Atomic Models, Quantum Theory, and the Periodic Table
Thomson Model of the Atom
In the Thomson model, electrons (e-) are embedded in a sphere of uniform positive charge, like plums in a pudding. There is no distinct nucleus.
Rutherford’s Nuclear Model
The Rutherford model proposes a nucleus that is very small in comparison with the volume of the atom. This nucleus contains almost the entire mass of the atom and all of its positive charge. Electrons form a “crust” (electron cloud) spinning around the nucleus and are relatively far from it.
The Neutron: Discovery and Role
The observation that the mass of atoms is always larger than the combined mass of their protons and electrons led to the hypothesis that there must be another particle without electric charge: the neutron. Neutrons have a mass slightly higher than that of a proton and a zero electric charge.
The existence of neutrons justifies the stability of atomic nuclei. Protons within the nucleus are subject to strong electrostatic repulsive forces. The function of the nuclear forces, mediated by neutrons, is to create an attractive force greater than the electrostatic repulsion, thus holding the nucleus together.
Key Wave Properties
- Wavelength (λ): The distance between two consecutive points on a wave that are in the same phase or vibratory state. Typically measured in nanometers (nm) or meters.
- Frequency (ν): The number of cycles or oscillations performed by a wave in a unit of time. Measured in Hertz (Hz).
- Period (T): The time it takes for a wave to complete one full cycle or oscillation. It is the reciprocal of frequency (T = 1/ν).
Planck’s Quantum Theory (1900)
Max Planck proposed that when a body is heated and emits radiant energy, this energy is not emitted continuously but in discrete packets or “quanta.” These energy packets are also known as photons. This means energy is quantized, taking only specific, discrete values.
The Photoelectric Effect (Einstein, 1905)
Albert Einstein explained the Photoelectric Effect, observing that when light of a particular frequency (not just any light) shines on certain metals, they emit electrons. This phenomenon occurs because the metal absorbs energy from the incident light, and this energy is then used to eject electrons from the metal’s surface.
Bohr’s Atomic Model
Niels Bohr modified Rutherford’s model to explain why atomic spectra consist of discrete lines rather than a continuum. He proposed that electrons orbit the nucleus in specific, allowed energy levels or “stationary orbits.” Not all frequencies appear in the spectrum because not all orbits are allowed. If Rutherford’s model were entirely correct, without any restrictions on electron positions, the atom’s spectrum would be continuous.
Bohr’s postulates include:
- Electrons orbit the nucleus in specific, quantized circular paths called stationary orbits.
- Electrons in these stationary orbits do not emit or absorb energy. This is why they are called “stationary.”
- Energy is only emitted or absorbed when an electron jumps from one allowed orbit to another. The quantity of energy emitted or absorbed corresponds to the difference in energy between the two orbits.
Sommerfeld’s Correction to the Bohr Model
While the Bohr model successfully explained the spectrum of the hydrogen atom, it could not account for the spectra of multi-electron atoms, as there were additional spectral lines it could not explain. Arnold Sommerfeld proposed a correction: he supposed that electron orbits around the nucleus are not only circular but can also be elliptical.
To describe these elliptical orbits, additional parameters were needed, leading to the introduction of new quantum numbers. Thus, while Bohr’s model primarily used a single principal quantum number (n), Sommerfeld’s model introduced two additional quantum numbers:
- L (Azimuthal or Angular Momentum Quantum Number): Indicates the sublevel within each principal energy level and is related to the shape of the orbital.
- For n = 1, L = 0 (s orbital)
- For n = 2, L = 0, 1 (s, p orbitals)
- For n = 3, L = 0, 1, 2 (s, p, d orbitals)
- M (Magnetic Quantum Number): Related to the different orientations of the orbital in space. Its values range from –L to +L, including 0 (i.e., M = –L, …, 0, …, +L).
The Quantum Mechanical Model
Erwin Schrödinger and Werner Heisenberg developed the Quantum Mechanical Model, which describes electrons using a wave equation. This model acknowledges the dual wave-particle nature of matter, particularly for electrons moving at high speeds, where their behavior can be described as a wave.
In this equation, three parameters naturally emerge that correspond to the three primary quantum numbers. Instead of speaking of a precise position or trajectory for an electron, this model describes its location in terms of probability.
Atomic Orbitals
An atomic orbital is a region of space around the nucleus where there is the highest probability of finding an electron. From a physical point of view, an orbital represents an energy state determined by the values of the three primary quantum numbers.
Orbitals differ in shape and orientation:
- s orbitals: Spherical in shape.
- p orbitals: Dumbbell-shaped, oriented along the x, y, and z axes.
- d orbitals: More complex shapes.
- f orbitals: Even more complex shapes.
Common orbital filling order examples: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s…
Maximum electron capacity per subshell type:
- s subshell: 2 electrons
- p subshell: 6 electrons
- d subshell: 10 electrons
- f subshell: 14 electrons
The Periodic System of Elements
The Periodic Table is an organization of all known elements arranged in columns (groups) and rows (periods).
- Groups (Columns): All elements within the same group have identical external electron configurations and, consequently, similar chemical properties. There are 18 groups.
- Periods (Rows): All elements within the same period have their outermost electrons in the same principal energy level, meaning they are at a similar average distance from the nucleus. There are 7 periods.
The difference between an element and the next in its period is that the subsequent element has one more electron and proton. Elements whose outermost electron configuration ends in s or p orbitals are called representative elements, corresponding to groups 1, 2, and 13-18.