1. Chapter 6 Electronic Structure of Atoms

2. Waves

3. Waves
The number of waves passing a given point per unit of time is the frequency (ν).
For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

4. Electromagnetic Radiation
Continuous spectrum
All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00x108 m/s
Therefore,
c = 

5. The Nature of Energy
Max Planck explained it by assuming that energy comes in packets called quanta.
Energy Energy
Intensity Intensity
We assume that energy increases in a continuous stream. When we add heat to a pot of water it slowly gets warmer and it will eventually boil.
In the micro world energy increases in discrete units. It increases by a full quantum or not at all. Even when energy is applied to the electron, it will never be ejected from the atom unless the quantum of energy is applied.

6. The Photoelectric Effect
The energy is carried out by particles of light called photons.
He concluded that energy is proportional to frequency:
E = h
where h is Planck’s constant 6.63x10-34 Js

7. The Photoelectric Effect
Fact # 1: Highly intense low frequency light does not eject any electrons, even if it shines on the metal surface for several days.
Fact # 2: Only when the threshold frequency is reached is that electrons will be ejected from the metal.
Fact # 3: Increasing the intensity of the light at a frequency that will cause electrons to eject results in a higher ejection rate, but all ejected electrons share the same velocity.
Fact # 4: Increasing the frequency of the light increases the velocity of the ejected electrons, but all ejected electrons share the same velocity.

8. Einstein Theory 1905
A beam of light is a stream of particles called photons.
The energy of the photon is related to its frequency according to E = h
The quantum of Planck is a particle – a photon.
If the frequency of a photon is below a certain threshold, no electrons are ejected.
All these supports the idea that there must be a one to one relationship of electron to photon.

9. The Nature of Energy
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:
c = 
E = h

10. Bohr’s Model
Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:
Electrons in an atom can only occupy certain orbits (corresponding to certain energies).
n=1
n=2
n=3
n=4

11. Bohr’s Model F = k q1 q2 Coulomb’s Law d2
Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.
The force of attraction between the electrons and the nucleus (protons) determine the distance between the energy levels and the nucleus and therefore the distance between the outermost electrons and the nucleus. (atomic radius)
F = k q1 q2 Coulomb’s Law d2

12. Bohr’s Model
Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by
E = h

13. Bohr’s Model
The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:
E = −RH
( ) 1
nf2
ni2 -
where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron.

14. Line spectra and how it explains energy levels

15. Line spectrum and energy levels
Each line represents a wavelength/frequency of an electron transition. This transition is associated to an energy.
The separation between the lines corresponds to the difference in energy between energy levels.
Since all lines are not separated equally, not all transitions happen within the same energy levels and not all energy levels are equally separated.
These facts support Bohr model of the atom.

16. Bohr’s Model see animation
Based on the hydrogen atom.
The diagram shows the transitions of the electron in hydrogen as it moves from higher energy levels to energy level 1, 2, and 3.
The transitions to energy level 1 will release the greatest amount of energy. This energy forms a group of lines in the UV section of the spectrum.
Similarly the transitions to energy level 3 fall in the IR and the ones to energy level 2 fall in the Visible.

17. The Shell Model of the Atom
Ionization energy suggests that electrons are arranged in shells.
In this model electrons move in 3D shells. Each shell is an exact set distance from the nucleus, so electrons that remain in a given shell of a neutral atom are always the same distance from the nucleus.
hydrogen helium lithium

18. The Shell Model of the Atom
It requires much less energy to remove the most loosely held electron from Li because that electron is farther from the nucleus than the electrons in H and He.
The trend in the ionization energies suggests that n=2 can hold 8 electrons (Li  Ne)
The most loosely held electron in Na must be in another shell since its IE drops.
Li Be B C N O F Ne

19. The Shell Model of the Atom
Unexplained problems:
The 1st IE for boron (B) is less than for beryllium (Be).
The trend repeats in shell n=3 with Mg and Al

20. Inner Core and Valence Electrons
Inner core electrons are contained in the inner shells
Valence electrons are contained in the outer shells

21. Photoelectron Spectroscopy PES
High energy photons remove electrons from atoms.
Only one electron is removed from each atom, but that electron can come from any shell.
When the photon absorbs the electron, it is provided with the energy required to be ejected from the atom (IE) and the KE associated with its velocity after it has left the atom.
The IE for each ejected electron can be calculated by subtracting the KE of the ejected electron from the energy contained by the photon.

