Atomic Structure and Atomic Spectra

Atomic Structure and Atomic Spectra Chapter 13

Table 10.1 Hydrogenic radial wavefunctions R = (Nn,l) (polynomial in r) (decaying exponential in r) Ln,l(p) is an associated Laguerre polynomial

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 Unbound states in cm-1 • 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 Bound states

( ) En = -RH 1 n2 n=1 n=2 n=3 Fig 10.7 Energy of orbitals in a hydrogenic atom Energy only depends on principal quantum number n 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

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 • A photon can carry only one unit • of angular momentum • Some transitions are allowed, • other are forbidden Selection rules for allowed transitions: Δl = ±1 and Δml = 0, ±1

Atomic Structure and Atomic Spectra