Rules For Filling Up Of Electrons In Different Orbitals
The correct ground state electronic configuration of an atom is obtained on the basis of the following principles—Pauli’s exclusion principle, Hund’s rule, and the Aufbau principle.
Pauli’s exclusion principle
Principle: The knowledge of four quantum numbers is important in assigning the exact location of the electron within an atom.
After meticulous study of the line spectra of atoms, Wolfgang Pauli in 1925 proposed his exclusion principle which is widely known as Pauli’s exclusion principle.
According to this principle, no two electrons in an atom will have the same values for all four quantum numbers (n, l, m, and s).
If three of the quantum numbers of any two electrons are the same then they must differ in their fourth quantum number.
If the quantum numbers n, l, and m of two electrons have identical values, then the value of s should be different (+i for one and for the other).
Therefore, the corollary of this principle may be stated as—each orbital can accommodate a maximum of two electrons having an opposite spin.
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With the help of Pauli’s exclusion principle, the maximum number of electrons a subshell can accommodate can be calculated. For example—
s -subshell: In the case of s -subshell, 1 = 0. Therefore m = 0. Number of orbitals in s -subshell = 1.
According to Pauli’s exclusion principle, each orbital can hold a maximum number of two electrons. So, s -subshell can accommodate a maximum of 2 electrons.
p -subshell: For p -subshell, 1=1 and m = —1,0, +1. The number of orbitals in the -subshell is three (px, py, and pz ).
According to Pauli’s exclusion principle, since each orbital can hold a maximum of 2 electrons, the maximum accommodating capacity of p -subshell {i.e., three p orbitals) =3×2 = 6 electrons.
d -subshell: In the case of d -subshell, 1 = 2, m = -2, -1, 0 +1, +2. Thus, m has 5 values indicating the presence of 5 orbitals. As the maximum number of electrons that each orbital can hold is 2, the maximum number of electrons that a d -d-subshell can accommodate is 5 X 2 = 10.
f-subshell: For /-subshell, l = 3, m = -3, -2, -1, 0, +1, +2, +3. Seven values of m indicate the presence of seven orbitals. Hence the maximum number of electrons that may be present in /-subshell is 7 x 2 = 14 .
Pauli’s exclusion principle also permits the determination of the maximum number of electrons that can be present in a certain orbit or shell.
Example: For L -shell (n = 2), l has two values, i.e., 1 = 0 [ssubshell] and l = 1 [p -subshell].
The s -subshell can hold 2 electrons and p -subshell can accommodate 6 electrons. Therefore, the maximum accommodating capacity for L shell =(2 + 6) = 8 electrons.
Similarly, it can be shown that, the maximum number of electrons that can be accommodated in M-shell (n = 3) = 18 and the maximum number of electrons that may be present in IVshell (n = 4) =32.
Electron accommodating capacity of K, L, M, and JV-shell
Thus, it is seen that the maximum number of electrons accommodated in any electronic orbit with the principal quantum number’ n’ is 2n2.
Number of orbitals and electron accommodating capacity of different shells.
Hund’s multiplicity rule
This rule is helpful for deciding the mode of filling of the orbitals ofthe same energy level with electrons.
Rule: The pairing of electrons in the orbitals within the same subshell does not take place until the orbitals are singly filled up with electrons having parallel spin.
Discussion: The rule implies that orbitals with the same energy are filled up first with one electron and then the additional electron occupies the singly filled orbital orbital to form paired electrons (with opposite spin).
The energy order of the orbitals, the Aufbau principle, and the electronic configuration of atoms
The German word ‘Aufbau’ means ‘to build one by one! The Aufbau principle gives the sequence of gradual filling up of the different subshells of multi-electron atoms.
Aufbau principle:
Aufbau principle states that electrons are added progressively to the various orbitals in the order of increasing energy, starting with the orbital with the lowest energy.
Electrons never occupy the die orbital of higher energy leaving the orbital of lower energy vacant.
A study of the results of spectral analysis has led to the arrangement of the shells and subshell in the increasing order of their energies in the following sequence:
Is < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f< Sd < 6p < 7s < 5f< 6d ..
Electronic configuration always conforms to Pauli’s Exclusion Principle.
According to Hund’s rule, pairing of electrons in the orbitals within the same subshell (degenerate orbitals hating the same n ) cannot occur until the orbitals are singly filled up.
The energy of the subshell increases with an increase in the value of {n + l). In a multi-electron atom, the energy of a subshell, cannot be determined only by principal quantum number (n ), in exclusion of azimuthal quantum number (Z).
The correct order of energies of various subshells is determined by the (n + 1) rule or Bohr-Bury rule.
The implication of the rule can be better understood with the help ofthe following example.
