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  2. Trigonal pyramidal molecular geometry - Wikipedia

    en.wikipedia.org/wiki/Trigonal_pyramidal...

    The nitrogen in ammonia has 5 valence electrons and bonds with three hydrogen atoms to complete the octet.This would result in the geometry of a regular tetrahedron with each bond angle equal to arccos(− ⁠ 1 / 3 ⁠) ≈ 109.5°.

  3. VSEPR theory - Wikipedia

    en.wikipedia.org/wiki/VSEPR_theory

    VSEPR theory is used to predict the arrangement of electron pairs around central atoms in molecules, especially simple and symmetric molecules. A central atom is defined in this theory as an atom which is bonded to two or more other atoms, while a terminal atom is bonded to only one other atom.

  4. Molecular geometry - Wikipedia

    en.wikipedia.org/wiki/Molecular_geometry

    In accordance with the VSEPR (valence-shell electron pair repulsion theory), the bond angles between the electron bonds are arccos(− ⁠ 1 / 3 ⁠) = 109.47°. For example, methane (CH 4) is a tetrahedral molecule. Octahedral: Octa-signifies eight, and -hedral relates to a face of a solid, so "octahedral" means "having eight faces". The bond ...

  5. Seesaw molecular geometry - Wikipedia

    en.wikipedia.org/wiki/Seesaw_molecular_geometry

    Disphenoidal or seesaw (also known as sawhorse [1]) is a type of molecular geometry where there are four bonds to a central atom with overall C 2v molecular symmetry.The name "seesaw" comes from the observation that it looks like a playground seesaw.

  6. Talk:VSEPR theory - Wikipedia

    en.wikipedia.org/wiki/Talk:VSEPR_theory

    The VSEPR theory places each pair of valence electrons in a bond or a lone pair found in a local region of the molecule based on the Pauli exclusion principle. While this is frequently taught in chemistry textbooks in conjunction with orbital models such as orbital hybridisation and molecular orbital theory, the approach is completely different.

  7. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Some students studying math may develop an apprehension or fear about their performance in the subject. This is known as math anxiety or math phobia, and is considered the most prominent of the disorders impacting academic performance. Math anxiety can develop due to various factors such as parental and teacher attitudes, social stereotypes ...

  8. List of first-order theories - Wikipedia

    en.wikipedia.org/wiki/List_of_first-order_theories

    The theory of infinite divisible torsion-free abelian groups is complete, as is the theory of infinite abelian groups of exponent p (for p prime). The theory of finite groups is the set of first-order statements in the language of groups that are true in all finite groups (there are plenty of infinite models of this theory). It is not ...

  9. Spectral theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_theory

    In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. [1] It is a result of studies of linear algebra and the solutions of systems of linear equations and their ...