PPT Spectroscopy-I Electronic Spectroscopy of Atom

ELECTRONIC SPECTROSCOPY OF ATOM

By Yusuf Wicaksono and Regi Kusumaatmadja

INTODUCTION ●

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Electronic Spectroscopy of atom is the study of transitions ( absorption or emission ) between electronic states of an atom. Atoms are unique in this respect as they have only electronic degree of freedom. To understand electronic spectroscopy of atom, it is require to understand spectra of atom from alkali metal, Hydrogen, Helium, alkaline earth metal and other polyelectronic atom.

OUTLINE ●

Theory of Electronic Spectroscopy of Atom

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Apparatus of Electronic Spectroscopy of Atom

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Application of Electronic Spectroscopy of Atom

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Paper About Electronic Spectroscopy of Atom

THEORY OF ELECTRONIC SPECTROSCOPY ●

Atoms and Quantum Number of Atom

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Angular Momentum of Electrons in Atom

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Spectra of Varies Atoms

HAMILTONIAN OF POLYELECTRONIC ATOM ●

Recall Hamiltonian for hydrogen atom or hydrogen-like ions ( He+, Li2+, etc. ) which is have single electron: 2

ℏ Ze2 2 H= ∇ − 2μ 4 π ϵ0 r ●

Meanwhile for polyelectronic atom, the Hamiltonian should be 2

ℏ Ze2 e2 2 H= ∑ ∇ i −∑ 4 π ϵ r + ∑ 4 π ϵ r 2μ i i 0 i i< j 0 ij

which the third term is electron-electron repulsion interaction. ●

Schroedinger equation from Hamiltonian above is difficult to be solve, Using Hartree's approximation the Hamiltonian became 2

ℏ Ze2 2 H= ∇ i −∑ + ∑ V (r i) ∑ 2μ i i 4 π ϵ0 r i i

which mean the contribution to the potential energy due to electron repulsion as a sum of contribution from individual electron

EFFECT OF ELECRON REPULSION ●

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The effect of electron repulsion is remove degeneracy energy in hydrogen atom. In polyelectronic atom, the energy not only depends to quantum number n but also quantum number l The value of Ei for particular orbital increases with the nuclear charge of the atom Hydrogen atom energy level

Polyelectronic atom energy level

1s

POLYELECTRONIC ENERGY LEVEL ●

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Feeding in electron to energy level follows two principle; Aufbau's principle and Pauli exclusion principle The two principles forbid electron to have same set of quantum number n, l, ml and ms The total electron can fill energy level for any particular of n and l is 2(2l + 1). In polyelectronic atom, there are term of configuration and state, which is both of them is different –

Configuration describe the way in which electrons are distributed among various orbital

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Configuration may gives rise to more than one states

MOMENTUM ANGULAR OF ELECTRON ●

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Each electron in an atom has two possible kinds of angular momentum; orbital angular momentum and spin angular momentum The magnitude of orbital angular momentum is

[l(l+1)] ●

1/ 2

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ℏ=l ℏ

The magnitude of spin angular momentum is

[s (s +1)]1 /2 ℏ=s * ℏ ●

For electron having orbital and spin angular momentum there is a quantum number j ( angular momentum total ) which is have magnitude

[ j( j +1)]1/ 2 ℏ= j * ℏ

MAGNETIC MOMENT OF ELECTRON ●

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Electron circulating in an orbit give arise current flow and cause magnetic moment Magnetic moment which is arise from orbital momentum angular is called magnetic moment orbital (μL). Electron spinning about its own axis arise magnetic moment called magnetic moment spin (μS). The vector between l and μL also s and μS opposite each other.

MOMENTUM ANGULAR COUPLING ●

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Interaction between orbital and spin magnetic moment give arise coupling of the angular momentum The strength of coupling (spin-orbit coupling) depends on the atom concerned The possibility interaction between angular momentum is –

Spin one electron with spin other electron

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Spin one electron with own orbital angular momentum

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Orbital one electron with orbital other electron

There are two approximation to study about interaction between angular momentum: –

Coupling between spin-spin and orbital-orbital momenta neglected, but coupling between total momentum (j) week but appreciable

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Coupling between spin-orbital has been neglected but assume coupling between orbital-orbital is strong and between spin-spin is week but appreciable. (Russel-Saunders coupling).

