Energy Levels, Sublevels and Atomic Orbitals

Energy Levels and Sublevels

The diagram below shows first the first 4 main energy levels and their sublevels.

• In a closer and more exact study of the emission line Spectra of elements it was noted that what appeared to be a single line on a line spectrum was really two or more lines which were very close together.
• To explain this, scientists proposed that each main level excluding the 1st was made up of a number of sublevels.
• The sublevels were assigned the letters s, p, d and f in order of their energy value. The s sublevel was given the lowest energy, and the f sublevel was given the highest energy.
• The number of sublevels is the same as the number of the main level. Therefore, the main level one has one sublevel called the 1s, the second main level, 2, has two sublevels, the 2s and 2p sub levels and so on.

Organisation of Particles in Atoms of Elements Nos. 1–20

Atoms consist of three fundamental particles: protons, neutrons, and electrons. The protons and neutrons are located in the nucleus, while the electrons orbit in energy levels, or shells, around the nucleus.

For elements with atomic numbers 1–20, the electrons are arranged in main energy levels, also called shells, around the nucleus. The number of electrons in each energy level follows the rule 2n², where n is the number of the energy level:

• First energy level: maximum of 2 electrons

• Second energy level: maximum of 8 electrons

• Third energy level: maximum of 8 electrons (due to limitations in this range)

• Fourth energy level: remaining electrons. For example:

• Hydrogen (Z = 1) has 1 electron: 1 in the first energy level.

• Carbon (Z = 6) has 6 electrons: 2 in the first level, 4 in the second.

• Calcium (Z = 20) has 20 electrons: 2 in the first, 8 in the second, 8 in the third, and 2 in the fourth.

Classification of the First Twenty Elements Based on Outer Electrons

The chemical properties of an element are largely determined by the number of electrons in its outermost shell, also known as the valence electrons. The first twenty elements can be grouped based on these valence electrons:

• Group 1 (Alkali Metals): 1 valence electron (e.g., Hydrogen, Lithium, Sodium, Potassium).
• Group 2 (Alkaline Earth Metals): 2 valence electrons (e.g., Beryllium, Magnesium, Calcium).
• Group 13: 3 valence electrons (e.g., Boron, Aluminium).
• Group 14: 4 valence electrons (e.g., Carbon, Silicon).
• Group 15: 5 valence electrons (e.g., Nitrogen, Phosphorus).
• Group 16: 6 valence electrons (e.g., Oxygen, Sulfur).
• Group 17 (Halogens): 7 valence electrons (e.g., Fluorine, Chlorine).
• Group 18 (Noble Gases): Full outer shell (Helium has 2 electrons, others have 8, e.g., Neon, Argon). Elements in the same group exhibit similar chemical properties due to having the same number of outer electrons.

Heisenberg's Uncertainty Principle

The Heisenberg Uncertainty Principle, formulated by Werner Heisenberg, is a fundamental concept in quantum mechanics. It states that it is impossible to simultaneously know both the exact position and momentum of a particle, such as an electron, with perfect accuracy. The more precisely you know the position of an electron, the less precisely you can know its momentum, and vice versa.

• Implication: This uncertainty arises because electrons do not behave like classical particles with defined trajectories. Instead, they are better understood in terms of probabilities.
• Example: If you try to measure an electron's exact location, you introduce uncertainty in measuring its momentum (mass × velocity). Conversely, if you know its momentum very well, its position becomes highly uncertain. This principle highlights the limits of our ability to measure certain properties at the quantum level and is key to understanding the behavior of subatomic particles like electrons.

Wave Nature of the Electron:

Electrons exhibit wave-particle duality, meaning they have properties of both particles and waves. This concept was proposed by Louis de Broglie, who suggested that particles such as electrons could behave like waves under certain conditions.

• Electron Waves: Electrons can form standing waves as they move around the nucleus. This wave-like behavior is essential in explaining phenomena like electron diffraction, where electrons behave similarly to light waves when passed through a crystal or a small opening.
• Atomic Orbitals: The wave nature of the electron helps explain the formation of atomic orbitals, where electrons exist in specific regions around the nucleus. These regions, or orbitals, are defined by the probability of finding an electron in a given space, rather than the electron following a fixed path like a planet orbiting the Sun.

