Calculating The Effective Nuclear Charge
In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated from Coulomb's law.
However, in an atom with many electrons the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:
where
- Z is the number of protons in the nucleus (atomic number), and
- S is the average number of electrons between the nucleus and the electron in question (the number of nonvalence electrons).
S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (named after John C. Slater). Douglas Hartree defined the effective Z of a Hartree-Fock orbital to be:
where
H is the mean radius of the orbital for hydrogen, and Z is the mean radius of the orbital for an electron configuration with nuclear charge Z.
Note: Zeff is also often written Z*.
Read more about this topic: Effective Nuclear Charge
Famous quotes containing the words calculating the, calculating, effective, nuclear and/or charge:
“[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.”
—Henry Brooks Adams (1838–1918)
“Sin in this country has been always said to be rather calculating than impulsive.”
—Frank Moore Colby (1865–1925)
“... effective magic is transcendent nature ...”
—George Eliot [Mary Ann (or Marian)
“The reduction of nuclear arsenals and the removal of the threat of worldwide nuclear destruction is a measure, in my judgment, of the power and strength of a great nation.”
—Jimmy Carter (James Earl Carter, Jr.)
“I have never doubted your courage and devotion to the cause. But you have just lost a Division, and prima facie the fault is upon you; and while that remains unchanged, for me to put you in command again, is to justly subject me to the charge of having put you there on purpose to have you lose another.”
—Abraham Lincoln (1809–1865)