Alkali atom spectra , atoms with one valence electron.ppt

Alkali atom spectra , atoms with one valence electron

1. Chapter 5 Alkali atoms

2. Properties of elements in periodic table
The Alkali metals

3. Alkali atoms
Alkali atoms: atoms only has a valence electron which is weakly
bound outside, and all other electrons are in closed shells.
Shell structures:
3
Li
11
Na
19
K
37
Rb
55
Cs
87
Fr
(1s)
2
(2s)
1
(1s)
2
(2s)
2(
2p)
6
(3s)
1
(1s)
2
(2s)
2
(2p)
6
(3s)
2
(3p)
6
(4s)
1
(1s)
2
(2s)
2
(2p)
6
(3s)
2
(3p)
6
(4s)
2
(3d)
10
(4p)
6
(5s)
1
(1s)
2
(2s)
2
(2p)
6
(3s)
2
(3p)
6
(4s)
2
(3d)
10
(4p)
6
(5s)
2
(4d)
10
(5p)
6
(6s)
1
(1s)
2
(2s)
2
(2p)
6
(3s)
2
(3p)
6
(4s)
2
(3d)
10
(4p)
6
(5s)
2
(4d)
10
(5p)
6
(6s)
2
(4f)
14
(5d)
10
(6p)
6
(7s)
1

4. Valuesaregivenfortheneutralatom,andforsingly,doublyandtriplycharged
ions.Theionisationenergyisalwaysespeciallylargeforanoblegas
configuration(closedshell).Itisespeciallylowifthereisonlyoneelectron
morethananoblegasconfiguration.
Work of ionisation for the elements with Z=1 to 20.

5. Lifting of the ldegeneracy
The alkali atoms have the next simplest spectra after those of
hydrogen atom.
The comparison shows that in the alkali atoms, the l
degeneracy (orbital degeneracy) is lifted. States with the
sameprincipal quantum number nand differentorbital
angular momentum quantum numbers lhave different
energies.
We would like to understand this effect qualitatively.

6. The ldegeneracy is lifted
Simplified term diagram for the alkali metal atoms, showing the empirical positions of the most important
energy terms.The principal quantum number nis indicated by numerals, the secondary quantum numbers l
by the letters S, P, D, and F. For comparison, the levels of the H atom are given on the right.
1) Relative to the terms of H atom, those of alkalis lie lower;
2) For larger n, the terms are only slightly different from those of Hydrogen;
3) For small l are more strongly bound and their terms lie lower in the term diagram;
4) This effect becomes stronger with increasing Z.

7. Screening effect
+Ze
R r
-e
-(Z-1)e
Model of an alkali atom
The valence electron is screened from the
nuclear charge +Ze by the (Z-1) inner
electron.
Theclosedshellissphericallysymmetric,andisstronglyboundtothe
nucleus.Thevalenceelectronislocatedatarelativelylargedistancerfrom
thenucleus.Itmovesintheelectrostaticfieldofthenuclearcharge+Ze,
whichisforthemostpartscreenedbythe(Z-1)innerelectrons.
Wedescribethescreeningeffectoftheinnerelectronstogetherwiththe
nucleuspotentialbymeansofaneffectivepotentialV
eff(r)forthevalence
electron.Inthiswaywereducetheoriginalmany-bodyproblemtoasingle-
particlesystem,andwecantreattheenergylevelsofanalkaliatomas
termsofasingle-electronatom.

8. Effective potential V
efffor an Alkali atom
At small electron-nuclear distances, V
eff has the shape of the
unscreened nuclear Coulomb potential; at large distances, the nuclear
charge is screened to one unit of charge.
Effective potential V
eff(r)
for an alkali atom

9. The screening effectof the inner
electrons can be quantitatively calculated,
if one knows their charge distribution
with sufficient accuracy. Here we only
understand it qualitatively.

10. The energy term of alkali atoms,
compare to H atom, are determined by the
quantum numbers n and l. 







22,
),(
11
lnn
Rhc
n
RhcE
eff
ln
n
eff: an effective principle quantum number, not an integer;
(n,l)= n –n
eff: the quantum defect, associated with the
quantum numbers nand l.
The quantum defect (n,l)are empirical expressions of the
different degrees of screening of the s, p, d, etc. electrons by
the electrons of the inner shells.

11. The quantum defects (n,l)for the spectra
of the Na atom:
Theempiricallydeterminednumericalvaluesforthequantum
defectarelargestforselectrons,decreasewithincreasingorbital
angularmomentumquantuml,andarelargelyindependentofthe
principalquantumnumbern.
Theyincreasedownthecolumnofalkaliatomsfromlithiumto
cesium,orwithincreasingnuclearchargenumberZ.

12. Term diagramof the
Lithium atom with the most
important transitions ---
Grotrian diagram
The term diagram permits a
classification of the spectral
lines to series.
With selection rule for optical
transitions: Δl = ±1,
The quantum number lmust
change by 1.

13. Term scheme(Grotrian
diagram) of the Sodium atom.
The numbers in the diagram
indicate the wavelength of the
transition in Angstrom units.
The term diagram indicated on
the upper edge of the figure
also represent the quantum
numbers for the multiplicity
and the total angular
momentum.
With selection rule for optical
transitions: Δl = ±1,
The quantum number lmust
change by 1.

14. For the sodium atom, the three shortest-wave spectral
series decomposed from the total spectrum
The emission spectrum is a composition of these series. In absorption spectra,
normally only the principal series is observed, because in the ground state of
the Na atom the highest occupied term is the 3s term.

15. Four most important series
The principal series, with transitions from p to selectron terms:  
022
00
,
)1,(
1
)0,(
1
nn
nnnn
R
p 









The sharp or second secondary serieswith the transitions
from s to pelectron terms:  
1,
)0,(
1
)1,(
1
022
00









 nn
nnnn
R
s
n
0: the integral principal quantum number of the lowest state,
2 for Li, 3 for Na, 4 for K, 5 for Rb, 6 for Cs

16. Four most important series
The diffuse or first secondaryseries, with transitions from d to p
electron terms:  
022
00
,
)2,(
1
)1,(
1
nn
nnnn
R
d 









The Bergmann or fundamentalseries with the transitions
from f to delectron terms:  
1,
)3,(
1
)2,(
1
022
00









 nn
nnnn
R
f

17. Term scheme(Grotrian
diagram) of the Sodium atom.
For the electron with l= 0, 1,
2, 3 correspond to s, p, d, f
are historic,
p: for principal, ps;
s: for sharp, sp;
d: for diffuse, dp;
f: for fundamental, fd.
capital lettersfor terms with
several electrons in an atom;
lower case lettersfor the
terms for individual electrons.
Double D lines
(yellow)

18. The absorption spectrum
Under normal conditions, only the principal series is observed by absorption
spectroscopy, because only the ground state of the atoms is sufficiently
populated for transitions into higher states to be observed.
The lines of the principal series are resonance lines.
The best known is the D line of sodium, which is the transition 3s —3p.
The sum of the s terms can also be designated S, and of the p terms, P, so
that the sodium series can be written:
Principal series: 3S —nP
Secondary series: 3P —nS
Difuse series: 3P —nD, with n 3.
Capital letters are used for terms which apply to several electrons in an atom,
and lower case letters for the terms for individual electrons. In the alkali
atoms, which have only onevalence electron, the two notations are
equivalent.

19. Electrons in inner shells
Left: Grotrian diagram for the neutral potassium in the visible and infrared regions.
Right: term scheme for the K atom in the infrared, visible, ultraviolet and x-ray
regions. K, L, M… are inner shells.

20. homework
11.1, 11.3