sample3.shortdraft - The Pauli Exclusion Principle(This...

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“ The Pauli Exclusion Principle” (This “short’ draft received a B). Although students in many levels of chemistry and physics use the Pauli exclusion principle at an elementary level, many of them do not actually understand the concept which dictates this law. As many people know it, the Pauli exclusion principle simply states that each orbital, which holds two electrons, cannot contain two electrons of the same spin projection (m s = ±1/2). In other words, if an orbital has one “spin-up” electron, the level can only be filled up with a “spin-down” electron. This rule is used blindly by many students when examining the makeup of atoms on the periodic table. Let’s examine the theory behind this very important principle. In order to understand the Pauli exclusion principle fully, some basic knowledge of quantum mechanics is required. Quantum mechanics is the study of small-scale phenomena that cannot be described in classical terms. 1 Whereas classical mechanics is governed by Newton’s three laws, quantum mechanics is governed by the Schrödinger equation. In quantum mechanics, every system is assigned a wave function, Ψ (x,t) which follows this equation, defined as H Ψ (x,t) = i ħ δΨ (x,t) δ t , (1) where “H”, is the Hamiltonian, “ Ψ (x,t)” is the wave function, “i” is an imaginary number, ħ ” is a constant, and δΨ (x,t) δ t is the first derivative of the wave function with respect to time. The wave function is a function of both position and time. When properly
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