Electronic configuration Aufbau Pauli and Hund rules

Understanding the electronic configuration of atoms is fundamental to chemistry. It describes how electrons are arranged within the atomic orbitals. This arrangement dictates the chemical properties of an element and how it will interact with other atoms. We will explore the key principles that govern this arrangement: the Aufbau principle, the Pauli exclusion principle, and Hund's rule of maximum multiplicity.

The Aufbau Principle

The Aufbau principle, derived from the German word 'Aufbau' meaning 'building up', states that in the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. Think of it like filling seats in a stadium; you fill the front rows before moving to the back rows.

The order of filling orbitals is not simply based on the principal quantum number (n). It follows a specific sequence determined by both the principal quantum number (n) and the azimuthal quantum number (l). Generally, orbitals with lower (n+l) values are filled first. If two orbitals have the same (n+l) value, the orbital with the lower 'n' value is filled first.

This sequence can be visualized using the 'Aufbau diagram' or 'Madelung rule':

  • 1s
  • 2s, 2p
  • 3s, 3p, 3d
  • 4s, 4p, 4d, 4f
  • 5s, 5p, 5d, 5f, 5g
  • 6s, 6p, 6d, 6f, 6g, 6h
  • 7s, 7p, 7d, 7f, 7g, 7h, 7i

To determine the order of filling, draw diagonal arrows through this list. The order obtained is:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p → ...

Let's look at an example. For Nitrogen (Z=7), we have 7 electrons to place.

  1. The lowest energy orbital is 1s. It can hold a maximum of 2 electrons. So, 1s2. (5 electrons remaining)
  2. The next lowest energy orbital is 2s. It can hold 2 electrons. So, 2s2. (3 electrons remaining)
  3. The next set of orbitals are the 2p orbitals. There are three 2p orbitals (2px, 2py, 2pz), each capable of holding 2 electrons, for a total of 6 electrons. We have 3 electrons left. So, 2p3.

Thus, the electronic configuration of Nitrogen is 1s2 2s2 2p3.

Mnemonic for Aufbau Filling Order: Remember the sequence by visualizing a table. Write orbitals in columns by principal quantum number and rows by azimuthal quantum number.
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
And so on. Then draw diagonal arrows starting from the top right of 1s, going down and to the left.

The Pauli Exclusion Principle

The Pauli exclusion principle, formulated by Wolfgang Pauli, states that no two electrons in the same atom can have the identical set of all four quantum numbers. The four quantum numbers are:

  • Principal quantum number (n): Describes the electron shell or energy level.
  • Azimuthal quantum number (l): Describes the shape of the orbital (s, p, d, f).
  • Magnetic quantum number (ml): Describes the orientation of the orbital in space.
  • Spin quantum number (ms): Describes the intrinsic angular momentum of the electron, which can be either +1/2 (spin up) or -1/2 (spin down).

Since n, l, and ml define a specific orbital, the Pauli exclusion principle essentially means that a single atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins. If one electron has ms = +1/2, the other must have ms = -1/2.

Consider an orbital, say the 1s orbital. An electron in this orbital can be described by the quantum numbers n=1, l=0, ml=0. If a second electron is in the same orbital, it must have the same n, l, and ml values. Therefore, its spin quantum number (ms) must be different from the first electron. So, the two electrons in the 1s orbital will have quantum numbers (1, 0, 0, +1/2) and (1, 0, 0, -1/2).

This principle is crucial because it explains why subshells fill up in a specific way and why atoms have distinct electron configurations. Without it, all electrons might try to occupy the lowest energy level, which is not observed.

Example: Helium (Z=2). It has 2 electrons.

  1. The first electron goes into the 1s orbital with spin up: 1s1 (n=1, l=0, ml=0, ms=+1/2).
  2. The second electron also goes into the 1s orbital, but due to the Pauli exclusion principle, it must have opposite spin (spin down): 1s2 (n=1, l=0, ml=0, ms=-1/2).

The 1s orbital is now full, and no more electrons can enter it.

Hund's Rule of Maximum Multiplicity

Hund's rule, also known as the rule of maximum multiplicity, applies to the filling of degenerate orbitals (orbitals within the same subshell that have the same energy level, like the three 2p orbitals or the five 3d orbitals). It states that for a given electron configuration, the lowest energy state is the one in which the number of electrons with the same spin is maximized.

In simpler terms, when filling degenerate orbitals, electrons will individually occupy each orbital with parallel spins before any orbital is doubly occupied. This is because electrons repel each other, and placing them in separate orbitals minimizes this repulsion, leading to a more stable, lower energy state.

Let's revisit Nitrogen (1s2 2s2 2p3). The 2p subshell has three degenerate orbitals (2px, 2py, 2pz). According to Hund's rule, the three electrons in the 2p subshell will occupy each of these orbitals singly, with their spins all pointing in the same direction.

Visual Representation for Nitrogen's 2p electrons:

Correct (Hund's Rule): [↑] [↑] [↑] (in 2px, 2py, 2pz respectively)

Incorrect: [↑↓] [↑] [ ] or [↑] [↑↓] [ ]

Another example: Oxygen (Z=8). Electronic configuration: 1s2 2s2 2p4.

