Atomic Structure and the Periodic Table: Properties and Trends

Posted on Dec 18, 2024 in Chemistry

Limitations of the Bohr Model

The Bohr model could not explain why the orbits were quantized, nor why some properties of the elements are repeated periodically. Experimental results also did not fit this model:

By increasing the resolution of the spectrograph, it was shown that some lines of the spectrum were in fact two.
When making the spectrum while the substance is subjected to an intense magnetic field, it was observed that some spectral lines unfold into several.

Quantum Mechanical Model

The basic equations of this new model were developed by Heisenberg and Schrödinger. Characteristics:

1. Wave-Particle Duality: De Broglie proposed that material particles have wave properties and that, therefore, every particle in motion has a wave associated with it (λ = h / mv). These matter waves are only possible to detect in subatomic particles.

2. Principle of Uncertainty: This principle establishes that there is a limit to the accuracy with which one can determine both the position and momentum of a particle. The limit is so small that it is not observed on a macroscopic scale.

The model equations describe the quantum-mechanical behavior of electrons inside the atom, incorporating their wave character and the impossibility of predicting exact trajectories. Thus, the concept of an orbital is established.

Orbital: A region or volume of space of the atom where the probability of finding an electron with a given energy is very large.

Quantum Numbers

Quantum numbers describe the behavior of an atom.

Principal Quantum Number (n): Indicates the energy level. It can take any positive integer value: 1, 2… The first level (n=1) has the lowest energy, and subsequent levels have higher energies.

Orbital Angular Momentum Quantum Number (l): Determines the shape of the orbital and the energy within each level. It takes values between [0, n-1].

If n = 1, then l = 0.
If n = 2, then l = 0 or 1.
If n = 3, then l = 0, 1, or 2.

The values l = 0, 1, 2, and 3 correspond to s, p, and f orbitals, respectively.

Magnetic Quantum Number (m_l): Describes the orientation of the orbital in space and explains the splitting of spectral lines by applying an external magnetic field. It takes values between +l and -l, i.e., (2l + 1) values: -l, -l+1, …, 0, +1, …, l-1, l.

If l = 0 (s orbital), then m_l = 0.
If l = 1 (p orbital), then m_l = -1, 0, or +1.
If l = 2 (d orbital), then m_l = -2, -1, 0, +1, or +2.

Electron Spin Magnetic Quantum Number (m_s): Gives us the intrinsic value of a particle, the spin, for the electron and other elementary particles. It determines if the electron is aligned in parallel or antiparallel to an external magnetic field. It can have the values +1/2 and -1/2. Electrons with the same m_s are said to have parallel spins or are unpaired.

Electron Configuration

Rules for how to sort the orbital levels:

Pauli Exclusion Principle: Two electrons in a single atom cannot have four identical quantum numbers. Thus, in each orbital, there can only be two electrons, one with spin +1/2 and the other with -1/2.

Hund’s Rule: Orbitals with the same n and l values have the same energy. To fill them, first place one electron in each orbital, then complete with the second electron.

Electron Configuration Definition: The distribution of electrons in an atom at different levels and orbitals around the nucleus.

Periodic Classification of Elements

Mendeleev’s Table: It contained all the elements known so far, ordered according to atomic mass. The similarity of elements had to be ordered inversely to their physical and chemical properties.

Moseley’s Table: Identified elements by atomic number. This allowed him to state the periodic law: When the elements are placed in ascending order of their atomic numbers, there is a periodic repetition of various physical and chemical properties.

Electronic Structure and Periodic Table

By comparing the electronic configuration of elements with their position in the periodic table, it is observed that:

The elements of the same period all have the same number of electronic levels, complete or not. This coincides with the period number.
The elements of a group present the same electronic structure in their external or outer shell.

Periodic Properties

Periodic properties are the physical and chemical properties that vary regularly throughout the groups and periods.

Atomic Radius: Since atoms do not have defined limits, we cannot talk about the volume of an atom from a strict point of view. Therefore, each element is assigned an atomic radius from which we can know its approximate size and compare it with other atoms. To assign each element its atomic radius, the distance between the nuclei of the link is measured. The value is approximate since the distance between nuclei varies by the type of connection:

Within a group, the atomic radius increases with increasing atomic number (increases when descending from one period to another).
Within a period, the atomic radius increases as the atomic number decreases (it increases the load on the core nucleus, keeping the number of electronic levels constant).

Ionic Radius: When an atom ionizes, its volume changes. If it loses electrons, it becomes a cation, and its radius decreases. If it gains electrons, it becomes an anion, and its radius increases. Thus, the radius of a cation is smaller than that of the neutral atom, and the radius of an anion is greater.

Ionization Energy: The energy involved in the process by which a neutral atom of an element X in the gas phase gives up an electron from the outermost shell and becomes a monopositive ion X⁺, also in the gas phase. X(g) + e^– → X⁺(g). The ionization energy is positive for all elements. Thus, a high value of ionization energy indicates that the electron is strongly held by the atom.

Within a group, it usually increases as the atomic number decreases (increases when climbing in a group). In smaller atoms, the electron is closer to the core and experiences greater attraction.
Within a period, it tends to increase as the atomic number increases (increases when advancing in the period). By decreasing the atomic radius, the attraction of electrons by the nucleus increases, and they are more difficult to remove.

Electron Affinity: The energy exchanged in the process by which a neutral atom of an element X in the gas phase receives an electron and becomes a mononegative ion X^–, also in the gas phase. X(g) + e^– → X^–(g).

Within a group, it rises as the atomic number increases. When the atomic radius increases, the attraction of the nucleus to the new electron decreases, and thus A is enhanced.
Within a period, albeit with many exceptions, it increases as the atomic number decreases. A increases when moving into a period because the nuclear charge increases and the atomic radius decreases.

Electronegativity: Of an element is the ability of an atom to attract electrons of the molecule of which it forms a part.

Within a group, the most electronegative atoms are those with the lowest atomic number (those with the smallest size).
Within a period, the most electronegative atoms are those with the highest atomic number (those with the smallest size).