"http://wiki.answers.com/Q/Why_the_spin_quantum_number_of_an_electron_is_half_integral
Quantum numbers can be defined as a number that occurs in the hypothetical expression for the value of some quantized property of a subatomic particle, atom, or molecule and can only have certain integral or half-integral values.
a small land mammal such as a rat mouse ferret mole ect. A fundamebtal particle with half-integral spin, such as an electron.
According to Pauli's Exclusion principle it will be having anticlock wise spin if it is in the same orbital. Because no two electrons can have all the four(always spin is half) quantum number same. By the way, I don't think anyone actually calls them "clockwise" and "counterclockwise". It's usually "up" and "down" or "plus one-half" and "minus one-half".
According to Pauli's Exclusion principle it will be having anticlock wise spin if it is in the same orbital. Because no two electrons can have all the four(always spin is half) quantum number same. By the way, I don't think anyone actually calls them "clockwise" and "counterclockwise". It's usually "up" and "down" or "plus one-half" and "minus one-half".
A half quantum harmonic oscillator is a quantum system that exhibits properties of both classical harmonic oscillators and quantum mechanics. It has energy levels that are quantized in half-integer values, unlike integer values in regular quantum systems. This leads to unique characteristics such as fractional energy levels and non-integer spin values.
The answer is Valence Electrons. Atoms want a full number of electrons in their outer shell, which is why atoms with only one electron missing from their outer shell are most reactive, because they are close to completing that shell. Electrons as such are half-spin particles or fermions. A single particle electron orbital (intended as a solution of a 1-D Schrödinger equation) with occupancies 0 and 1 can have 2 allowed quantum states. Electrons are seen as indistinguishable particles in quantum mechanics. In other words electron 1 is the same as electron 2. We can then state that any electron of appropriate energy will be able to occupy the outermost shell of an element.
square root x
According to the Pauli exclusion principle, no two electrons in an atom can have the same set of four quantum numbers. Since electrons are fermions with half-integer spins, the two possible spin states for each electron (up or down) ensure that no two electrons in the same orbital have identical quantum properties. This helps stabilize the atom by minimizing electron-electron repulsion.
The element with the lowest atomic number that contains a half-filled d subshell at its ground state is scandium (atomic number 21). The electron configuration of scandium at ground state is [Ar] 3d^1 4s^2, where the 3d subshell is half-filled with one electron.
fermi statistics
The first half reaction concerns oxidant takenig up (an) electron(s), the other half is the one with a reductant producing (an) electron(s).
In probability theory, an "expectation value" is the average of all values of a measurable quantity that one would expect, if a measurement was repeated a large number of times on a given system. For example, for an unbiased coin, the expectation value for "heads" is half of all tosses. Each measurable quantity of a quantum system has an operator that, when mathematically applied to the system, gives a value of that quantity for that system. The expectation value for that quantity, for a given quantum system, is the product of that operator on a given state of the system, times the probability of the system being in that state, integrated over all possible states of the system. A more formally stated example: For a quantum state Ψ(x), where 'x' can vary from -∞ to ∞, and for which Q(x) is a measurable quantity, then the expectation value of Q(x) would be equal to ∫Ψ*(x)Ψ(x)Q(x)dx integrated from x = -∞ to x = ∞ As an example, suppose we wanted the expectation value for the radial position of an electron in its '1S' state within a hydrogen atom. When doing the formal math, we find that this value exactly equals the Bohr Radius. In contrast to the Bohr Model of an atom, this expectration value does NOT state that this electron IS at this radius, only that an AVERAGE of all radial measurements of such an electron would be the Bohr Radius.