Chapter7-1

# Sailor uc san diego 08 1 12 45 derivation of particle

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Unformatted text preview: gths: λ= 2L/n, where n = 1, 2, 3, … Relative Energy de Broglie relationship: λ = h/mv so mv = h/λ Classical physics: E = ½ mv2 or E = ½ (mv)2/m substituting, E = ½ (h/λ)2/m = ½ h2/λ2m Since λ = 2L/n (from above) Then E = ½ h2n2/22L2m, or 2 20 n=4 15 10 n=3 5 n=2 n=1 2 nh E= 2 8mL 0 -0.2 0 Chem 6A Michael J. Sailor, UC San Diego 0.2 0.4 x 0.6 L 0.8 1 1.2 46 Stern-Gerlach Experiment: Ag atoms Screen OVEN Containing Ag Magnet The atoms split into two paths in a magnetic field This experiment tells us that each individual electron has a magnetic moment; there must be a 4th quantum number: Electron spin, or ms 47 Chem 6A Michael J. Sailor, UC San Diego Quantum numbers Quantum Number Called Describes n l Principle quantum number SIZE and ENERGY Angular momentum (Azimuthal) quantum number SHAPE ml ms Magnetic quantum number ORIENTATION Electron spin quantum number INTRINSIC ANGULAR MOMENTUM OF THE ELECTRON 48 Chem 6A Michael J. Sailor, UC San Diego Allowable values for quantum numbers Quantum Number n l ml ms values example 1, 2, 3, …∞ 0…n-1 2 -l …+l -1,0,1 +1/2, -1/2 +1/2 0, 1 49 Chem 6A Michael J. Sailor, UC San Diego Quantum numbers 50 Chem 6A Michael J. Sailor, UC San Diego Problem: Quantum numbers The set of quantum numbers n = 4, l = 2, ml = 0 and ms =+1/2 describes an electron in which orbital? a) 4f b) 4d c) 4p d) 4s e) none of the above 51 Chem 6A Michael J. Sailor, UC San Diego Answer: Quantum numbers n = 4 is principle QN (energy) l = 2 is the type of orbital: type s pdf So this is a d-type orbital value of l 0 1 2 3 ANSWER: 4d Not needed for this problem: ml = 0 is the orientation of the d-orbital ms =+1/2 is the spin on the electron 52 Chem 6A Michael J. Sailor, UC San Diego Question: How many orbitals in a shell? How many orbitals are in the n = 4 level? a) 16 b) 4 c) 32 d) 18 e) none of the above 53 Chem 6A Michael J. Sailor, UC San Diego Answer: How many orbitals in a shell? One way to think of this is that each time n increases by 1, it adds an additional l value, adding an additional set o...
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