Atomic orbital in the context of "Sigma bond"

The electron (e
, or β
in nuclear reactions) is a subatomic particle whose electric charge is negative one elementary charge. It is an elementary particle that comprises the ordinary matter that makes up the universe, along with up and down quarks.

Electrons are extremely lightweight particles. In atoms, an electron's matter wave occupies atomic orbitals around a positively charged atomic nucleus. The configuration and energy levels of an atom's electrons determine the atom's chemical properties. Electrons are bound to the nucleus to different degrees. The outermost or valence electrons are the least tightly bound and are responsible for the formation of chemical bonds between atoms to create molecules and crystals. These valence electrons also facilitate all types of chemical reactions by being transferred or shared between atoms. The inner electron shells make up the atomic core.

In chemistry, a hydrogen bond (H-bond) is a specific type of molecular interaction that exhibits partial covalent character and cannot be described as a purely electrostatic force. It occurs when a hydrogen (H) atom, covalently bonded to a more electronegative donor atom or group (Dn), interacts with another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor (Ac). Unlike simple dipole–dipole interactions, hydrogen bonding arises from charge transfer (nB → σ*AH), orbital interactions, and quantum mechanical delocalization, making it a resonance-assisted interaction rather than a mere electrostatic attraction.

The general notation for hydrogen bonding is Dn−H···Ac, where the solid line represents a polar covalent bond, and the dotted or dashed line indicates the hydrogen bond. The most frequent donor and acceptor atoms are nitrogen (N), oxygen (O), and fluorine (F), due to their high electronegativity and ability to engage in stronger hydrogen bonding.

In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940.

In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of all four of their quantum numbers, which are: n, the principal quantum number; ℓ, the azimuthal quantum number; m_ℓ, the magnetic quantum number; and m_s, the spin quantum number. For example, if two electrons reside in the same orbital, then their values of n, ℓ, and m_ℓ are equal. In that case, the two values of m_s (spin) pair must be different. Since the only two possible values for the spin projection m_s are +1/2 and −1/2, it follows that one electron must have m_s = +1/2 and one m_s = −1/2.

The alkaline earth metals are six chemical elements in group 2 of the periodic table. They are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). The elements have very similar properties: they are all shiny, silvery-white, somewhat reactive metals at standard temperature and pressure.

Together with helium, these elements have in common an outer s orbital which is full—that is, this orbital contains its full complement of two electrons, which the alkaline earth metals readily lose to form cations with charge +2, and an oxidation state of +2. Helium is grouped with the noble gases and not with the alkaline earth metals, but it is theorized to have some similarities to beryllium when forced into bonding and has sometimes been suggested to belong to group 2.

Organolead chemistry is the scientific study of the synthesis and properties of organolead compounds, which are organometallic compounds containing a chemical bond between carbon and lead. The first organolead compound was hexaethyldilead (Pb₂(C₂H₅)₆), first synthesized in 1858. Sharing the same group with carbon, lead is tetravalent.

Going down the carbon group the C–X (X = C, Si, Ge, Sn, Pb) bond becomes weaker and the bond length larger. The C–Pb bond in tetramethyllead is 222 pm long with a dissociation energy of 49 kcal/mol (204 kJ/mol). For comparison the C–Sn bond in tetramethyltin is 214 pm long with dissociation energy 71 kcal/mol (297 kJ/mol). The dominance of Pb(IV) in organolead chemistry is remarkable because inorganic lead compounds tend to have Pb(II) centers. The reason is that with inorganic lead compounds elements such as nitrogen, oxygen and the halides have a much higher electronegativity than lead itself and the partial positive charge on lead then leads to a stronger contraction of the 6s orbital than the 6p orbital making the 6s orbital inert; this is called the inert-pair effect.

The subatomic scale is the domain of physical size that encompasses objects smaller than an atom. It is the scale at which the atomic constituents, such as the nucleus containing protons and neutrons, and the electrons in their orbitals, become apparent.

The subatomic scale includes the many thousands of times smaller subnuclear scale, which is the scale of physical size at which constituents of the protons and neutrons—particularly quarks—become apparent.

In quantum mechanics, the azimuthal quantum number ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_ℓ, and the spin quantum number m_s).

For a given value of the principal quantum number n (electron shell), the possible values of ℓ are the integers from 0 to n − 1. For instance, the n = 1 shell has only orbitals with ${\displaystyle \ell =0}$, and the n = 2 shell has only orbitals with ${\displaystyle \ell =0}$, and ${\displaystyle \ell =1}$.