Everything about Principal Quantum Number totally explained
In
atomic physics, the
principal quantum number symbolized as
n is the firstof 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:
»
» 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 principle quantum number is related to the radial quantum number,
, by:
where
l is the
azimuthal quantum number and
is equal to the number of
nodes in the radial wavefunction.
Further Information
Get more info on 'Principal Quantum Number'.
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