Electron Subshells In Order Of Increasing Energy

Understanding the order of electron subshells by increasing energy is fundamental to grasping how electrons are arranged within atoms, which in turn governs the chemical properties of elements. This arrangement, also known as the electron configuration, dictates how atoms interact with each other to form molecules and compounds.

The Basics of Electron Configuration

Electron configuration describes which orbitals are occupied by electrons in an atom. Orbitals are regions of space around the nucleus where an electron is most likely to be found. These orbitals are organized into shells and subshells, each characterized by specific energy levels. The arrangement of electrons follows certain rules and principles that determine the order in which subshells are filled.

Quantum Numbers: The Address of an Electron

To fully understand electron configuration, it's essential to know about quantum numbers. These numbers describe the properties of atomic orbitals and can help specify the characteristics of an electron within an atom. There are four main types of quantum numbers:

Principal Quantum Number (n): This number describes the energy level or shell of the electron. It can be any positive integer (n = 1, 2, 3, ...), with higher numbers indicating higher energy levels and greater average distance from the nucleus.
Azimuthal Quantum Number (l): Also known as the angular momentum or orbital quantum number, l defines the shape of the electron's orbital and its angular momentum. Its values range from 0 to n-1. Each value of l corresponds to a specific subshell:
- l = 0 corresponds to an s subshell (spherical shape).
- l = 1 corresponds to a p subshell (dumbbell shape).
- l = 2 corresponds to a d subshell (more complex shape).
- l = 3 corresponds to an f subshell (even more complex shape).
Magnetic Quantum Number (ml): This number describes the orientation of the orbital in space. Its values range from -l to +l, including 0. For example, if l = 1 (p subshell), ml can be -1, 0, or +1, indicating three possible orientations of the p orbital along the x, y, and z axes.
Spin Quantum Number (ms): This number describes the intrinsic angular momentum of an electron, which is quantized and referred to as spin. Electrons behave as if they are spinning, creating a magnetic dipole moment. The spin quantum number can be either +1/2 or -1/2, often referred to as "spin up" and "spin down."

Subshells and Their Energy Levels

Each shell (n) contains one or more subshells (l). The number of subshells within a shell is equal to the principal quantum number, n. The subshells are denoted by the letters s, p, d, and f, corresponding to l = 0, 1, 2, and 3, respectively. Each subshell contains a specific number of orbitals:

s subshell: 1 orbital (can hold up to 2 electrons)
p subshell: 3 orbitals (can hold up to 6 electrons)
d subshell: 5 orbitals (can hold up to 10 electrons)
f subshell: 7 orbitals (can hold up to 14 electrons)

Understanding the energy levels of these subshells is crucial for predicting the electron configuration of an atom.

Determining the Order of Increasing Energy

The order in which electron subshells are filled follows the Aufbau principle, which states that electrons first occupy the lowest energy levels available to them. However, due to the complex interactions between electrons, the energy levels of subshells can overlap, particularly for higher principal quantum numbers.

The Aufbau Principle

The Aufbau principle (from the German word "Aufbauen," meaning "to build up") is a guideline for determining the electron configuration of an atom by filling the lowest energy levels first. The general order of filling subshells according to the Aufbau principle is as follows:

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

This sequence is a good starting point, but it's not always accurate due to exceptions and the complexities of electron-electron interactions.

The (n + l) Rule

A more reliable method for determining the order of subshells by increasing energy is the (n + l) rule, also known as the Madelung rule or the Klechkowski's rule. This rule states that:

Electrons first fill the subshell with the lowest value of (n + l).
If two subshells have the same (n + l) value, the subshell with the lower n value is filled first.

Here's how to apply the (n + l) rule:

1s: n = 1, l = 0; (n + l) = 1
2s: n = 2, l = 0; (n + l) = 2
2p: n = 2, l = 1; (n + l) = 3
3s: n = 3, l = 0; (n + l) = 3
3p: n = 3, l = 1; (n + l) = 4
4s: n = 4, l = 0; (n + l) = 4
3d: n = 3, l = 2; (n + l) = 5
4p: n = 4, l = 1; (n + l) = 5
5s: n = 5, l = 0; (n + l) = 5
4d: n = 4, l = 2; (n + l) = 6
5p: n = 5, l = 1; (n + l) = 6
6s: n = 6, l = 0; (n + l) = 6
4f: n = 4, l = 3; (n + l) = 7
5d: n = 5, l = 2; (n + l) = 7
6p: n = 6, l = 1; (n + l) = 7
7s: n = 7, l = 0; (n + l) = 7
5f: n = 5, l = 3; (n + l) = 8
6d: n = 6, l = 2; (n + l) = 8
7p: n = 7, l = 1; (n + l) = 8

Based on the (n + l) rule, the order of increasing energy is:

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

Note that when two subshells have the same (n + l) value, the one with the lower n value is filled first. For example, 4s (n + l = 4) is filled before 3d (n + l = 5).

Visual Aid: The Diagonal Rule

A helpful visual aid to remember the order of filling subshells is the diagonal rule. Write the subshells in the following format:

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

Then, draw diagonal arrows from the top right to the bottom left. Follow the arrows to determine the order of filling subshells:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so on.