Atomic Orbitals

Then the Austrian scientist Erwin Schrödinger developed mathematical equations to describe the probability of finding an electron in an Atom. As a result of Schrödinger's work, orbitals were used to describe the movement of electrons in an Atom.

Properties of Atomic Orbitals

It is required that you know the shapes of the s and p orbitals.

Each orbital can hold 2 electrons. This follows Paulie's exclusion principle where he stated that no more than two electrons can occupy an orbital and when they do they must have opposite spin.

The s orbitals are spherical there is only one s orbital for each sublevel.

The p orbitals have a dumbbell shape. There are three p orbitals for each sub level. They are called the px, py and the pz orbitals.

These p orbitals are at right angles to each other as shown in the diagram. It is important to note that any p sublevel can accommodate 6 electrons.

There are five d orbitals. It is not required that you know the names or shapes of these orbitals. It is important to note that the d sublevel can accommodate 10 electrons.

Energy Levels and Sub-levels:

The first 36 elements have electrons arranged in main energy levels (n = 1, 2, 3, etc.), which are further divided into sub-levels (s, p, d, f). The sub-levels are filled in a specific order of increasing energy.

• 1st Energy Level: Contains 1s (holds a maximum of 2 electrons).
• 2nd Energy Level: Contains 2s (2 electrons) and 2p (6 electrons).
• 3rd Energy Level: Contains 3s (2 electrons), 3p (6 electrons), and part of 3d (but 3d is not filled until after 4s).
• 4th Energy Level: Contains 4s (2 electrons) and part of 4p (starts being filled from element 31 onwards). The order of filling is based on increasing energy, and follows this sequence: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p.

Electronic Configuration of the First 36 Elements:

Here is how the electrons are arranged in the first 36 elements (with element numbers and names included for reference):

1. Hydrogen (H): 1s¹
2. Helium (He): 1s²
3. Lithium (Li): 1s² 2s¹
4. Beryllium (Be): 1s² 2s²
5. Boron (B): 1s² 2s² 2p¹
6. Carbon (C): 1s² 2s² 2p²
7. Nitrogen (N): 1s² 2s² 2p³
8. Oxygen (O): 1s² 2s² 2p⁴
9. Fluorine (F): 1s² 2s² 2p⁵
10. Neon (Ne): 1s² 2s² 2p⁶
11. Sodium (Na): 1s² 2s² 2p⁶ 3s¹
12. Magnesium (Mg): 1s² 2s² 2p⁶ 3s²
13. Aluminium (Al): 1s² 2s² 2p⁶ 3s² 3p¹
14. Silicon (Si): 1s² 2s² 2p⁶ 3s² 3p²
15. Phosphorus (P): 1s² 2s² 2p⁶ 3s² 3p³
16. Sulfur (S): 1s² 2s² 2p⁶ 3s² 3p⁴
17. Chlorine (Cl): 1s² 2s² 2p⁶ 3s² 3p⁵
18. Argon (Ar): 1s² 2s² 2p⁶ 3s² 3p⁶
19. Potassium (K): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹
20. Calcium (Ca): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²
21. Scandium (Sc): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹
22. Titanium (Ti): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²
23. Vanadium (V): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³
24. Chromium (Cr): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵ (an exception where 4s and 3d orbitals exchange electrons for stability)
25. Manganese (Mn): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁵
26. Iron (Fe): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶
27. Cobalt (Co): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷
28. Nickel (Ni): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁸
29. Copper (Cu): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰ (another exception for stability)
30. Zinc (Zn): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰
31. Gallium (Ga): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p¹
32. Germanium (Ge): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p²
33. Arsenic (As): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p³
34. Selenium (Se): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁴
35. Bromine (Br): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵
36. Krypton (Kr): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶

Examples

Nitrogen has extra stability as the two-p sub level is half full and a half full sublevel is the next most stable to a full sublevel.

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Electronic Configuration of Ions

What is the electronic configuration of the magnesium ion $Mg^{2+}$? What neutral atom has the same configuration?

The magnesium atom has 12 electrons and therefore the magnesium ion has 10 electrons as it has lost 2 electrons. Therefore, the electronic configuration of the magnesium ion is:

$Mg^{2+}: 1s^2, 2s^2, 2p^6$

This ion has the same configuration as neon