How Many Electrons in an Atom Can Have the Same Quantum State?

Quantum Numbers,
Atomic Orbitals, and
Electron Configurations

Contents:
Quantum Numbers and Atomic Orbitals
1. Principal Quantum Number (n)
2.  Athwart Momentum (Secondary, Azimunthal) Quantum Number (l)
3.  Magnetic Quantum Number (gfifty )
4.  Spin Breakthrough Number (msouth )
Table of Allowed Quantum Numbers
Writing Electron Configurations
Properties of Monatomic Ions
References

Breakthrough Numbers and Atomic Orbitals

By solving the Schr�dinger equation (Hy = Ey), we obtain a set of mathematical equations, chosen wave functions (y), which describe the probability of finding electrons at sure energy levels within an cantlet.

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 blueprint with 1 free energy to a wave pattern with a different energy (normally accompanied past the assimilation or emission of a photon of light).

Each electron in an atom is described past four dissimilar breakthrough numbers. The first three (n, l, thousandl ) specify the detail orbital of involvement, and the fourth (msouth ) specifies how many electrons can occupy that orbital.

  1. Main Quantum Number (n): n = 1, two, 3, …,
    Specifies the free energy of an electron and the size of the orbital (the altitude from the nucleus of the peak in a radial probability distribution plot). All orbitals that take 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=ii orbital, it is in an excited state. The total number of orbitals for a given n value is due north 2.
  1. Angular Momentum (Secondary, Azimunthal) Breakthrough Number (50): l = 0, ..., n-i.
    Specifies the shape of an orbital with a particular primary breakthrough number. The secondary breakthrough number divides the shells into smaller groups of orbitals called subshells (sublevels). Unremarkably, a letter code is used to place fifty to avoid confusion with due north:
50 0 1 two 3 four 5 ...
Letter south p d f g h ...

The subshell with n=two and l=1 is the 2p subshell; if n=three and l=0, information technology is the threes subshell, and so on. The value of fifty too has a slight effect on the energy of the subshell; the free energy of the subshell increases with l (s < p < d < f).

  1. Magnetic Quantum Number (kl ): ml = -l, ..., 0, ..., +l.
    Specifies the orientation in space of an orbital of a given energy (due north) and shape (l). This number divides the subshell into private orbitals which hold the electrons; there are 2l+ane orbitals in each subshell. Thus the s subshell has just one orbital, the p subshell has three orbitals, and so on.
  1. Spin Breakthrough Number (ms ): gs = +½ or -½.
    Specifies the orientation of the spin centrality of an electron. An electron tin spin in only i of 2 directions (sometimes chosen upwards and down).

    The Pauli exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states that no two electrons in the same atom can have identical values for all four of their quantum numbers. What this ways is that no more than than two electrons tin can occupy the same orbital, and that two electrons in the same orbital must have contrary spins.

    Because an electron spins, it creates a magnetic field, which can be oriented in one of two directions. For ii electrons in the aforementioned orbital, the spins must be opposite to each other; the spins are said to exist paired. These substances are not attracted to magnets and are said to be diamagnetic. Atoms with more electrons that spin in 1 direction than another contain unpaired electrons. These substances are weakly attracted to magnets and are said to be paramagnetic.

Table of Allowed Quantum Numbers

n fifty ml Number of
orbitals
Orbital
Proper noun
Number of
electrons
ane 0 0 1 is 2
ii 0 0 1 2southward 2
1 -1, 0, +1 3 iip 6
3 0 0 1 threesouthward two
1 -1, 0, +1 3 threep 6
ii -2, -one, 0, +1, +two 5 3d 10
four 0 0 ane 4due south 2
one -1, 0, +1 three 4p half dozen
two -2, -1, 0, +1, +2 v 4d 10
3 -iii, -ii, -one, 0, +1, +2, +3 vii 4f xiv

Writing Electron Configurations

The distribution of electrons among the orbitals of an atom is called the electron configuration. The electrons are filled in according to a scheme known as the Aufbau principle ("building-up"), which corresponds (for the about part) to increasing free energy of the subshells:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f