NON EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION ●

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Non-equivalent electrons = those that have different value of either n or l. ( example: 3p1 3d1 or 3p1 4p1). [ ll coupling ] : Consider two electron, n1l1 (electron 1) and n2l2 (electron 2) have ll coupling. The total orbital angular momentum is

L=l 1 +l 2, l 1 +l 2 −1,.... ,|l 1−l 2| with magnitude 1/ 2

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[ L(L+1)] ℏ=L ℏ ●

Example : The two electron = 2p13d1, Total angular momentum (L) = 3,2 or 1 and the magnitude is 121/2, 61/2 or 21/2 hbar.

NON EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (2) ●

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The term of the atom are labelled S, P, D, F, G, …. corresponding to L = 0, 1, 2, 3, 4, …. Example : configuration two electron = 2p13d1; L = 1,2 or 3; term = P D F. For filled sub-shell, L = 0. It is because ML = L, L-1, …. , -L, where ML = Σi(ml)i = 0. Example : we have atom Carbon in exited configuration = 1s2 2s2 2p1 3d1. In 1s1 and 2s2, L = 0 and 2p1 3d1, L = 3,2 or 1 arises term F D P.

NON EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (3) ●

[ ss coupling ] : Consider two electron with s = ½, the magnitude is (3/2)1/2. The total spin angular momentum (S) is

S =s 1 +s 2, s1 + s2 −1,.... ,|s1 −s 2| for two electron the value of S will be 1 or 0. And the magnitude of S is

[S (S+1)]1 /2 ℏ=S * ℏ and the value of magnitude of S will be only 0 or 21/2 hbar. ●

Total spin angular momentum indicate total states in term S, P, D, F, …. where total states can be represented by 2S+1. ( example: S = 0, total states = 1 (singlet). If S = 1, total states = 3 (singlet) )

NON EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (4) ●

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The label of total states write as pre-superscript to the S, P, D, F, …. or we can write 2S+1(S, P, D, F, ….) For two electron, S = 0 because MS = S, S-1, …., -S where Σi(ms)i = 0 so MS = Σi(ms)i = 0. For all occupied orbital are filled, the terms will be arise only 1S. So if we have Carbon atom with configuration 1s2 2s2 2p1 3d1 the term will be have is 1P 1D 1F for singlet and 3P 3D 3F for triplet.

NON EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (5) ●

To know what states is possible in one term, it will be using total angular momentum (J), where J is

J =L+S , L+S −1,.... ,|L−S| and the magnitude is 1 /2

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[J (J +1)] ℏ=J ℏ ●

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The states of term is express by 2S+1LJ In example if we have Carbon atom with configuration 1s2 2s2 2p1 3d1, the possibility states is 1

P1 3P0 3P1 3P2 1D2 3D1 3D2 3D3 1F3 3F2 3F3 3F4

EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION ●

Equivalent electron = those that have same n and l example : Carbon ( ground configuration ) = 1s2 2s2 2p2

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In equivalent electron we must consider to not violent Pauli exclusion principle; pair of quantum number (ms) and (ml) cannot simultaneously have same value for different electron. Electron is indistinguishable

EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (2) ●

Consider Carbon with configuration 1s2 2s2 2p2. The term arising from 2 equivalent p electron is

EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (3) ●

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Comparing between non-equivalent term Carbon which is 1S 3S 1P 3P 1D 3D (first excitation configuration) and equivalent term of Carbon which is 1S 3P 1D show that Pauli exclusion rule forbid 3S 1P 3D. Another comparison show below:

EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (4) ●

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HUND RULES = Determine which of the term arising from equivalent electron lies lowest in energy HUND RULES : 1) Of the term arising from equivalent electron those with the highest multiplicity lie lowest energy. 2) Of these, the lowest is that with the highest value of L example : ground configuration Carbon has term 1S 3P 1D. The term with highest multiplicity = 3P. So the ground state