In case of 3d -subshell, (n + Z) = (3 + 2) = 5, but for 4s -subshell, (n + Z) = (4 + 0) = 4 .
From this, it is clear that the energy of the 4s -subshell is less than that of the 3d -subshell. Hence, the electron goes to the 4s subshell first, in preference to the 3d -subshell.
If Two subshells have the same value for{n + l), then the electron enters that subshell which has a lower value of n.
For example, for 3d -subshell, {n + l) = (3 + 2) = 5 and for 4p -subshell, {n + l) = (4 + 1) = 5 In this case, the electron first enters the 3d -subshell which has a.lower value of n.
The sequence in which the subshells are filled with electrons.
The figure depicts the sequence of filling up of the subshells with electrons. The electronic configuration of any atom can be easily predicted from this diagram.
Exceptions to (n+1) rule: Exceptions to the {n + Z) rule are found to occur in the case of filling up of electrons in Lanthanum (La) and Actinium (Ac).
The values of {n + l) in the case of both the subshells 4/ and 5d (4 + 3 = 7 = 5 + 2) are found to be the same.
Similarly the values of (n +1) in the case of both the subshells 5/ and 6d (5 + 3 = 8 = 6 + 2) are equal. So, the order of energies of these subshells is 4/< 5d and 5/< 6d.
According to the (n + Z) rule, the expected electronic configuration of La (57) and Ac (89) should be [Xe]4/15d06s2 and [Rn]5/16d°7s2 respectively.
However, the electronic configuration of La and Ac are actually [Xe]4/ and [Rn]5/°6d17s2 respectively. In other words, lanthanum and actinium are exceptions to the (n + l) rule.
Method of writing electronic configuration of an atom 1) In order to express the electronic configuration of an atom, the principal quantum number (n = 1, 2, 3… etc.) is written first.
The symbol ofthe subsheU(s, p, d, f, etc.) is written to the right ofthe principal quantum number. For example, s -subshell of the first shell is expressed as Is; sand subshells of the second shell are expressed as 2s and 2p respectively.
The total number of electrons present in any subshell is then written as the right superscript of the subshell symbol.
For example, the electronic configuration, ls22s22p5 suggests that the s -subshell of the first shell contains 2 electrons, and the s, and p -subshells of the second shell contain 2 electrons and 5 electrons respectively. Thus, the total number of electrons present is equal to 9.
Examples: Electronic configuration of 17 CL atom: The atomic number of chlorine is 17. Number of electrons present in chlorine atom is 17.
Out of these 17 electrons, 2 electrons are present in the s -subshell of first shell (K-shell), 2 electrons and 6 electrons in the s – and p -subshell of the second shell (L -shell) respectively, and 2 and 5 electrons are present in the s – and p -subshell of the third shell (Mshell) respectively.
Thus, the electronic configuration of the chlorine atom is ls²2s²2p63s²3p5.
Electronic configuration of 26Fe atom: The atomic number of iron is 26. Number of electrons present in an atom of iron is 26. These 26 electrons are distributed in K, L, M, and N-shells in such a way that their electronic configuration becomes ls²2s²2p63s²3pe3de4s².
Here the symbol signifies an orbital and the arrow sign (↑) means an odd electron and the paired arrow sign (↓↑) stands for a pair of electrons with opposite spins.
Stability of half-filled or completely filled subshells The electronic configurations of some atoms have certain characteristic features.
It is seen that half-filled and completely filled subshells are more stable compared to nearly half-filled or nearly completely filled subshells.
Hence, if the (n-1)d -subshell of any atom contains 4 or 9 electrons and the ns -subshell contains 2 electrons, then one electron from the ns -subshell gets shifted to the (n-1) d subshell, thereby making a total number of either 5 or 10 electrons in it. As a result, ns -subshell is left with 1 electron instead of 2.
The extra stability of half-filled and completely filled subshells can be explained in terms of the symmetrical distribution of electrons and exchange energy.
Symmetrical distribution of electrons: The subshells with half-filled or completely filled electrons are found to have a more symmetrical distribution of electrons.
Consequently, they have lower energy which ultimately results in greater stability of the electronic configuration.
Electrons present in the same subshell have equal energy but their spatial distribution is different. As a result, the magnitude of the shielding effect of another is quite small and so, the electrons are more strongly attracted by the nucleus.
Interelectronic repulsion: Two types of interactions are possible between electrons of the same subshell due to interelectronic repulsive force.
Interaction due to electronic charge: The magnitude of the repulsive force acting between two electrons situated at n distance r from each other is inversely proportional to the square of the distance between them.
