6f Angular Momentum Quantum Number

Quantum Numbers,
Atomic Orbitals, and
Electron Configurations

Contents:
Quantum Numbers and Diminutive Orbitals
one. Chief Quantum Number (north)
2. Angular Momentum (Secondary, Azimunthal) Quantum Number (50)
3. Magnetic Quantum Number (m_l )
4. Spin Breakthrough Number (m_s )
Tabular array of Immune Breakthrough Numbers
Writing Electron Configurations
Properties of Monatomic Ions
References

Quantum Numbers and Atomic Orbitals

By solving the Schr�dinger equation (Hy = Ey), we obtain a ready 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 cantlet is called an atomic orbital; this atomic orbital describes a region of infinite in which at that place is a high probability of finding the electron. Free energy changes inside an atom are the outcome of an electron changing from a wave blueprint with i energy to a wave blueprint with a different energy (commonly accompanied by the assimilation or emission of a photon of light).

Each electron in an cantlet is described by 4 different quantum numbers. The first 3 (n, l, m_fifty ) specify the particular orbital of interest, and the fourth (grand_southward ) specifies how many electrons can occupy that orbital.

Chief Quantum Number (north): n = i, 2, 3, …, ∞
Specifies the energy of an electron and the size of the orbital (the distance from the nucleus of the acme in a radial probability distribution plot). All orbitals that accept the same value of due north are said to be in the aforementioned vanquish (level). For a hydrogen cantlet 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 full number of orbitals for a given due north value is n ².

Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n-i.
Specifies the shape of an orbital with a particular primary quantum number. The secondary breakthrough number divides the shells into smaller groups of orbitals called subshells (sublevels). Usually, a alphabetic character code is used to identify l to avoid confusion with n:

l	0	ane	two	3	4	5	...
Alphabetic character	s	p	d	f	thousand	h	...

The subshell with north=2 and l=1 is the 2p subshell; if n=3 and fifty=0, it is the iiisouth subshell, and so on. The value of 50 also has a slight event on the energy of the subshell; the energy of the subshell increases with fifty (due south < p < d < f).

Magnetic Quantum Number (thousand_l ): m_l = -50, ..., 0, ..., +fifty.
Specifies the orientation in space of an orbital of a given energy (northward) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 250+i orbitals in each subshell. Thus the s subshell has simply one orbital, the p subshell has three orbitals, and so on.

Spin Quantum Number (m_southward ): 1000_s = +½ or -½.
Specifies the orientation of the spin axis of an electron. An electron tin can spin in merely one of 2 directions (sometimes called upwardly and downwardly).
The Pauli exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states that no two electrons in the same cantlet can have identical values for all 4 of their quantum numbers. What this means is that no more than two electrons can occupy the same orbital, and that two electrons in the same orbital must have opposite spins.

Because an electron spins, information technology creates a magnetic field, which tin can exist oriented in one of ii directions. For two electrons in the same orbital, the spins must be reverse to each other; the spins are said to exist paired. These substances are non attracted to magnets and are said to be diamagnetic. Atoms with more than electrons that spin in one direction than another comprise unpaired electrons. These substances are weakly attracted to magnets and are said to be paramagnetic.

Tabular array of Allowed Breakthrough Numbers

*northward*	*fifty*	*1000_l*	Number of orbitals	Orbital Name	Number of electrons
one	0	0	i	1s	2
ii	0	0	1	2s	2
	one	-1, 0, +1	3	2p	six
3	0	0	1	iiisouthward	ii
	ane	-1, 0, +1	3	iiip	half-dozen
	2	-2, -i, 0, +one, +2	5	3d	10
iv	0	0	1	fours	2
	1	-1, 0, +1	3	ivp	6
	two	-2, -ane, 0, +one, +2	5	4d	ten
	3	-3, -2, -1, 0, +1, +ii, +3	seven	4f	14

Writing Electron Configurations

The distribution of electrons amid the orbitals of an cantlet 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 nearly 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