Exceptions to the Rules

While the Aufbau principle and the (n + l) rule are useful guidelines, there are exceptions to these rules due to the complex interactions between electrons. These exceptions are particularly common for transition metals and lanthanides/actinides.

Stability of Half-Filled and Fully-Filled Subshells

One reason for these exceptions is the extra stability associated with half-filled and fully-filled d and f subshells. Electrons tend to arrange themselves to achieve these more stable configurations, even if it means violating the Aufbau principle.

Chromium (Cr): The expected electron configuration based on the Aufbau principle is [Ar] 4s² 3d⁴. However, the actual electron configuration is [Ar] 4s¹ 3d⁵. By promoting one electron from the 4s subshell to the 3d subshell, chromium achieves a half-filled 3d subshell (d⁵), which is more stable.
Copper (Cu): The expected electron configuration is [Ar] 4s² 3d⁹. However, the actual electron configuration is [Ar] 4s¹ 3d¹⁰. By promoting one electron from the 4s subshell to the 3d subshell, copper achieves a fully-filled 3d subshell (d¹⁰), which is more stable.

Other elements that exhibit similar exceptions include molybdenum (Mo), silver (Ag), and gold (Au).

Ionization and Electron Configuration

The electron configuration of ions (atoms that have gained or lost electrons) also follows specific rules. When forming positive ions (cations), electrons are removed from the subshells with the highest principal quantum number (n) first. For example, when iron (Fe) forms Fe²⁺, it loses two electrons from the 4s subshell, not the 3d subshell.

Significance of Electron Configuration

Understanding the order of electron subshells by increasing energy and determining the electron configuration of elements is essential for several reasons:

Predicting Chemical Properties: The electron configuration determines how an atom will interact with other atoms to form chemical bonds. Elements with similar electron configurations tend to have similar chemical properties.
Understanding Periodic Trends: The periodic table is organized based on electron configurations. Elements in the same group (vertical column) have similar valence electron configurations, which explains their similar chemical behavior.
Explaining Atomic Spectra: The electron configuration and energy levels of electrons determine the wavelengths of light that an atom can absorb or emit. This is the basis for atomic spectroscopy, which is used to identify elements and study their electronic structure.
Predicting Magnetic Properties: The electron configuration determines whether an atom or ion is paramagnetic (attracted to a magnetic field) or diamagnetic (repelled by a magnetic field). Paramagnetic substances have unpaired electrons, while diamagnetic substances have all their electrons paired.

Examples of Electron Configurations

Here are a few examples of determining electron configurations using the Aufbau principle and the (n + l) rule:

Hydrogen (H, Z=1): 1s¹
Helium (He, Z=2): 1s²
Lithium (Li, Z=3): 1s² 2s¹
Beryllium (Be, Z=4): 1s² 2s²
Boron (B, Z=5): 1s² 2s² 2p¹
Carbon (C, Z=6): 1s² 2s² 2p²
Nitrogen (N, Z=7): 1s² 2s² 2p³
Oxygen (O, Z=8): 1s² 2s² 2p⁴
Fluorine (F, Z=9): 1s² 2s² 2p⁵
Neon (Ne, Z=10): 1s² 2s² 2p⁶
Sodium (Na, Z=11): 1s² 2s² 2p⁶ 3s¹
Magnesium (Mg, Z=12): 1s² 2s² 2p⁶ 3s²
Aluminum (Al, Z=13): 1s² 2s² 2p⁶ 3s² 3p¹
Silicon (Si, Z=14): 1s² 2s² 2p⁶ 3s² 3p²
Phosphorus (P, Z=15): 1s² 2s² 2p⁶ 3s² 3p³
Sulfur (S, Z=16): 1s² 2s² 2p⁶ 3s² 3p⁴
Chlorine (Cl, Z=17): 1s² 2s² 2p⁶ 3s² 3p⁵
Argon (Ar, Z=18): 1s² 2s² 2p⁶ 3s² 3p⁶
Potassium (K, Z=19): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹
Calcium (Ca, Z=20): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
Scandium (Sc, Z=21): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹
Titanium (Ti, Z=22): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²
Vanadium (V, Z=23): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³
Chromium (Cr, Z=24): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵ (exception)
Manganese (Mn, Z=25): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵
Iron (Fe, Z=26): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶
Cobalt (Co, Z=27): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷
Nickel (Ni, Z=28): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁸
Copper (Cu, Z=29): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ (exception)
Zinc (Zn, Z=30): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰

These examples demonstrate how the Aufbau principle and the (n + l) rule can be used to predict the electron configurations of atoms. Note the exceptions for chromium and copper, which highlight the importance of considering the stability of half-filled and fully-filled subshells.

Conclusion

Understanding the order of electron subshells by increasing energy is a cornerstone of chemistry. By applying the Aufbau principle, the (n + l) rule, and considering the stability of half-filled and fully-filled subshells, one can accurately predict the electron configurations of atoms and ions. This knowledge is essential for understanding chemical properties, periodic trends, atomic spectra, and magnetic properties, providing a solid foundation for further exploration in chemistry and related fields.