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Consider there is splitting of term by L·S coupling, which is propotional with J

E J − EJ −1=A J If A > 0 multiplet normal and if A < 0 multiplet inverted ●

So there is additional rules for ground terms which tell us whether a multiplet arising from equivalent electron is normal or inverted

EQUIVALENT ELECTRON RUSSELSAUNDERS COUPLING APPROXIMATION (5) ●

Normal multiplets arise from equivalent electron when a partially filled orbital is less than half full example : Carbon ground configuration = 1s2 2s2 2p2

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Equivalent and less than half-full = normal multiplet

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The lowest term is 3P with states 3P2 3P1 3P0

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The ground states is 3P0

Inverted multiplets arise from equivalent electrons when a partially filled orbital is more than half-full example : Oxygen ground configuration = 1s 2 2s2 2p4 –

Equivalent and more than half-full = inverted multiplet

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The lowest term is 3P with states 3P2 3P1 3P0

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The ground states is 3P2

THE FINE STRUCTURE OF HYDROGEN ATOM SPECTRUM ●

The selection rule for hydrogen atom is Δn = anything, Δl = ± 1 only

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There is selection rule for j, which is Δj = 0, ±1

THE SPECTRUM OF LITHIUM AND OTHER HYDROGEN-LIKE SPECIES ●

The selection rule for hydrogen lithium and other hydrogen-like is like hydrogen which is Δn = anything, Δl = ± 1 only

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There is selection rule for j is like hydrogen too, which is Δj = 0, ±1

THE SPECTRUM OF HELIUM AND THE ALKALINE EARTHS ●

The relevant selection rules for many-electron systems are: ΔS = 0, ΔL = ±1, ΔJ = 0, ±1

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Note that, with J = 0 cannot make a transition to another J = 0 states.

APPARATUS OF ELECTRONIC SPECTROSCOPY OF ATOM ●

Photoelectron Spectroscopy Theory

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Experimental Method –

Source of Monochromatic Ionizing Radiation

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Electron velocity analysers

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Electron detector

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Ionization process and Koopmans' theorem

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Photoelectron spectra and their interpretation –

UV photoelectron spectra of atom

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X-ray photoelectron spectra of atom

PHOTOELECTRON SPECTROSCOPY (THEORY) ●

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Spectroscopy will be use for electronic spectroscopy of atom is photoelectron spectroscopy Photoelectron spectroscopy involves the ejection of electron from atoms following bombardment by photon Electron will be ejected if threshold frequency is reached, because the energy from photon equal to work function of the sample. hυt = Φ

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If frequency of photon higher than threshold frequency, electron will have kinetic energy when ejected hυt = Φ + ½ mev2

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For samples in the gas phase equation above will be hυt = I + ½ mev2

PHOTOELECTRON SPECTROSCOPY (THEORY) [2] ●

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Photoelectron spectroscopy have many type, but the most essential methods for atom is Ultraviolet Photoelectron, X-ray Photoelectron

Process in XPS and UPS is ejection of photoelectron following interaction of the atom which is ionized to produced singly charged A+ M + hυ → M+ + e

EXPERIMENTAL METHOD ●

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In UV or X-ray photoelectron spectrometer, sample in the target chamber is bombarded with photons and then photoelectron are ejected in all direction Electron energy analyser will be separates the electrons according to their kinetic energy After that spectrum will be recorded by electrons detector in the number of electron per unit time as a function of binding energy or ionization energy

EXPERIMENTAL METHOD – MONOCHROMATIC SOURCE [ ULTRAVIOLET ] ●

Ultraviolet Photoelectron Spectroscopy : –

Source providing 20 eV – 50 eV → the energy required to ionized electron from lowest energy ionization ( around 10 eV ) and higher-energy ionization

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Source produced by a discharge in He or Ne gas resulting in emission of far-UV radiation from the atom or positive ion ●

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Helium I radiation : Helium discharged produce 21.22 eV radiation due to the 21P1(1s1 2p1) – 11S0(1s2) Helium II radiation : Helium is ionized predominantly to He+. The radiation is due mainly from n = 2 to n = 1 with energy 40.81 eV. Neon radiation : Neon discharged produce 16.67 eV and 16.85 eV.

