An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping includes lithium (Li), sodium (Na), and potassium (K). All of these elements are shiny, conduct heat and electricity well, and have similar chemical properties. A second grouping includes calcium (Ca), strontium (Sr), and barium (Ba), which also are shiny, good conductors of heat and electricity, and have chemical properties in common. However,...

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the...

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their electron configurations are added to the table, a periodic recurrence of similar electron configurations in the outer shells of these elements is observed. Because they are in the outer shells of an atom, valence electrons play the most important role in chemical reactions. The outer electrons have the highest energy of the electrons in an atom...

A three-phase generator produces three voltages that are equal in magnitude but have a phase difference of 120 degrees. This identical magnitude and equal phase separated voltages are known as the balanced voltages and help to minimize power loss while ensuring a steady delivery of energy to connected loads. As voltage sources in a three-phase system can be configured in a wye or a delta formation, the loads connected to these systems can also be arranged in either configuration. This...

AC power distribution systems have three categories: single-phase, two-phase, and three-phase systems. The single-phase circuit, common in residential settings, typically employs a two-wire system connecting a single AC source to various loads. These circuits support standard household appliances operating at 120 volts (V) and 240 V, such as lamps, televisions, and microwaves. The first generators, Niagara Falls hydro plant installed in 1895, were two-phase and designed by Nikola Tesla. The...