Erwin Schrodinger’s Proposal
Erwin Schrodinger proposed various characteristics of electrons’ behavior. For example, he argued that electrons depict both wave and Patrice-like behaviors. He presented electrons as matter waves. He developed the equation Ĥψ=Eψ. The equation yields a series of various wave functions, ψ. Each of the waves describes unique binding energy (E) for an electron. Considering that various electromagnetic waves have different energies (E) associated with them, Erwin Schrodinger argued that electrons exhibit a wave-like pattern (Brown et al., 2014). Indeed, unique wave functions correspond to the different orbitals of an electron. Since the equation, Ĥψ=Eψ, yields unique energy, which describes distinctive waves that define the probability of finding an electron in the space of an atom, Schrodinger presented another characteristic, namely, the particulate behavior of an electron.
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Electromagnetic Radiation Properties in Terms of Wavelength and Frequency
Electromagnetic radiation refers to specific waves, among them, radio waves, X-rays, and infrared radiations that propagate through space. According to Brown et al. (2014), they carry with them radiant energy. The above radiations have instantaneous oscillations that mainly consist of magnetic and electric waves, which travel at the speed of light in an empty space. According to Brown et al. (2014), frequency and wavelength distinguish the different types of electromagnetic radiation. Radio waves, which depict the longest wavelength that goes beyond one meter, have the least frequency of less than 0.3GHz. The wavelength of microwaves ranges from one meter to a millimeter. Their frequency varies from 0.3 GHz (Gigahertz) to 300 GHz. Infrared rays have a frequency that oscillates between 3 THz and 300 THz and a wavelength whose range lies between 1 µm and 1 mm. Visible light has a wavelength of the range of 400 nm (nanometers) to 700 nm. Brown et al. (2014) confirm that Gamma rays and X-rays have ionizing effects. The frequency of X-rays ranges from 300 PHz to 30EHz and a wavelength that oscillates between 1 nm and 10 pm. Gamma rays have frequencies that fall between 30 EHz and 30 0EHz. Their wavelengths are found in the 10 pm to 1 pm range.
The Difference Between Ground State and Excited State of Electrons
Ground and excited states describe the different conditions of electrons in atoms. Different shells have dissimilar amounts of energy associated with them. The ground state describes an electron in the lowest energy condition. When an electron in the ground state acquires energy, it climbs up the stairs of an atom to occupy a different shell that has an equivalent amount of power that has been taken in. The excited state denotes such an electron. Any electron in the excited state discharges an amount of energy, which is identical to what it absorbed when it moved from a higher energy zone to its ground state. According to Brown et al. (2014), the case of a valence electron that absorbs energy best explains the difference between the two terms. Before energy absorption, the electron is in a ground state. Upon acquiring energy, it is upgraded to an excited state. Hence, such an electron or any other electron in a different orbital level jumps from the original position (ground state) to occupy an empty higher orbital that is further away from the nucleus. For instance, an atom originally in the “1s” orbital is in a ground state. However, upon moving to, say 2p, orbital after gaining energy, it changes to an excited state.
Quantum Numbers, Orbital, Shells, Sub-shells, and the Meaning of the Letters s, p, d, and f
Quantum numbers are values that are deployed to illustrate the various energy levels of molecules and atoms. An electron possesses four quantum numbers, which sufficiently define its state. The state yields a solution to Schrödinger’s wave equation. Principal quantum number (n) identifies an energy level. This quantum number takes an integer value (equal to or greater than 1) and describes the shell position where an electron is located in the space of an atom (Brown et al., 2014). A shell refers to orbitals that bear identical quantum numbers.
Azimuthal quantum number (ℓ) identifies a sub-shell. ℓ here takes the form of an integer with a value of zero or more, but equal to or even less than n-1 (where n refers to the principal quantum number of an electron). A sub-shell refers to orbitals within a shell. Such orbitals must have the same Azimuthal quantum number (ℓ). An orbital refers to any section within an atom where the chances of encountering an electron within 90% of most of its time are high. Two characters, say 1s, 2p, 3d, or 4f, classify the shell and sub-shell of an orbital. For example, in the case of 2p, the first character refers to a shell where n=2 while “p” refers to sub-shell ℓ=1. Similarly, the letter “s” refers to sub-shell ℓ=0, “d” means sub-shell ℓ=2, and “f” denotes the sub-shell ℓ=3.
Magnetic quantum numbers (mℓ) describe a sub-shells orbital. A magnetic quantum number is an integer that assumes the value of negative ℓ to positive ℓ. It describes an orbital’s orientation in space (Brown et al., 2014). Spin quantum number (ms) describes the least energy level of atoms or molecules. According to Brown et al. (2014), electrons in an orbital depict a spinning behavior in either clockwise or anticlockwise direction. When one electron is randomly given the value of ms = +1/2, the other electron takes the value of ms = -1/2.
Electron Configuration of Atoms, Hund’s Rule, and the Significance of Valence Electrons
The electron configuration of atoms describes the manner in which electrons are arranged or distributed in orbits within the shells and sub-shells. The configuration is critical in predicting properties such as electrical, magnetic, and/or chemical characteristics of any substance (Brown et al., 2014). For example, considering the electronic configuration of an atom, one can predict the possibility of a chemical reaction with another atom. In the case of reactions, the configuration enhances the prediction of the effect and strength of the reaction. Electrons are configured in an atom in a manner that the overall energy possessed by the atom remains at the least value to guarantee stability.
Hund’s rule specifies the manner in which energy interactions determine a ground state. Pauli’s exclusion principle dictates that in any one system, it is impossible for two electrons to have corresponding quantum numbers. Consequently, within any spatial orbital, only one space is available for just two electrons with ms = +1/2 and -1/2. Although Hund developed three laws, the term Hund’s rule refers to his first proposition, which defines the smallest energy atomic condition as the one that capitalizes on the entire spin quantum value of the electrons present in the free sub-shell. The rule holds that individual electrons, which depict parallel spins populate shell orbitals before any likely double occupation occurs.
The term valence shell refers to the furthermost shell of an atom. Valence electrons take up this shell. When two atoms come into close vicinity, they first interact through their valence shells. Therefore, valence electrons are the ones that lead to chemical reactions. They are responsible for bonding between atoms. Irrespective of the type of bonding, valence electrons’ electrical forces hold atoms in intact.
Brown, T., LeMay, E., Bursten, B., Woodward, P., Stoltzfus, M., & Murphy, C. (2014). Chemistry: The central science (13th ed.). London, England: Pearson.