Answer:
QUANTUM NUMBERS, ATOMIC ORBITALS, AND ELECTRON CONFIGURATIONS
Quantum Numbers and Atomic Orbitals
By solving the Schrödinger equation (Hy = Ey), we obtain a set of mathematical equations,
called wave functions (y), which describe the probability of finding electrons at certain energy
levels within an atom.
A wave function for an electron in an atom is called an atomic orbital; this atomic orbital
describes a region of space in which there is a high probability of finding the electron. Energy
changes within an atom are the result of an electron changing from a wave pattern with one energy
to a wave pattern with a different energy (usually accompanied by the absorption or emission of a
photon of light).
Each electron in an atom is described by four different quantum numbers. The first three (n, l,
ml) specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can
occupy that orbital.
1. Principal Quantum Number (n): n = 1, 2, 3, …, 8 .
Specifies the energy of an electron and the size of the orbital (the distance from the nucleus of
the peak in a radial probability distribution plot). All orbitals that have the same value of n
are said to be in the same shell (level). For a hydrogen atom with n=1, the electron is in its
ground state; if the electron is in the n=2 orbital, it is in an excited state. The total number of
orbitals for a given n value is n
2
.
2. Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n-1.
Specifies the shape of an orbital with a particular principal quantum number. The secondary
quantum number divides the shells into smaller groups of orbitals called subshells (sublevels).
Usually, a letter code is used to identify l to avoid confusion with n:
l 0 1 2 3 4 5 . . .
Letter s p d f g h . . .
The subshell with n=2 and l=1 is the 2p subshell; if n=3 and l=0, it is the 3s subshell, and so
on. The value of l also has a slight effect on the energy of the subshell; the energy of the
subshell increases with l (s < p < d < f).
3. Magnetic Quantum Number (ml): ml
= -l, ..., 0, ..., +l.
Specifies the orientation in space of an orbital of a given energy (n) and shape (l). This
number divides the subshell into individual orbitals which hold the electrons; there are 2l+1
orbitals in each subshell. Thus the s subshell has only one orbital, the p subshell has three
orbitals, and so on.
Explanation:
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