22. Photoelectron Spectroscopy PES
The Ionization energy decreases from left to right.
The greater the IE the closer the electrons are to the nucleus.
The height of the peaks corresponds to the number of electrons with that IE. H He Li Be
Relative number of electrons
 Ionization Energy (MJ/mol)
2.37
1.31
H: 1 electron in n = 1
He: 2 electrons in n = 1
Li: 2 electrons in n = 1 and 1 electrons in n = 2
Be: 2 electrons in n = 1 and 2 electrons in n = 2

23. Photoelectron Spectroscopy PES
The shell model does not separate the 8 electrons in n = 2. But The PES for boron does not support that.
PES data tells us that the model must be revised, as the n = 2 shell must contain 2 subshells with different IE.
Each peak corresponds to a subshell or sublevel. H He Li Be B
Relative number of electrons
 Ionization Energy (MJ/mol)
2.37
1.31
H: 1 electron in n = 1
He: 2 electrons in n = 1
Li: 2 electrons in n = 1 and 1 electrons in n = 2
Be: 2 electrons in n = 1 and 2 electrons in n = 2
B: 2 electrons in n = 1, 2 electrons in n = 2, 2s and 1 electron in 2p

24. Photoelectron Spectroscopy PES
C: 1s2 2s2 2p2 three peaks
N: 1s2 2s2 2p3 three peaks
O: 1s2 2s2 2p4 three peaks
F: 1s2 2s2 2p5 three peaks
Ne:1s2 2s2 2p6 three peaks
In all cases the size of the first 2 peaks is the same, but the third one gets larger due to the presence of more electrons in that subshell. C N O F Ne
Relative number of electrons
 Ionization Energy (MJ/mol)
The IE increases from C to Ne for the same peak, except between N and O. (will be discussed later)

25. Photoelectron Spectroscopy PES
Problem 1. How many peaks can you predict for the elements
Na through Ar?
K and Ca?
Sc?

26. Chemical models of the atom
Since atoms are very small, models must be used to explain them.
When models are not consistent with the experimental data, they need to be refined or replaced by a new one that fits the experimental data.
The shell model of the atom constructed through ionization energy was replaced with the quantum mechanical model as additional information was considered.

27. Chemical models of the atom so far
Dalton’s model is incorrect. (Mass spec demonstrates evidence that the atom is NOT indivisible and all atoms of the same element are NOT identical).
Bohr model – electrons follow circular orbits that are at exact distances from the nucleus. (the equations that predicted the energy levels of the orbits only worked for hydrogen)
Shell model – electrons circulate on the perimeters of spheres that are at exact distances from the nucleus. (PES data indicates that there are subshells within each shell)

28. Quantum Mechanics Electrons do not follow orbits.
Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.
It is known as quantum mechanics.

29. Quantum Numbers
Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.
An orbital graphically describes the space that an electron occupies 90% of the time.
An orbital is described by a set of three quantum numbers.
Every electron within a given subshell of a given atom is at the same quantized energy level.

30. s Orbitals

31. p Orbitals

32. d Orbitals

33. Energies of Orbitals
For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.
That is, they are degenerate.

34. Energies of Orbitals
As the number of electrons increases, though, so does the repulsion between them.
Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate and they split.

35. Spin Quantum Number, ms
In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.
The “spin” of an electron describes its magnetic field, which affects its energy.

36. Pauli Exclusion Principle
No two electrons in the same atom can have exactly the same energy.
For example, no two electrons in the same atom can have identical sets of quantum numbers.

37. Electron Configurations
Distribution of all electrons in an atom.
Consist of
Number denoting the energy level.
Letter denoting the type of orbital.
Superscript denoting the number of electrons in those orbitals.
4p5

38. Orbital Diagrams Each box represents one orbital.
Half-arrows represent the electrons.
The direction of the arrow represents the spin of the electron.

39. Hund’s Rule
“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

40. Periodic Table We fill orbitals in increasing order of energy.
Different blocks on the periodic table, then correspond to different types of orbitals.

41. Electron Configurations
Orbital diagram.
Complete electron configuration.
Noble gas notation. It uses the previous noble gas.

42. Periodic Table and Electron Configurations

43. Paramagnetism and Diamagnetism
Paramagnetism: Atoms with one or more unpaired electrons are attracted to a magnetic field.
Diamagnetism: Atoms with all electrons paired will have no magnetic moment since the magnetic moments generated by each electron cancels out when they are paired.
Orbital diagram