; main quantum number;… …   Chemijos terminų aiškinamasis žodynas

  • principal quantum number — noun : an integer associated with the energy of an atomic electron in any one of its possible stationary states and including both the azimuthal and the radial quantum number called also total quantum number * * * Physics. the nonnegative,… …   Useful english dictionary

  • principal quantum number — Physics. the nonnegative, integral quantum number that defines the stationary orbits in the Bohr model of the atom. Also called total quantum number. [1920 25] * * * …   Universalium

  • Quantum number — Quantum numbers describe values of conserved numbers in the dynamics of the quantum system. They often describe specifically the energies of electrons in atoms, but other possibilities include angular momentum, spin etc.Since any quantum system… …   Wikipedia

  • quantum number — Physics. 1. any integer or half of an odd integer that distinguishes one of the discrete states of a quantum mechanical system. 2. any number that distinguishes among different members of a family of elementary particles. [1915 20] * * * ▪… …   Universalium

  • quantum number — One of a set of numbers describing possible quantum states of a system, e.g., nuclear spin. See principal quantum number spin …   Dictionary of automotive terms

  • Azimuthal quantum number — The azimuthal quantum number (or orbital angular momentum quantum number, second quantum number) symbolized as ℓ (lower case L) is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the… …   Wikipedia

  • Magnetic quantum number — In atomic physics, the magnetic quantum number is the third of a set of quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”