It 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 mode:

Periodic Table with Quantum Numbers

Or, to summarize:

Periodic Table with Quantum Number scheme

In electron configurations, write in the orbitals that are occupied by electrons, followed by a superscript to indicate how many electrons are in the set of orbitals (e.g., H 1s^ane)

Some other fashion to indicate the placement of electrons is an orbital diagram, in which each orbital is represented past a square (or circle), and the electrons every bit arrows pointing up or down (indicating the electron spin). When electrons are placed in a set of orbitals of equal energy, they are spread out as much equally possible to give as few paired electrons equally possible (Hund's rule).

examples volition be added at a later on date

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

Backdrop 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 every bit the valence shell. The inner, core electrons (inner shell) do not normally play a part in chemical bonding.

Elements with similar properties by and large have like outer shell configurations. For instance, we already know that the brine metals (Grouping I) ever class ions with a +1 charge; the "extra" s ¹ electron is the 1 that'south lost:

IA	Li	1s²2s¹	Li+	1s²
	Na	1sⁱⁱ2s²2p^vi3s¹	Na+	1s²2s²2p⁶
	G	1s^two2s²2p^six3s²3p⁶4s^one	Thou+	1s²2s^two2p⁶3s²3p⁶

The next beat out downwardly is now the outermost beat, which is now total — meaning there is very fiddling trend to gain or lose more electrons. The ion's electron configuration is the aforementioned as the nearest noble gas — the ion is said to exist isoelectronic with the nearest noble gas. Atoms "prefer" to have a filled outermost shell because this is more electronically stable.

The Group IIA and IIIA metals too tend to lose all of their valence electrons to form cations.

IIA	Be	1s²2s²	Beⁱⁱ⁺	1s²
	Mg	1s^two2s²2p⁶3s²	Mg^two+	1s²2s^two2p⁶
IIIA	Al	1sⁱⁱ2sⁱⁱ2p⁶3sⁱⁱ3p¹	Al3+	1s²2s^two2p⁶

The Group IV and Five metals can lose either the electrons from the p subshell, or from both the south and p subshells, thus attaining a pseudo-noble gas configuration.

IVA	Sn	[Kr]4d¹⁰5s^two5p²	Snⁱⁱ⁺	[Kr]4d^ten5s^two
			Sn⁴⁺	[Kr]4d¹⁰
	Pb	[Xe]4f^xiv5d^x6s²6p²	Pb²⁺	[Xe]4f^xiv5d¹⁰6s²
			Pb⁴⁺	[Xe]4f¹⁴5d^ten
VA	Bi	[Xe]4f¹⁴5d¹⁰6s²6pⁱⁱⁱ	Biⁱⁱⁱ⁺	[Xe]4f¹⁴5d^x6sⁱⁱ
			Bi⁵⁺	[Xe]4f^xiv5d^ten

The Group 4 - VII non-metals gain electrons until their valence shells are total (8 electrons).

IVA	C	1s²2s²2p^two	C4-	1s²2s²2p⁶
VA	N	1s²2s²2p³	N3-	1s^two2sⁱⁱ2p^half-dozen
VIA	O	1s²2s²2p⁴	O2-	1s²2s²2p⁶
VIIA	F	1s²2sⁱⁱ2p^v	F-	1sⁱⁱ2s²2p^{half dozen}

The Group VIII noble gases already possess a total outer shell, and then they have no trend to form ions.

VIIIA	Ne	1s²2s²2p⁶
	Ar	1s^two2s²2p^vi3s^two3p⁶

Transition metals (B-group) usually course +2 charges from losing the valence southward electrons, but can also lose electrons from the highest d level to form other charges.

B-group	Fe	1s²2s²2p⁶3s^two3p⁶3d⁶4s²	Fe^two+	1s²2s²2p⁶3s²3p^{half dozen}3d⁶
			Fe³⁺	1s²2s²2p^{half dozen}3s^two3p^vi3d^five

References

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