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### QuantumNumbers

Course: PHYS 131, Spring 2011
School: Cuyamaca College
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Word Count: 566

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Numbers So Quantum far, we are aware of three integer quantum numbers for atoms: the principal (n &gt; 0), the angular (0 l &lt; n), and the magnetic (-l m l ). It was subsequently shown that there must be a fourth quantum number bearing a separate resonance of the electron itself when it exists apart from the atom as a particle-like entity. It is called the spin quantum number and given the unfortunate...

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Numbers So Quantum far, we are aware of three integer quantum numbers for atoms: the principal (n > 0), the angular (0 l < n), and the magnetic (-l m l ). It was subsequently shown that there must be a fourth quantum number bearing a separate resonance of the electron itself when it exists apart from the atom as a particle-like entity. It is called the spin quantum number and given the unfortunate symbol ms. This quantum number is not an integer and can have one of only two values regardless of the situation: + or . You will be expected to be able to distinguish valid sets of quantum numbers (n, l, m , ms) from invalid ones using the rules above. For instance, the set (0, 2, -3, 1) actually has four fatal flaws: n cannot be zero; l cannot be greater than n; the magnitude of m cannot be greater than l; and ms must be either or -. Each set of distinct quantum numbers represents a distinct electron in a given atom. Two cannot have the same numbers as their resonances would cancel out. This is called the Pauli exclusion principle. l l l Even though these numbers were found by the excitation to higher and higher energies of the electron in the hydrogen atom, they describe the possible component resonances of the electrons in all atoms. Chemistry texts often take the time to describe orbitals of electrons in atoms, but usually fail to mention that these are simply the regions of wave function resonance (anti-nodes) for the standing waves that compose the atoms, that give them their unique chemical characteristics. Virtually everything with which you will ever interact the has properties it does because of these resonance patterns. The principal quantum number occurs in the classical radius of the atom. This is the mean distance of the strongest resonance zone from the nucleus for any give shell. The values n = 1, 2, 3, . . . correspond to the shells K, L, M, . . .. For the moment, we will not care about these capital letters, only the numbers. The angular quantum number is said to specify the subshell. The values l = 1, 2, 3, 4, 5, . . . have been given the subshell designations s, p, d, f, g, . . .. The first four stand for sharp, principal, diffuse, and fundamental, but then the decision was made to simply start following the alphabet after f. The first subshell (l=0) of the fourth shell (n=4) is thus identified by the label 4s. Every s subshell has an overall spherical geometry and (doing the math) holds up to two electrons. Every p orbital is barbell-shaped and holds six. Every d orbital, which holds up to ten electrons, is either clover-shaped or else like a barbell with a donut around it. The f orbitals hold up to 14 electrons and are still more complicated. These numbers determine the shape of the period table. Rearranged slightly, it looks like the image below: f (14 elements) Lanth anides Actinides d (10 element s) p (6 elements) 3d transitions 4d transitions 5d transitions 6d transitions B C N O F Ne Al S i P S C l Ar Ga G e As Se Br Kr I n Sn Sb T e I X e Tl Pb Bi Po A t Rn (Elem. 113 118) s (2 elements) H He Li Be Na Mg K Ca Rb Sr Cs Ba Fr Ra No t y e t fo u n d n=1 n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9
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Cuyamaca College - PHYS - 131
(Quiz 01 was simply attendance on the first day.)First find |E|=kQ/r. This requires finding r = (x + y) = (8 + 6) = 100 = 10.So |E| = -kQ/100. (Note that Q has been replaced with -Q as specified.Next, Ex = |E|(x/r) = (-kQ/100)(-8/10) = +8kQ/1000 = kQ/1
Cuyamaca College - PHYS - 131
(Quiz 01 was simply attendance on the first day.)First find |E|=kQ/r. This requires finding r = (x + y) = (8 + 6) = 100 = 10.So |E| = -kQ/100. (Note that Q has been replaced with -Q as specified.Next, Ex = |E|(x/r) = (-kQ/100)(-8/10) = +8kQ/1000 = kQ/1
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RC CircuitsA circuit consisting of one resistor and one capacitor can exhibit exponential behaviordue to the time it takes to charge the capacitor and to the resistors prevention ofunlimited current flow. The curves shown below are intended to remind y
Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
Refraction EffectsSuppose, for ease of calculation, that we have a sample of a material with an index ofrefraction of exactly 2, and we are observing the effects of shining a laser out of thematerial to the surrounding air (n = 1) at various angles. As
Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
The Rydberg EquationUsing the quantum mechanical resonance model for the electron cloud in atoms, we canunderstand the absorption or emission of photons as resulting from the electron cloudexpanding out to a larger shell or contracting inward to a smal
Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
Thin LensesA lens wouldnt be much good if theonly function it had was to focus orspread parallel rays coming from anear-infinite distance. Fortunately,lenses perform interesting operationson rays under other conditions, too.For instance, a convergi
Cuyamaca College - PHYS - 131
Radiation ToxicityThe image at right depicts a molecule of an extremely toxic substance. Since itsinitial identification in 1917, it has been shown that a dose as little as 10 mg canresult in painful softening and swelling of the bones, yellowing and p
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Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
WaviclesIt has previously been shown to follow directly from Maxwells equations that for anelectromagnetic wave of constant average intensity, the photonic pressure P in emptyspace is given by P = P/Ac, where P is the power in the wave, A is the area,
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