Atomic Structure and Quantum Theory Fundamentals
Z (Atomic Number) = Number of Protons = Number of Electrons.
A (Mass Number) = Protons + Neutrons.
Origins of Quantum Theory
Although the Rutherford model successfully explained the observed experimental evidence, it was inherently inconsistent. It was known that when an electric charge (q) moves with accelerated motion, it loses energy in the form of electromagnetic radiation. The electron in circular motion around the nucleus is subjected to centripetal acceleration; therefore, it must lose energy. This energy loss would lead to an electron trajectory increasingly closer to the nucleus until the electron ultimately collapsed into it. However, we know that the atom is a stable particle system. Therefore, it was necessary to establish another atomic model that, besides explaining observed phenomena, does not violate the laws of physics.
Planck’s Quantum Theory
Hot solid bodies emit radiation that depends on temperature.
The Black Body
In 1900, Planck studied the radiation emitted by a black body. A black body is an ideal surface that reflects no incident radiation. For experimental purposes, it is convenient to consider an approximate black body as an opening into a cavity. Radiation that affects the opening is trapped in the cavity and not reflected.
Bohr Model
The principles on which Bohr’s atomic model is based are:
- The electron moves in circular orbits around the nucleus.
- The space surrounding the nucleus is quantized, meaning that there are permitted areas (levels) and others that are not.
- While an electron remains in a given orbit, its energy remains unchanged.
- Allowed orbits are those in which the electron’s angular momentum is an integer multiple of h/2π, where h is Planck’s constant.
- An atom absorbs or emits energy in full values (quanta), and this is due to the electron undergoing a transition between levels. This can be summarized with the expression: |Ef – Ei| = hν.
- If Ef > Ei, the atom absorbs energy. If Ef < Ei, the atom emits energy.
Modifications to the Bohr Model
The most important modification to the Bohr model was made by physicist Sommerfeld. He suggested that the electron could describe elliptical orbits around the nucleus within the same energy level. Sommerfeld proposed that the electron energy depends on two quantum numbers: n and l. The values of l depend on the principal quantum number (n) of the level that the electron occupies, and can take all integer values between 0 and n-1. Furthermore, a third quantum number, ml, was introduced to define the orientations of the electron orbit in space. Two other physicists proposed the rotation of the electron on itself, ms.
Pauli Exclusion Principle
Two electrons in an atom cannot have the same four quantum numbers equal.
Hund’s Rule of Maximum Multiplicity
When several electrons occupy degenerate orbitals of the same energy, they will do so in different orbitals with unpaired electrons, as much as possible.
Moeller Diagram
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 5f14 6d10