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Unformatted text preview: Figure 7.3 InÂ» Wavefunctions for 13â€” and 230rbitals for atonï¬‚c hydrogen. The 23
functinn (scaled by a factor of 2) has a node at r = 2 buhr. Figure 7.4 h Cï¬‚ï¬‚tï¬‚lllâ€˜ map if 13 urbital in tha x, yplane. Figure 7.5 Ir Scatter plot 0f Electmn pasition mea
suraments in a hydrogen 1:: orbital. r/bohr Figure 7.5 Iv Donaity pmâ€œ) 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) 8â€”2372 152p; z
w = (27 â€” 132:Â» + 22%2 {2â€™73
33 Elm ) ï¬zï¬ï¬‚ â€”Zr 3
79173;); = W (5 â€” Zï¬‚ze f Â¢3px, $331, analogous 27W 22 2 z /3
3 _ â€” Pâ€˜
â€22 81m ( r )6 Â«252â€? _
mdï¬‚ W 2:): e 2â€™73 maï¬a, $39!â€ analï¬‚gnus 3::
H 1
0:: 43:33 1 Lyman Balmer :1
It Fl
['1 E=U
E=1.51
E:â€”3.4O
E=â€”13.0U av Figure 7.7 h Energy levels 0f atï¬‚nï¬‚c hydmgan. â€”1l} â€”5 CI 5 1D Figure 7.8 IÂ» Centaur plat 0132;); orbital. Negative values are shown in red. Scale units
in behrs. 0.1 _"Â£â€œ_ ,'' â€œ Figure 7.1 1 P Some radial distribution functions. Fig. 3.2. Potential energy (lower curve) and groundstate 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. Groundstate of the hydrogen atom: (a) wave function 11/10Â»), ( ability density 4x130), (c) radial distribution P1(r), and (a) classically f
region. â€˜ 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%â€œ 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 ï¬nite,
nonzero value at the nucleus. 0 7.5 15 22.5
(e) erau (fl ' Znâ€™a'o The radial wavefunctions of the ï¬rst few states of hydrogenic atoms of atomic number Z. Note that the orbitals with Z: 0 have a
vi?" 0 and ï¬nite 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
â€”hcï¬?H 3
9
â€”thH 2
4
>
2â€™
ID
I: m 
Classrcally
allowed
energies â€”thH 1 H9195 The energy levels of a hydrogen
atom. The values are relative to an inï¬nitely separated, stationary electron and
a proton. ...
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 Spring '07
 Whaley
 Physical chemistry, pH

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