Question

You have learned that each orbital is allowed two electrons, and this pattern is evident on the periodic table. What if each orbital was allowed three electrons? How would this change the appearance of the periodic table? For example, what would be the atomic numbers of the noble gases?

Short answer

In the hypothetical scenario where each orbital could accommodate three electrons instead of two, the periodic table would change significantly. The noble gases, which typically have fully occupied electron shells, would have new atomic numbers as their electron configurations change. The new atomic numbers for the first three noble gases would be 3, 12, and 39. This pattern results from the altered electron capacities of the s, p, and d orbitals, ultimately affecting the entire periodic table's structure.

Step-by-step solution

Understanding Orbitals

In the real periodic table, each orbital can accommodate two electrons, following the Pauli Exclusion Principle. We have four types of orbitals (s, p, d, and f) in which electrons can be placed. Each type of orbital can hold a different number of electrons: 1. s-orbital: 1 orbital x 2 electrons = 2 electrons 2. p-orbitals: 3 orbitals x 2 electrons = 6 electrons 3. d-orbitals: 5 orbitals x 2 electrons = 10 electrons 4. f-orbitals: 7 orbitals x 2 electrons = 14 electrons

Modified Orbitals

Now, let's consider the hypothetical scenario in which each orbital can accommodate three electrons. In this case, the number of electrons that each type of orbital can hold would be as follows: 1. s-orbital: 1 orbital x 3 electrons = 3 electrons 2. p-orbitals: 3 orbitals x 3 electrons = 9 electrons 3. d-orbitals: 5 orbitals x 3 electrons = 15 electrons 4. f-orbitals: 7 orbitals x 3 electrons = 21 electrons

Reconstructing the Periodic Table

To determine how the periodic table would change, we need to analyze the number of electrons gained by adding an extra electron to each orbital. Typically, the noble gases are elements with fully occupied shells, making them highly stable and inert. In the real periodic table, their atomic numbers are 2 (He), 10 (Ne), 18 (Ar), 36 (Kr), 54 (Xe), and 86 (Rn). In the altered periodic table scenario, we need to determine the new atomic numbers for the noble gases by reorganizing the electron configurations.

New Atomic Numbers of Noble Gases

1. Atomic number of the first noble gas: - One fully occupied s-orbital: 3 electrons - New atomic number: 3 2. Atomic number of the second noble gas: - One fully occupied s-orbital (3 electrons) and one fully occupied p-orbital (9 electrons): 3 + 9 = 12 electrons - New atomic number: 12 3. Atomic number of the third noble gas: - Two fully occupied s-orbitals (3 x 2 = 6 electrons), two fully occupied p-orbitals (9 x 2 = 18 electrons), and one fully occupied d-orbital (15 electrons): 6 + 18 + 15 = 39 electrons - New atomic number: 39 To generalize, we can observe a pattern of the atomic numbers of the noble gases: 3, 12, 39, and so on. The sum of the electron capacities of the orbitals, multiplied by their respective orbitals, contributes to the change in the growth pattern. In conclusion, allowing three electrons in each orbital instead of two would substantially change the electron configuration, leading to alterations in the periodic table's structure and the atomic numbers of the noble gases.

Key concepts

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom's orbitals. Orbitals are regions around the nucleus where electrons are likely to be found. Each type of orbital—s, p, d, and f—has a specific capacity for electrons. These capacities are currently determined to be:

• s-orbitals: can hold 2 electrons
• p-orbitals: can hold 6 electrons
• d-orbitals: can hold 10 electrons
• f-orbitals: can hold 14 electrons

In a hypothetical scenario where each orbital can hold 3 electrons, the capacities would change respectively to 3, 9, 15, and 21 electrons.
This change alters the electron configuration significantly, affecting the periodic table's arrangement and the distribution within it.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental rule in quantum physics that states no two electrons can have identical quantum numbers within a single atom. This principle enforces the restriction of only two electrons occupying a single orbital, with opposite spins.
In essence, it explains why orbitals are filled in the observed manner, each s-orbital holding two electrons, each p-orbital holding six, and so on.
By imagining a scenario where this rule allows three electrons per orbital, we would move beyond the constraints defined by the Pauli Exclusion Principle. Such a change would lead to a fascinating but purely theoretical reordering of the periodic table.

Atomic Numbers

The atomic number of an element is the count of protons in its nucleus, and it uniquely identifies each chemical element. The atomic number also correlates directly with the electron configuration of an atom. This is because in a neutral atom, the number of protons (atomic number) equals the number of electrons.
In typical conditions, noble gases have specific atomic numbers—2 for Helium, 10 for Neon, 18 for Argon, and so on. These atomic numbers reflect their stable electron configurations.
Imagine each orbital could host an extra electron: this would change the sum of electrons needed to reach a noble gas configuration and subsequently alter their atomic numbers, requiring recalibration of the periodic table itself.

Noble Gases

Noble gases are elements found in Group 18 of the periodic table. They are known for their inertness, resulting from having full electron shells, which make them highly stable. Their typical electron configurations are spherically symmetric—s and p orbitals being fully occupied.
In our current periodic table, noble gases have atomic numbers like 2 (Helium), 10 (Neon), and so forth, encompassing fully filled outermost shells.

• Helium has 2 electrons filling the 1s orbital.
• Neon fills the 2s and 2p orbitals (2 + 6 = 8 electrons in total).

If each orbital could contain three electrons, the atomic numbers corresponding to these gases would shift.
For instance, with the imaginary capacity increase, the first noble gas in the rearranged table would have an atomic number of 3, derived from a fully filled 1s orbital.