EXPERIMENTAL METHOD – MONOCHROMATIC SOURCE [ X-RAY ] ●

X-ray Photoelectron Spectroscopy –

Source used of X-ray radiation are MgKα and AlKα ( Kα mean that an electron has been ejected from the K shell and the vacancy will fill by electron in L shell.

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The MgKα produce energy primarily 1253.7 eV and 1253.4 eV; the AlKα produce energy primarily 1486.7 eV and 1486.3 eV.

EXPERIMENTAL METHOD – MONOCHROMATIC SOURCE [ BREMSSTRAHLUNG ] –

In addition there are is a weak bremsstrahlung radiation and also several satellites lines accompanying both doublets

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Bremsstrahlung radiation is results from collisions between the electron of the beam and the atoms of the target material which is make the electron decelerated and a photon X-ray energy is produced.

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The both of them can be remove by monochromator

EXPERIMENTAL METHOD – MONOCHROMATIC SOURCE [ X-RAY MONOCHROMATOR ] –

Component and arrangement of monochromator is : ●

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Q is Quartz crystal which is bent to form a concave X-ray diffraction grating. ( Quartz used to get narrow band ) X-Ray source and Target Chamber placed in position on the Rowland circle

Monochromator is useful too for narrowing the otherwise broad lines.

EXPERIMENTAL METHOD – MONOCHROMATIC SOURCE [ SYNCHROTRON RADIATION SOURCE ] ●

An important source of both far-UV and X-ray radiation is synchrotron radiation source (SRC).

EXPERIMENTAL METHOD - ELECTRON VELOCITY ANALYSER ●

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Measurement of the kinetic energy of the photoelectron involves measurement of their velocity Measurement of the velocity of photoelectron has been achieved by various type of analysers, two basic types of electron analyzers are encoutered: –

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Retarding field analyser ●

Slotted grid analayser

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The spherical grid analyser

Dispersion analyser ●

The Cylindrical analayser

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The Hemispherical analysers

EXPERIMENTAL METHOD - ELECTRON VELOCITY ANALYSER [ SLOTTED GRID ANALYSER ] ●

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Component of analyser: –

The slotted grid

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The retarding grid

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Collector

How the analyser work is: –

The photoelectron are generated along the axis of cylindrical electron collector.

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A retarding potential, applied to the cylindrical retarding grid

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An increasing potential difference applied across the grids to retard the electron flowing from the source to the collector

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At a high enough potential difference, electrons of energy E2 will be retarded and the collector signal will be decrease

EXPERIMENTAL METHOD - ELECTRON VELOCITY ANALYSER [ SPHERICAL GRID ANALYSER ] ●

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The spherical grid analyser has the advantage of collecting all the photoelectrons generated at the center, in whatever direction they are travelling There are two spherical retarding grid in this design The uses of two grid is same in slotted grid analyser Slotted grid analyser and spherical grid analyser useful mainly for gaseous sample Retarding-field instruments are relatively simple and efficient but do not have the high resolution of dispersion system

EXPERIMENTAL METHOD - ELECTRON VELOCITY ANALYSER [ CYLINDRICAL ANALYSIS ] ●

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Cylindrical analyser used to gaseous sample and solid sample. The process of the analyser is: –

In this analyser electron beam is deflected by an electrostatic field in such a way that the electron travel in a curved path.