Consequently, the stability of two-electron or multi-electron ions or atoms increases with an increase in distance r. Thus, die two electrons present in the d -d-subshell prefer to be in two separate d -orbitals instead of one leading to the increased stability ofthe atom or ion.
Interaction due to rotation of electrons: Two electrons tend to remain close to each other if they have opposite spins. On the other hand, if both the electrons have parallel spin, then they prefer to remain far from each other.
The electrons occupying degenerate orbitals (orbitals of the same energy) can exchange their positions with other electrons with the same spin. In this process, exchange energy is released.
The greater the probability of exchange, the more stable the configuration. The probability of exchange is greater in the case of a half-filled or completely filled subshell.
Thus, the magnitude of exchange energy is greatest for half-filled or completely filled subshells leading to their exceptionally high stability.
This exchange energy forms the basis of Hund’s multiplicity rule. The relative magnitude of exchange energy can be calculated by the formula,
No. of exchanges \(=\frac{n !}{2 \times(n-2) !}\)
(n = number of degenerate electrons with parallel spin.)
Number of interactions in case of d4 electronic configuration
Total number of exchanges for d4 electronic configuration
=3+2+1=6
Number of interactions in case of d5 electronic configuration
Electronic configuration of ions
When an additional electron is added to an orbital of an atom, a negatively charged ion called an anion is formed while the removal of an electron from the orbital of an atom produces a positively charged ion called cation.
Electronic configuration of anions: The total number of electrons present in an anionic species is = (Z + n) where Z = atomic number and n = number of electrons gained. The electronic configuration ofthe anion is written on the basis of the total number of electrons present in it.
Examples: Fluoride ion (F-): Total number of electrons present in F- ion = (9 + 1) = 10
∴ Electronic configuration of F- ion: ls²2s²2p6
Nitride ion (N³¯ ): Total number of electrons present
in N3- ion = (7 + 3) = 10
Electronic configuration of N3- ion: ls22s22p6
Oxide ion (O²¯): Total number of electrons present in O²¯ ion =(8 + 2) = 10.
∴ Electronic configuration of O2- ion: ls22s22p6
Sulphide Ion (S²¯) : Total number ofelectrons present in S2- ion =(1.6 + 2) = 18
Electronic Configuration of cations:
A total number of electrons present in a cationic species = (Z-n) where Z = atomic number and n = number of electrons lost.
For writing the electronic configuration of the cation, the electronic configuration of the neutral atom is written first.
Then requisite no. of electrons is removed from the outermost shell. Electrons from the ns -subshell should be removed before removing any electron from the (n- l)d -subshell.
The total number of electrons present in a cationic species = (Z-n) where Z = atomic number and n = number of electrons lost.
For writing the electronic configuration of the cation, the electronic configuration of the neutral atom is written first.
Then requisite no. of electrons is removed from the outermost shell. Electrons from the ns -subshell should be removed before removing any electron from the (n- l)d -subshell.
Examples:
Sodium ion (Na+) : Electronic configuration of \({ }_{11} \mathrm{Na}: 1 s^2 2 s^2 2 p^6 3 s^1 \text {. So, } \mathrm{Na}^{+} \text {lon: } 1 s^2 2 s^2 2 p^6\)
2. Chromium Ion (Cr3+): Electronic Configuration of
\({ }_{24} \mathrm{Cr}: 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^5 4 s^1\)⇒ \(\mathbf{C r}^{3+} \text { ion: } 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^3\)
Manganese ion (Mn2+): Electronic configuration of:
Mn2+ ion: 1s22s22p63s2363d5
Ferrous (Fez+) and Ferric (Fe3+) ion: Electronic
Configuration of 26Pe: ls22s2263sz3763d64s2
Ferrous ion (Fe2+): ls22s22p63s23p63d6
Similarly, ferric ion (Fe3+): ls22s22/763s23/?63d5
Cuprous (Cu+) and Cupric (Cu2+) ion: Electronic configuration of 2gCu: ls²2s²2p63s23p63dl04s1
Cu+ ion: ls22s22/763s23/763d10
similarly, cupric ion (Cu2+): 1s²2s22p63s23p63d9
Orbital angular momentum of electron = Jl(l + 1) x ( l = azimuthal quantum number).
Molecules, atoms, or ions containing one or more unpaired electrons exhibit paramagnetic properties. Paramagnetic substances are attracted by the magnetic field.
The magnetic moment of paramagnetic substances depends on the number of unpaired electrons.
Magnetic moment = Jx(x + 2) BM BM = Bohr Magneton (unit of magnetic moment) x = Number of impaired electrons.
Molecules, atoms, or ions containing an even number of electrons exhibit diamagnetic properties. Diamagnetic substances are repelled by the magnetic field.