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Chem120A+Notes+10-3-08

Chem120A+Notes+10-3-08 - Figure 7.3 In Wavefunctions for...

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Unformatted text preview: Figure 7.3 In» Wavefunctions for 13— and 23-0rbitals for atonflc hydrogen. The 23- functinn (scaled by a factor of 2) has a node at r = 2 buhr. Figure 7.4 h Cflfltfllll‘ map if 13 urbital in tha x, y-plane. Figure 7.5 Ir Scatter plot 0f Electmn pasition mea- suraments in a hydrogen 1:: orbital. r/bohr Figure 7.5 Iv- Donaity pm“) and radial distribution function D(r) for a hydrogen 13 orbital. TABLE 7.1 I Real Hydrogenic Orbitals in Atomic Units Iable: 23/2 $23 = (1 _ E) 8—2372 152p; z w = (27 — 132:» + 22%2 {2’73 33 Elm ) fizfifl —Zr 3 79173;); = W (5 — Zflze f ¢3px, $331, analogous 27W 22 2 z /3 3 _ — P‘ ”22 81m ( r )6 «252”? _ mdfl W 2:): e 2’73 mafia, $39!” analflgnus 3:: H 1| 0:: 43:33 1 Lyman Balmer :1 It Fl ['1 E=U E=-1.51 E:—3.4O E=—13.0U av Figure 7.7 h Energy levels 0f atflnflc hydmgan. —1l} —5 CI 5 1D Figure 7.8 I» Centaur plat 0132;); orbital. Negative values are shown in red. Scale units in behrs. 0.1 _-"£“_ -,'-' “- Figure 7.1 1 P Some radial distribution functions. Fig. 3.2. Potential energy (lower curve) and ground-state wave function (upper curve) for the electron in a hydrogen atom. V51 (1") (a) | E I an 1" w I W) (b) 03E) 9' PM = 4mm E (c) 1 l I an 3" (d) Fig. 3.4. Ground-state of the hydrogen atom: (a) wave function 11/10»), ( ability density 4x130), (c) radial distribution P1(r), and (a) classically f region. ‘ O Effective potential energy, Lg. Radius, r Hg. 10.2 The effective potential energy of an electron in the hydrogen atom. When the electron has zero orbital angular momentum, the effective potential energ}.r is the Coulombic potential energy. When the electron has nonzero orbital angular momentum, the centrifugal effect gives rise to a positive contribution that is very large close to the nucleus. We can expect the i = 0 and let 0 wavefunctions to be very different near the nucleus. Wavefunetion, 4%“ Radius, r Fig. 10.3 Close to the nucleus, orbitals with Z: 1 are proportional to r, orbitals with Z: 2 are proportional to 1'2, and orbitals with I: 3 are proportional to r3. Electrons are progressively excluded from the neighbourhood of the nucleus as I increases. An orbital with l = 0 has a finite, nonzero value at the nucleus. 0 7.5 15 22.5 (e) erau (fl ' Zn’a'o The radial wavefunctions of the first few states of hydrogenic atoms of atomic number Z. Note that the orbitals with Z: 0 have a vi?" 0 and finite value at the nucleus. The horizontal scales are different in each case: orbitals with high principal quantum numbers are it distant from the nucleus. Energy of widely separated stationary electron and nucleus 0 —hcfi?H 3 9 —thH 2 4 > 2’ ID I: m - Classrcally allowed energies —thH 1 H9195 The energy levels of a hydrogen atom. The values are relative to an infinitely separated, stationary electron and a proton. ...
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