(because the electron is bound)
iii) n= by definition has
energy zero, hence E E1
= ionization energy (13.6 eV)
= Ry (109 677 cm1)
Important
Slide 57
Corresponds to the total removal of an electron (i.e., transition to n=)
Since in the ground state Hatom n=1 is the highest occupied atomic orbital, the ionization energy is given by:
Important
See later for Koopman’s theorem
Slide 58
Slide 59
A) Other single electron atoms/ions (Hlike atoms)
The ions He+, Li2+, Be3+, B4+, . etc. are said to be with the Hatom (same electron configuration).
Again ns, np, nd etc. levels are degenerate.
However the attractive Coulomb force is much bigger due to the Z+charge of the nuclei.
The energy levels are given by a similar expression to that for the Hatom with the inclusion of a :
Slide 60
Note that exponential function decays faster as Z
Orbitals contract with increasing Z
Slide 61
Orbitals contract with increasing Z
Y2s
Slide 62
Hlike atoms/ions : Summary
The orbitals contract with increasing Z
The effect of the Z2 term is to increase the energy level spacing.
E.g., The energy level spacings in the He+ spectrum are approx. 4 times those in the Hatom whilst in Be3+ they are 16 times larger (Z=4).
This is only approximate because of the slight mass dependence of the Rydberg constant.
Ry(H) = 109 677cm1 Ry(mass) = 109 737 cm1
Compare ionisation energies for IE(H) = 13.6eV, IE(He+) = 54.4eV, IE(Li2+)=122.4eV
Slide 63
B) Multielectron Atoms
Schrödinger equation cannot be solved analytically anymore (apart from He)
Need to develop an approximate picture for multielectron atoms
2+


Helium atom
Slide 64
The orbital approximation in quantum mechanics
Y(r1, r2, …) = y(r1) y(r2)….
Total wavefunction of many electron atom
Each electron is occupying its individual orbital with nuclear charge modified to take account of all other electrons’ presence (repulsion!)
Slide 65
The orbital approximation in words