List These Electron Subshells In Order Of Increasing Energy

Electrons in an atom don't just float around randomly; they occupy specific energy levels and sublevels. Understanding the order of increasing energy for these electron subshells is crucial for predicting an atom's electronic configuration, chemical behavior, and various other properties. It's a fundamental concept in chemistry, informing how atoms interact and form molecules.

Understanding Electron Shells and Subshells

Before diving into the order, let's clarify some basic concepts:

• Electron Shells (Principal Energy Levels): These are the main energy levels within an atom, designated by the principal quantum number n (n = 1, 2, 3, ...). Higher n values indicate higher energy levels and greater distance from the nucleus. The first shell (n=1) is closest to the nucleus and has the lowest energy.
• Electron Subshells (Sublevels): Within each electron shell, there are subshells, each with a slightly different energy. These subshells are designated by the letters s, p, d, and f.
  • s subshells are spherical in shape and can hold a maximum of 2 electrons.
  • p subshells are dumbbell-shaped and can hold a maximum of 6 electrons.
  • d subshells have more complex shapes and can hold a maximum of 10 electrons.
  • f subshells have even more complex shapes and can hold a maximum of 14 electrons.

The Aufbau Principle: Building Up the Electronic Configuration

The Aufbau principle (from the German word Aufbauen meaning "to build up") provides a guiding rule for determining the order in which electrons fill the subshells. It states that electrons first occupy the lowest energy levels available to them. This principle, however, is not always straightforward due to the interplay of various factors, including the energy level (n) and the shape of the orbital (l).

The n + l Rule

A more reliable method for determining the order of filling is the n + l rule. This rule states:

1. Electrons first fill the subshell with the lowest value of n + l, where:
   • n is the principal quantum number (shell number).
   • l is the azimuthal quantum number, which defines the shape of the orbital (subshell):
     • l = 0 for s subshells
     • l = 1 for p subshells
     • l = 2 for d subshells
     • l = 3 for f subshells
2. If two subshells have the same n + l value, the subshell with the lower n value is filled first.

Applying the n + l Rule: Step-by-Step

Let's apply the n + l rule to determine the order of increasing energy for the electron subshells:

1. 1s: n = 1, l = 0, n + l = 1 + 0 = 1
2. 2s: n = 2, l = 0, n + l = 2 + 0 = 2
3. 2p: n = 2, l = 1, n + l = 2 + 1 = 3
4. 3s: n = 3, l = 0, n + l = 3 + 0 = 3
5. 3p: n = 3, l = 1, n + l = 3 + 1 = 4
6. 4s: n = 4, l = 0, n + l = 4 + 0 = 4
7. 3d: n = 3, l = 2, n + l = 3 + 2 = 5
8. 4p: n = 4, l = 1, n + l = 4 + 1 = 5
9. 5s: n = 5, l = 0, n + l = 5 + 0 = 5
10. 4d: n = 4, l = 2, n + l = 4 + 2 = 6
11. 5p: n = 5, l = 1, n + l = 5 + 1 = 6
12. 6s: n = 6, l = 0, n + l = 6 + 0 = 6
13. 4f: n = 4, l = 3, n + l = 4 + 3 = 7
14. 5d: n = 5, l = 2, n + l = 5 + 2 = 7
15. 6p: n = 6, l = 1, n + l = 6 + 1 = 7
16. 7s: n = 7, l = 0, n + l = 7 + 0 = 7
17. 5f: n = 5, l = 3, n + l = 5 + 3 = 8
18. 6d: n = 6, l = 2, n + l = 6 + 2 = 8
19. 7p: n = 7, l = 1, n + l = 7 + 1 = 8

Notice some subshells have the same n + l value (e.g., 3s and 2p). In such cases, the subshell with the lower n value is filled first (e.g., 2p before 3s).

The Complete Order of Increasing Energy

Based on the n + l rule, the order of increasing energy for electron subshells is:

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

This sequence is crucial for writing electronic configurations and understanding the chemical behavior of elements.

A Helpful Mnemonic Device: The Diagonal Rule

While the n + l rule is the most accurate, remembering the order can be challenging. The diagonal rule (also known as the Madelung rule or the Klechkowski's rule) provides a visual mnemonic device to help you recall the filling order.

1. Write the subshells in order of increasing principal quantum number (n) in columns:

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

2. Draw diagonal arrows starting from the top right and continuing downwards and to the left:

   1s
   2s  2p <-
   3s  3p  3d <-
   4s  4p  4d  4f <-
   5s  5p  5d  5f  5g <-
   6s  6p  6d  6f  6g  6h <-
   7s  7p  6d  6f  6g  6h  6i <-
   

3. Follow the arrows to determine the filling order:

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

While the diagonal rule is a helpful mnemonic, it's important to remember that it is a simplified approximation. Deviations from this rule occur, especially for heavier elements, due to complex interelectronic interactions.

Why Does This Order Matter?

