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Shows location of unpaired electrons, bonded atoms, and bond angles. The bond angle for water is 104.5°. Valence shell electron pair repulsion ( VSEPR ) theory ( / ˈ v ɛ s p ər , v ə ˈ s ɛ p ər / VESP -ər , [ 1 ] : 410 və- SEP -ər [ 2 ] ) is a model used in chemistry to predict the geometry of individual molecules from the number of ...
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 ...
This is equal to the number of electrons in its valence shell if all the valence shell electrons are used for bonding. If they are not, the remainder will form non-bonding electron pairs, usually known as lone pairs. The valence of a bond, S, is defined as the number of electron pairs forming the bond. In general this is not an integral number.
In VSEPR theory the electron pairs on the oxygen atom in water form the vertices of a tetrahedron with the lone pairs on two of the four vertices. The H–O–H bond angle is 104.5°, less than the 109° predicted for a tetrahedral angle, and this can be explained by a repulsive interaction between the lone pairs. [2] [3] [4]
This increased p character in those orbitals decreases the bond angle between them to less than the tetrahedral 109.5°. The same logic can be applied to ammonia (107.0° HNH bond angle, with three N(~sp 3.4 or 23% s) bonding orbitals and one N(~sp 2.1 or 32% s) lone pair), the other canonical example of this phenomenon.
During the period between 1916 and 1925, much progress was being made concerning the arrangement of electrons in the periodic table.In order to explain the Zeeman effect in the Bohr atom, Sommerfeld proposed that electrons would be based on three 'quantum numbers', n, k, and m, that described the size of the orbit, the shape of the orbit, and the direction in which the orbit was pointing. [10]
In some cases it is convenient to express the classical electron radius in terms of the Compton wavelength: = ¯ = /, where is the fine structure constant (~1/137) and ¯ = / is the reduced Compton wavelength of the electron (~0.386 pm), so that the constant in the cross section may be given as:
In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number ( m l or m [ a ] ) distinguishes the orbitals available within a given subshell of an atom.