ManyElectronHw11

# ManyElectronHw11 - MasteringPhysics Assignment Print View Page 1 of 14 Print View Physics 228 Spring 2008 Many-Electron Atoms Due at 11:59pm on

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[ Print View ] Physics 228 Spring 2008 Many-Electron Atoms Due at 11:59pm on Monday, April 14, 2008 View Grading Details Many-Electron Atoms Learning Goal: To understand how electrons are placed into subshells as atomic number increases and how this leads to the trends of the periodic table. The Schrödinger equation was highly successful at describing the hydrogen atom. Unfortunately, for any other atom the equation becomes too complex to solve, because of the interactions of the electrons with one another. Luckily, approximations can be made to get some useful results, including an explanation of the periodic table of elements! The most useful approximation is called the central field approximation . In the central field approximation, the potential energy is described by a spherically symmetric function (i.e., a function dependent only on distance from the center of the atom). In this approximation, it is assumed that the electrons closest to the nucleus ( ) experience a force from the full charge on the nucleus, but electrons further out experience force from only a fraction of that charge, because the inner electrons "screen" the nucleus. To understand this, think of the probability distribution of the electrons as a spherically symmetric charge distribution. From Gauss's law, you know that the electric field at a distance from the nucleus will be proportional to the net charge contained within a sphere of radius . Since such a sphere will always contain the positive charge on the nucleus, increasing leads to a decreased net charge, as more of the charge from the electrons is included to cancel the nucleus's charge. This approximation tells us several important things. First, since the potential is spherically symmetric, the electrons must have the same angular wave functions and as the hydrogen atom. This means that the same quantum numbers and will be used to describe electrons in many-electron atoms, and that the same rules that apply to these numbers in hydrogen will apply in many-electron atoms. Part A Which of the following gives the correct permitted values of for ? ANSWER: Page 1 of 14 MasteringPhysics: Assignment Print View 5/8/2008 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1116522

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Part B A second important result is that electrons will fill the lowest energy states available. This would seem to indicate that every electron in an atom should be in the state. This is not the case, because of Pauli's exclusion principle . The exclusion principle says that no two electrons can occupy the same state. A state is completely characterized by the four numbers , , , and , where is the spin of the electron. An important question is, How many states are possible for a given set of quantum numbers? For instance, means that with are the only possible values for those variables. Thus, there are two possible states: and . How many states are possible for ? Express your answer as an integer.
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## This note was uploaded on 11/25/2010 for the course PHYSICS 228 taught by Professor Staff during the Spring '08 term at Rutgers.

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ManyElectronHw11 - MasteringPhysics Assignment Print View Page 1 of 14 Print View Physics 228 Spring 2008 Many-Electron Atoms Due at 11:59pm on

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