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Linear organic molecules, such as acetylene (HC≡CH), are often described by invoking sp orbital hybridization for their carbon centers. Two sp orbitals. According to the VSEPR model (Valence Shell Electron Pair Repulsion model), linear geometry occurs at central atoms with two bonded atoms and zero or three lone pairs (AX 2 or AX 2 E 3) in ...
Angular: Angular molecules (also called bent or V-shaped) have a non-linear shape. For example, water (H 2 O), which has an angle of about 105°. A water molecule has two pairs of bonded electrons and two unshared lone pairs. Tetrahedral: Tetra-signifies four, and -hedral relates to a face of a solid, so "tetrahedral" literally means "having ...
For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimal when they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopt a linear geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the ...
In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
There are several variants of bending, where the most common is AX 2 E 2 where two covalent bonds and two lone pairs of the central atom (A) form a complete 8-electron shell. They have central angles from 104° to 109.5°, where the latter is consistent with a simplistic theory which predicts the tetrahedral symmetry of four sp 3 hybridised ...
Any other pair of linearly independent vectors of R 2, such as (1, 1) and (−1, 2), forms also a basis of R 2. More generally, if F is a field , the set F n {\displaystyle F^{n}} of n -tuples of elements of F is a vector space for similarly defined addition and scalar multiplication.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
Lone pairs (shown as pairs of dots) in the Lewis structure of hydroxide. In chemistry, a lone pair refers to a pair of valence electrons that are not shared with another atom in a covalent bond [1] and is sometimes called an unshared pair or non-bonding pair. Lone pairs are found in the outermost electron shell of atoms.
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