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Chapter 13
Atomic Structure and Atomic Atomic Structure and Atomic SpectraSpectra
Table 10.1 Hydrogenic radial wavefunctionsTable 10.1 Hydrogenic radial wavefunctions
n2e)(Ln
N)r(R l,n
l
l,nl,n
oaZr2
LLn,ln,l(p) is an (p) is an associatedassociated
Laguerre polynomialLaguerre polynomial
R = (NR = (Nn,ln,l) (polynomial in r) (decaying exponential in r)) (polynomial in r) (decaying exponential in r)
Fig 10.4
Potential energy between an electron and proton
in a hydrogen atom
ao
++ + -- -
One-electron wavefunction = an atomic orbital
Fig 10.5 Energy levels of a hydrogen atom
2H
n
hcR
• Principle quantum number
n = 1, 2, 3,...,∞
• Angular momentum QN
l = 0, 1, 2,..., (n-1)
• Magnetic QN
ml = -l, ..., +l• Spin QN
ms = ±1/2
in cm-1
Bound
states
Unbound
states
Fig 10.7 Energy of orbitals in a hydrogenic atom
Energy only depends on principal quantum number n
En = -RH ( )1n2
n=1
n=2
n=3
Why the degeneracy?!
Fig 10.9 Balance of kinetic and potential energies that
accounts for the ground state of hydrogenic atoms
Fig 10.10 Electron densities of 1s and 2s orbitals
in a hydrogen atom
Fig 10.11 Boundary surface of an s-orbital within which
there is a 90% probability of finding Mz. Electron
r90
Orbitals don’t have edges!
Fig 10.13 Probability density for an s-orbital
s-orbital is
spherically symmetrical
Fig 10.14 Radial distribution function for an s-orbital
oaZr2
eraZ
4)r(P 2
3
o
Fig 10.15 Boundary surfaces for p-orbitals
ml = -1 ml = 0 ml = 1
Fig 10.16 Boundary surfaces for d-orbitals
ml = -2 ml = -1 ml = 0 ml = 1 ml = 2
Fig 10.17 Grotrian diagram for the spectrum of H
Selection rules for allowed
transitions:
Δl = ±1 and Δml = 0, ±1
• A photon can carry only one unitof angular momentum
• Some transitions are allowed,other are forbidden