The first three 2p electrons fill the orbitals singly with parallel spins, as in Nitrogen. The fourth 2p electron must now pair up with one of the existing electrons in an orbital, and it will have the opposite spin.

Visual Representation for Oxygen's 2p electrons:

Correct (Hund's Rule): [↑↓] [↑] [↑] (in 2px, 2py, 2pz respectively)

This means that in the 2p subshell of Oxygen, there is one pair of electrons and two unpaired electrons. The total number of unpaired electrons is 2.

Hund's Rule Analogy: Imagine three empty seats on a bus (degenerate orbitals). People (electrons) will first take individual seats before anyone sits next to someone else. They also prefer to sit with their "arms" (spins) in the same direction as much as possible.

Applying the Rules Together

To determine the electronic configuration of an element, you apply these three rules in sequence:

  1. Aufbau Principle: Fill orbitals starting from the lowest energy level.
  2. Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons, and they must have opposite spins.
  3. Hund's Rule: Fill degenerate orbitals singly with parallel spins before pairing up electrons.

Example: Sulfur (Z=16)

Total electrons = 16.

  1. 1s orbital: Lowest energy. Fills with 2 electrons (opposite spins). Configuration: 1s2. (14 electrons left)
  2. 2s orbital: Next lowest. Fills with 2 electrons. Configuration: 1s2 2s2. (12 electrons left)
  3. 2p orbitals: Degenerate. Fills with 6 electrons (3 orbitals, 2 electrons each, opposite spins). Configuration: 1s2 2s2 2p6. (6 electrons left)
  4. 3s orbital: Next lowest. Fills with 2 electrons. Configuration: 1s2 2s2 2p6 3s2. (4 electrons left)
  5. 3p orbitals: Degenerate. We have 4 electrons left. According to Hund's rule, we fill each of the three 3p orbitals with one electron first (parallel spins), and then the fourth electron pairs up in one of the orbitals with opposite spin. Configuration: 1s2 2s2 2p6 3s2 3p4.

Final electronic configuration for Sulfur: 1s2 2s2 2p6 3s2 3p4.

Example: Calcium (Z=20)

Total electrons = 20.

  1. 1s2 (18 left)
  2. 2s2 (16 left)
  3. 2p6 (10 left)
  4. 3s2 (8 left)
  5. 3p6 (2 left)
  6. 4s orbital: According to the Aufbau diagram, 4s is filled before 3d. So, the remaining 2 electrons go into the 4s orbital.

Final electronic configuration for Calcium: 1s2 2s2 2p6 3s2 3p6 4s2.

Notice that the 3d subshell, which has a higher energy than 4s according to the Aufbau principle (n+l for 3d is 3+2=5, while for 4s it's 4+0=4), remains empty.

Key Exam Point: Understanding the subtle energy level differences, especially between orbitals like 4s and 3d, is crucial. The (n+l) rule helps predict this order. Elements in periods 4 and 5 often show complex filling patterns due to the proximity of d and f subshells to s and p subshells.

Exceptions to the Rules

While the Aufbau principle, Pauli exclusion principle, and Hund's rule provide a general framework, there are some notable exceptions, particularly for transition metals. These exceptions arise from the desire for a particularly stable electron configuration, such as a completely filled subshell (d10 or p6) or a half-filled subshell (d5 or p3). These configurations have extra stability due to symmetry and reduced electron-electron repulsion.

1. Chromium (Cr, Z=24): Expected configuration based on Aufbau: 1s2 2s2 2p6 3s2 3p6 4s2 3d4. Actual configuration: 1s2 2s2 2p6 3s2 3p6 4s1 3d5. Explanation: The atom promotes one electron from the 4s orbital to the 3d orbital to achieve a more stable half-filled 3d subshell (3d5).

2. Copper (Cu, Z=29): Expected configuration based on Aufbau: 1s2 2s2 2p6 3s2 3p6 4s2 3d9. Actual configuration: 1s2 2s2 2p6 3s2 3p6 4s1 3d10. Explanation: The atom promotes one electron from the 4s orbital to the 3d orbital to achieve a more stable completely filled 3d subshell (3d10).

These exceptions highlight that stability plays a significant role in determining the final electron arrangement. The energy difference between the involved subshells (like 4s and 3d) is often small enough that achieving greater stability through a filled or half-filled subshell is energetically favorable.

It's important to memorize these common exceptions for exams, as they are frequently tested.

Summary of Electron Filling Rules
Rule Statement Significance
Aufbau Principle Electrons fill orbitals starting from the lowest energy level. Determines the general order of orbital filling (e.g., 1s, 2s, 2p, 3s...).
Pauli Exclusion Principle No two electrons in an atom can have the same four quantum numbers. An orbital can hold a maximum of two electrons with opposite spins. Limits the number of electrons per orbital to two and explains electron pairing.
Hund's Rule Electrons fill degenerate orbitals singly with parallel spins before pairing up. Maximizes the number of unpaired electrons and minimizes electron-electron repulsion in subshells like p, d, and f.
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