The order of increasing energy for electron subshells is not just an academic exercise. It has profound implications for understanding:

• Electronic Configuration: The electronic configuration describes the arrangement of electrons within an atom. By knowing the filling order, you can predict how electrons will populate the subshells, leading to the correct electronic configuration. For example, Potassium (K) has 19 electrons. Its electronic configuration is 1s²2s²2p⁶3s²3p⁶4s¹. Note that the 4s subshell is filled before the 3d subshell.
• Chemical Properties: An element's chemical properties are largely determined by its valence electrons – the electrons in the outermost shell. The filling order dictates which subshells are occupied by valence electrons, influencing how the atom interacts with other atoms to form chemical bonds.
• Ionization Energy: Ionization energy is the energy required to remove an electron from an atom. The filling order helps predict which electrons are easiest to remove, thus affecting the ionization energy. For example, it's easier to remove an electron from the 4s subshell of Potassium than from the inner 3p subshell.
• Spectroscopy: When atoms absorb energy, their electrons can jump to higher energy levels. When these electrons return to lower energy levels, they emit light of specific wavelengths. The filling order and energy differences between subshells dictate the wavelengths of light emitted, providing information about the atom's electronic structure in spectroscopic techniques.
• Magnetic Properties: The presence of unpaired electrons in a subshell leads to paramagnetism (attraction to a magnetic field). The filling order helps determine the number of unpaired electrons, thus influencing the magnetic properties of a substance.

Exceptions to the Rule

While the n + l rule and the diagonal rule are valuable tools, there are exceptions, particularly for transition metals and heavier elements. These exceptions arise due to:

• Interelectronic Repulsions: The n + l rule assumes that electrons behave independently, but in reality, electrons repel each other. These repulsions can alter the energy levels of subshells, leading to deviations from the predicted filling order.
• Exchange Energy: This is a quantum mechanical effect that favors having electrons with parallel spins (same spin quantum number) in degenerate orbitals (orbitals with the same energy). This effect can also influence the filling order.
• Relativistic Effects: For heavier elements, the inner electrons move at speeds approaching the speed of light. These relativistic effects can significantly alter the energies of orbitals, leading to deviations from the predicted filling order.

Examples of Exceptions:

• Chromium (Cr): The predicted electronic configuration is [Ar] 4s²3d⁴. However, the actual configuration is [Ar] 4s¹3d⁵. This is because a half-filled d subshell (d⁵) is more stable than a partially filled d subshell (d⁴). One electron from the 4s subshell moves to the 3d subshell to achieve this stability.
• Copper (Cu): The predicted electronic configuration is [Ar] 4s²3d⁹. However, the actual configuration is [Ar] 4s¹3d¹⁰. This is because a completely filled d subshell (d¹⁰) is more stable than a partially filled d subshell (d⁹). One electron from the 4s subshell moves to the 3d subshell to achieve this stability.

Summary of Key Points

• Electrons occupy specific energy levels (shells) and sublevels (subshells) within an atom.
• The principal quantum number (n) defines the energy level of a shell.
• The azimuthal quantum number (l) defines the shape of a subshell (s, p, d, f).
• The Aufbau principle states that electrons fill the lowest energy levels first.
• The n + l rule provides a more accurate method for determining the filling order.
• The diagonal rule is a mnemonic device to help remember the filling order.
• 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 < ...
• Exceptions to the filling order occur due to interelectronic repulsions, exchange energy, and relativistic effects.
• Understanding the filling order is crucial for predicting electronic configurations, chemical properties, ionization energies, spectroscopic behavior, and magnetic properties.

Conclusion

Understanding the order of increasing energy for electron subshells is a cornerstone of chemistry. While the n + l rule and the diagonal rule provide valuable guidelines, it's essential to be aware of the exceptions that can occur due to complex electronic interactions. By mastering these concepts, you'll gain a deeper understanding of the behavior of atoms and the formation of chemical compounds. This knowledge is vital for success in chemistry and related fields.

Frequently Asked Questions (FAQ)

Q: Why is the 4s subshell filled before the 3d subshell?

A: According to the n + l rule, the 4s subshell (n + l = 4 + 0 = 4) has a lower energy than the 3d subshell (n + l = 3 + 2 = 5). Therefore, the 4s subshell is filled before the 3d subshell.

Q: Are there any elements that completely disregard the Aufbau principle?

A: No, there are no elements that completely disregard the Aufbau principle. The Aufbau principle provides a general guideline, but deviations occur due to factors like interelectronic repulsions and exchange energy. Even in these exceptions, the electrons are still trying to achieve the lowest possible energy configuration, just with these additional factors influencing what that configuration looks like.

Q: How do I write the electronic configuration of an ion?

A: First, write the electronic configuration of the neutral atom. Then, if the ion is positively charged (cation), remove electrons starting from the subshell with the highest n value. If the ion is negatively charged (anion), add electrons to the subshell according to the filling order. For example, to write the electronic configuration of Fe²⁺, first write the configuration of Fe: [Ar] 4s²3d⁶. Then, remove two electrons from the 4s subshell, resulting in the configuration [Ar] 3d⁶.

Q: Is the diagonal rule always accurate?

A: No, the diagonal rule is a helpful mnemonic, but it's not always accurate, especially for transition metals and heavier elements. The n + l rule is more reliable, but even it has exceptions.

Q: Where can I learn more about electron configurations and the Aufbau principle?

A: You can find more information in general chemistry textbooks, online chemistry resources like Khan Academy and Chemistry LibreTexts, and university-level chemistry courses. You can also search for scholarly articles on specific elements and their electronic configurations.