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