Wednesday, December 28, 2011

Chemistry HW - 8/29/10

Aufbau principle

            The word Aufbau is German for building up.
The rules of placing electrons within shells is known as the Aufbau principle . The Aufbau principle states that the electrons added one at a time to the lowest energy orbitals available then proceeding to the one with higher energy. If an atom is ‘excited’, e.g., by being heated, one or more of its electrons may temporarily be transferred to an orbital of higher energy, but it will soon return to its ground state.
            It is therefore important that we know the relative energies of the orbitals. In general, the higher the number of the main energy level, the higher the energy, Also, within a main energy level the energy increases through s, p, d, f and so on.

Hund’s Rule

            Hund's rule refer to a set of rules used to determine which is the term symbol that corresponds to the ground state of a multi-electron atom. They were proposed by Friedrich Hund.
The Hund’s rule states that in filling up a set of degenerate orbitals, the orbitals are occupied by one electron at a time with the electrons having the same spin.
            Only when the degenerate orbitals have one electron each would double occupancy of the orbitals take place.
            Electrons occupy equal-energy orbitals so that a maximum number of unpaired electrons results. This rule will help you decide how to fill a sublevel consisting of more than one orbital. 

Pauli’s Exclusion Principle

            The Pauli’s Exclusion Principle is a quantum mechanical principle formulated by the Austrian physicist Wolfgang Pauli in 1925.  It states that no two electrons in the same atom can have the same set of four quantum numbers. The consequence of this principle can be stated simply as: ‘Only two electrons may occupy an orbital, and they must have different spins’.
            Applying this rule, the maximum number any s sublevel can accommodate is two electrons. Each p sublevel has three orbitals and can therefore accommodate six electrons at most.

Quantum Theory / Mechanics

Quantum mechanics, the final mathematical formulation of the quantum theory, was developed during the 1920s. In 1924, Louis de Broglie proposed that not only do light waves sometimes exhibit particle-like properties, as in the photoelectric effect and atomic spectra, but particles may also exhibit wavelike properties. This hypothesis was confirmed experimentally in 1927 by C. J. Davisson and L. H. Germer, who observed diffraction of a beam of electrons analogous to the diffraction of a beam of light. Two different formulations of quantum mechanics were presented following de Broglie's suggestion. The wave mechanics of Erwin Schrödinger (1926) involves the use of a mathematical entity, the wave function, which is related to the probability of finding a particle at a given point in space. The matrix mechanics of Werner Heisenberg (1925) makes no mention of wave functions or similar concepts but was shown to be mathematically equivalent to Schrödinger's theory. 

Quantum theory explains the discrete nature of energy levels in microscopic systems comprised of atoms. A quantum is a small and exact amount of energy. Each photon contains a quantum of energy. An atom can only experience a transition through absorption of a particular frequency photon. This is the quantum theory.

Types of Quantum No.                                                            

An orbital can be described by the four quantum numbers n, l, ml and ms.

Principal Quantum Number, n

            The principal quantum number, n, was proposed by Niels Bhor. It Describes the electron shell or main energy level of an orbital in which the electron is present.. The value of n ranges from 1 to "n", where "n" is the shell containing the outermost electron of that atom.
            By knowing these quantum numbers many things like energy of electron, number of sub shells in an orbit, number of orbital’s in an orbit and number of electrons in a orbit can be calculated 
           As the value of 'n' increases, the distance from the nucleus as well as the energy of the electrons increases.

            This number also represents the radial distance that the region where the electron is most likely to be found extends out from the nucleus. The higher the n, the greater is the radial distance.
    •             Maximum number of electrons in n is 2 n 2
Azimuthal Quantum Number, l

            The azimuthal quantum number, l, is also called angular momentum number, orbital angular momentum quantum number, ORBITAL TYPE quantum number ,  or  subsidiary number. It was introduced by Sommerfeld. It represents energy sublevels in n to which the electron belongs and can have values beginning with zero and increasing until the integer n-1 is reached (0 = s orbital, 1 = p orbital, 2 = d orbital, 3 = f orbital, etc.).
            The azimuthal quantum number also defines the shape of the orbital. Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2).  Orbitals even take on more complex shapes as the value of the angular quantum number becomes larger.

Magnetic Quantum Number, ml

            The magnetic quantum number, ml,  was proposed by Lande.  It describes the specific orbital within that subshell. and can have an integral value from –l to +l, including 0.
            A faster way of determining the number of ml­ values per sublevel is by using the formula 2l+1.

Spin Quantum Number, ms
            describes the spin of the electron within that orbital. Uhlenbeck and Goudsmith are the persons who proposed this quantum numbers.  
There are only two possible values for this quantum number, ms: ms = + ½ and ms = - ½ . There two values corresponds to the only two possible orientations for the electron spin. These two orientations are loosely designated as clockwise and counterclockwise spins. These two orientations are also sometimes represented by an arrow pointing up and an arrow pointing down. These are also referred to as 'spin up' and 'spin down'.
            When an electron is assigned to an orbital in atom, it may take either of the two possible orientations. If a second electron is assigned to the same orbital, it can only have an orientation opposite to that of the first.

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