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The radius of curvature is dependent upon the kinetic energy energy of the electron and the magnitude of the field

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By varying the field, electron of various kinetic energies can be focused on the detector

The relationship between the plate voltage V1 and V2 and the energy of the electron Ek is given by V 2−V 1=2 E k R log (

R1 ) R2

EXPERIMENTAL METHOD - ELECTRON VELOCITY ANALYSER [ HEMISPHERICAL ANALYSER ] ●

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The work same as cylindrical analyser but has the advantage of collecting more photoelectron. Consisting of two concentric plates which are parts of hemispheres, socalled spherical sector plates This analyser often used in a spectrometer which operates for both UPS and XPS

EXPERIMENTAL METHOD – ELECTRON DETECTOR ●

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Detector may be a simple electrometer when using a cylindrical or spherical grid analyser Other type analyser need electron multiplier to increase sensitivity. Electron multiplier consists of a number of dynodes, each of which produces more electron than it receives. Alternatively, multichannel electron multiplier in the focal plane of the analyser can be used to collect simultaneously electron with a range of energies

EXPERIMENTAL METHOD – RESOLUTION ●

XPS is usually limited by the line width of the ionizing radiation

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Resolution in UPS depends on such factor as

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The efficiency of shielding of the spectrometer from stray magnetic field

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The cleanliness of the analyser surface

Resolution of UPS decrease when the kinetic energy of photoelectron is below about 5 eV; The highest resolution obtained is about 4 meV

IONIZATION PROCESS AND KOOPMANS' THEOREM ●

Ionization process in XPS and UPS as before can be write as: M + hυ → M+ + e –

When M is an atom the total change in angular momentum for process above must obey selection rule Δl = ± 1

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Meanwhile the photoelectron can take away any amount of momentum

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Example: ●

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Electron removed from d orbital of M which is l = 2, so the photoelectron carries away l = 1 or 3 depend on Δl = -1 or +1. So the wavefunction of of a free electron has just p and f character

The energy required to eject an electron from an orbital is a direct measure of the orbital energy. Koopmans theorem : for a closed-shell atom the ionization energy of an electron in a particular orbital approximately equal to the negative of the orbital energy calculated by a self-consistency field method

IONIZATION PROCESS AND KOOPMANS' THEOREM [2] ●

In equation Koopmans' theorem can be write as SCF

I i≃−ϵ i

The negative sign is due to the convention that orbital energies εi are negative ●

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In the level of simple valence theory this theorem is strong, but with more accurate theory this theorem no longer strong The three most important factor that may contribute to Koopmans' theorem relate to the main deficiencies in SCF calculations : –

Electron reorganization. The orbital in M+ are not quite the same as in M because there is one electron fewer. SCF

ϵi –

Electron correlation

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Relativistic effect

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SCF

(M )≠ϵi

(M )

PHOTOELECTRON SPECTRA AND THEIR INTERPRETATION ●

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The most important information derived from photoelectron spectra is the ionization energies for valence and core electrons Before the development of photoelectron spectroscopy very few of these ware known For core electrons ionization energies were previously unobtainable and illustrate the extent to which core orbitals differ from the pure atomic orbital pictured in simple valence theory Using Koopmans' theorem for closed-shell atom ionization, we shall see UV photoelectron spectra and X-ray photoelectron spectra

PHOTOELECTRON SPECTRA AND THEIR INTERPRETATION [ UV PHOTOELECTRON SPECTRA ] ●

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The atom will be use for example is Ar with UV source is He I (21.22 eV) He I give removal of electron at 3p orbital Ar(KL 3s2 3p6) → Ar+(KL 3s2 3p5)

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State arising from Ar = 1S0 and state arising from Ar+ = 2P1/2 and 2P3/2 with 2P3/2 is ground state. There are splitting by 0.178 eV because spin-orbit coupling The Ionization process Ar+(2P3/2) – Ar(1S0) is approximately twice as intense as Ar+(2P1/2) – Ar(1S0) because of degeneracy

PHOTOELECTRON SPECTRA AND THEIR INTERPRETATION [ X-RAY PHOTOELECTRON SPECTRA ] ●

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If ionization is done by more energetic X-ray sources, more peak are observe in the spectra of Argon The horizontl scale gives the binding energy which is the energy required to remove the electron to form a particular state of the ion and is calculated by subtracting the photoelectron energy from the photon energy

TERIMA KASIH