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Now, there are in actuality four electrons in this box. There is a rule of quantum mechanics called the Pauli Exclusion Principle that says no more than two electrons can occupy the same orbital. 5. The energy levels of the particle in a box are given by Equation (A. 14). An electron in the n = 2 level can in theory absorb a photon of light and undergo a spectroscopic transition to the n = 3 level. Thus, the resulting absorbance feature would appear at an energy that is the difference between n = 2 and n = 3 levels.

This means that b, the F-intercept of the hne, should equal zero. In other words, the Une should pass through the origin. Sometimes plots of absorbance versus concentration have nonzero F-intercepts. At the origin the analyte concentration is zero, so should not the absorbance be zero as well? Not necessarily; part of the reason is absorbance by interferents. For example, solvent or impurity molecules may absorb at the same wavenumber as the analyte. Noise is also a culprit; the line may not pass exactly through zero due to the noise in the absorbance data.

A 180° angle has n radians, a 360° angle contains 2n radians, etc. Thus, Equation (A. 11) is true if CL = nn (A. 12) where n = 0,1,2,3... which simply depends on the fact that the sin of multiples of n radians is zero. Combining Equation (A. 12) with C = {2mE)^^^/fi gives mi = {2mE)^'^L/fi (A. 13) We next remember that fi = h/2n, substitute this into Equation (A. 13), and rearrange to solve for E as follows: E = h^n^/SmL^ (A. 14) where n = 0,1,2,3... the quantum number This is the equation we have been seeking; it gives the quantized energy levels for the particle in a box.

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Essential Oils Analysis by Kubeczka

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