Information technology is not necessary to memorize this listing, because the order in which the electrons are filled in can be read from the periodic table in the following fashion:

Periodic Table with Quantum Numbers

Or, to summarize:

Periodic Table with Quantum Number scheme

In electron configurations, write in the orbitals that are occupied past electrons, followed by a superscript to point how many electrons are in the set of orbitals (east.g., H 1s1)

Another mode to betoken the placement of electrons is an orbital diagram, in which each orbital is represented by a square (or circumvolve), and the electrons equally arrows pointing up or down (indicating the electron spin). When electrons are placed in a ready of orbitals of equal energy, they are spread out as much as possible to give as few paired electrons every bit possible (Hund'south rule).

examples will be added at a later engagement

In a ground state configuration, all of the electrons are in as low an energy level as information technology is possible for them to be. When an electron absorbs free energy, information technology occupies a higher energy orbital, and is said to be in an excited state.

Properties of Monatomic Ions

The electrons in the outermost shell (the ones with the highest value of n) are the most energetic, and are the ones which are exposed to other atoms. This shell is known as the valence shell. The inner, core electrons (inner shell) do not usually play a part in chemical bonding.

Elements with similar backdrop generally accept like outer shell configurations. For instance, we already know that the alkali metals (Group I) always form ions with a +1 charge; the "extra" s 1 electron is the ane that's lost:

IA Li 1s22si Li+ 1s2
Na 1s22s22p63s1 Na+ 1s22s22phalf-dozen
Thou 1stwo2s22pvi3s23phalf-dozen4s1 K+ 1stwo2s22phalf dozen3stwo3psix

The next shell downwardly is now the outermost beat, which is now full — meaning in that location is very trivial tendency to gain or lose more than electrons. The ion's electron configuration is the same every bit the nearest noble gas — the ion is said to be isoelectronic with the nearest noble gas. Atoms "prefer" to have a filled outermost shell considering this is more than electronically stable.

  • The Group IIA and IIIA metals also tend to lose all of their valence electrons to form cations.
IIA Be 1sii2s2 Betwo+ 1s2
Mg 1s22s22phalf dozen3s2 Mg2+ 1s22s22p6
IIIA Al 1s22s22p63s23p1 Al3+ 1sii2s22p6
  • The Grouping IV and V metals can lose either the electrons from the p subshell, or from both the s and p subshells, thus attaining a pseudo-noble gas configuration.
IVA Sn [Kr]4d105s25p2 Sn2+ [Kr]4dten5sii
Sn4+ [Kr]4d10
Pb [Xe]4fxiv5dten6s26p2 Lead2+ [Xe]4fxiv5d106s2
Pb4+ [Xe]4f145d10
VA Bi [Xe]4fxiv5d106sii6piii Bi3+ [Xe]4fxiv5d106stwo
Bi5+ [Xe]4f145d10
  • The Group Iv - VII non-metals proceeds electrons until their valence shells are full (8 electrons).
IVA C 1s22sii2p2 C4- 1s22sii2phalf dozen
VA Due north 1s22s22pthree N3- 1sii2s22pvi
VIA O 1s22s22piv O2- 1s22s22phalf dozen
VIIA F 1s22stwo2p5 F- 1s22sii2p6
  • The Grouping Viii noble gases already possess a total outer vanquish, so they accept no tendency to form ions.
VIIIA Ne 1s22s22p6
Ar 1s22s22p63sii3phalf dozen
  • Transition metals (B-group) usually form +2 charges from losing the valence s electrons, but tin also lose electrons from the highest d level to form other charges.
B-grouping Iron 1s22sii2pvi3sii3psix3d64sii Feii+ 1s22sii2p63s23pvi3d6
Fe3+ 1stwo2sii2p63sii3psix3dv

References

Martin South. Silberberg, Chemistry:  The Molecular Nature of Thing and Change, 2nd ed.  Boston:  McGraw-Hill, 2000, p. 277-284, 293-307.

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Source: https://www.angelo.edu/faculty/kboudrea/general/quantum_numbers/Quantum_Numbers.htm

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