1. Quantum Theory and Atomic Structure
Chapter
Quantum Theory and
Atomic Structure

2. Learn from yesterday, live for today, hope for tomorrow
Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning.
Albert Einstein

3. Light Made up of electromagnetic radiation.
Waves of electric and magnetic fields at right angles to each other.
There are many different l and f.
Radio waves, microwaves, x rays and gamma rays are all examples of EM radiation.
Light is only the part our eyes can detect.
Gamma
rays
Radio waves

4. Low energy
High energy
Radiowaves
Microwaves
Infrared .
Ultra-violet
X-Rays
GammaRays
Low Frequency
High Frequency
Long Wavelength
Short Wavelength
Visible Light

5. In 1900’s
Matter and energy were seen as different from each other in fundamental ways.
Matter was particles.
Energy could come in waves, with any frequency.
Max Planck found that the cooling of hot objects couldn’t be explained by viewing energy as a wave. Blackbody experiment

6. Results

7. Energy is Quantized Planck found DE came in chunks with size hf
DE = nhf
where n is an integer; h is Planck’s constant h = x J s
these packets of hf are called quanta

8. Einstein is next
Electromagnetic radiation is quantized in particles called photons.
Each photon has E = nhf (Plank)
Wave equation: c=lf, f= c/l
Combine this with Einstein’s E = mc2
You get the apparent mass of a photon.
De Broglie thus assigned a wavelength to every mass, m = h / (lc)

9. Spectrum Hydrogen spectrum
The range of frequencies present in light. White light has a continuous spectrum.
Called an emission spectrum because these are the colors it gives off or emits.
There are just a few discrete lines showing line spectrum
Hydrogen spectrum
434 nm
656 nm
410 nm
486 nm

10. Line spectra are
unique to each element.

11. What this means
Only certain energies are allowed for the hydrogen atom.
Can only give off certain energies.
Use DE = hf = hc / l
Energy in the in the atom is quantized.

12. Niels Bohr Developed the quantum model of the hydrogen atom.
He said the atom was like a solar system.
The electrons were attracted to the nucleus because of opposite charges.
Didn’t fall in to the nucleus because it was moving around; centrifugal force
Bohr found a flaw in Newtonian laws of mechanics (which govern large mass). They do not govern particles that have a small mass. Therefore, a new set of laws was developed.

13. The Bohr Ring Atom
He didn’t know why but only certain energies were allowed.
He called these allowed energies energy levels.
Putting Energy into the atom moved the electron away from the nucleus.
From ground state to excited state.
When it returns to ground state it gives off light of a certain energy.

14. The Bohr Ring Atom
n = 4
n = 3
n = 2
n = 1

15. The Bohr Model
Balmer created an equation that described the spectrum for Hydrogen.
= RH ( )
R = 1.10 x 107 /m n = energy level
used to calculate wavelength, frequency or energy of the light emitted in a transition from one energy level to another.
1 λ
1 nf 2
1 ni 2

16. The Quantum Mechanical Model
The Bohr Model
Only works for hydrogen atoms.
Electrons don’t move in circles.
The quantization of energy is right, but not because they are circling like planets.
A totally new approach must be taken
De Broglie said matter could be like a wave; specifically standing waves
Similar to the vibrations of a stringed instrument.
The Quantum Mechanical Model

17. Schroedinger’s Equation
What’s possible?
You can only have a standing wave if you have complete waves.
There are only certain allowed waves.
In the atom there are certain allowed waves given to each electron.
1925 Erwin Schroedinger described the wave function of the electron in 3-D;
Solutions to the equation are called orbitals which describe the energy and motion of an eֿ around a nucleus.
mathematical expression These are not Bohr orbits.
Each solution is tied to a certain energy. These are the energy levels.
Schroedinger’s Equation

18. There is a limit to what we can know
We can’t know how the electron is moving or how it gets from one energy level to another.
There is a limit to how well we can know both the position and the momentum of an object.
The Heisenberg Uncertainty Principle.

19. Probability
Distance from nucleus

20. Analogy
If you have a regular camera and try to get pictures of a bullet that was fired
A) You can take many pictures in fast succession…you get blurry images but a good sense of the speed of the bullet (don’t know the position but do know the motion of the bullet)
B) You can take one clear picture…you get a clear idea of the position but the motion of the bullet is unclear (position known but motion unclear)

21. Quantum Numbers There are many solutions to Schroedinger’s equation
Each solution can be described with four quantum numbers (n, l, ml and ms) that describe some aspect of the solution.
Principal quantum number (n) size and energy of of an orbital.
Has integer values >0
Represents the main shell

22. Quantum numbers Angular momentum quantum number, l .
Describes the shape of the orbital.
Sometimes called a subshell
integer values from 0 to n-1
l = 0 is called s sharp
l = 1 is called p principal
l = 2 is called d diffuse
l = 3 is called f fundamental

23. S orbitals one s orbital for every energy level
Spherical shaped, only 1 orientation possible
Each s orbital can hold 2 electrons
Called the 1s, 2s, 3s, etc.. orbitals.

24. P orbitals Start at the second energy level
3 different directions, x, y and z called -1,0 and 1
Each can hold 2 electrons
Total of 6 electrons if all the p orbitals (x,y and z) are filled with 2 electrons each

25. P Orbitals

26. D orbitals Start at the third energy level n = 3; l=2
5 different orientations
Each can hold
Total of 10 electrons
Orientations called -2,-1,0,1,2

27. F orbitals Start at the fourth energy level Have seven
different orientations
2 electrons
per shape for a total of 14 electrons, orientations called -3,-2,-1,0,1,2,3

28. Quantum numbers Magnetic quantum number (m l)
integer values between - l and + l
tells direction/orientation of each shape.
Shape s (l=0)
ml=0…1 orientation…called 0
Shape p (l=1)
ml=-1,0,1…3 orientations…called x,y,z
Shape d (l=2)
ml=-2,-1,0,1,2…5 orientations…
Shape f (l=3)
ml=-3,-2,-1,0,1,2,3…7 orientations…

29. Quantum numbers Electron spin quantum number (m s) Can have 2 values.
either +1/2 or -1/2
Either clockwise or counterclockwise
He has 2 electrons in the first shell
Electronic configuration of He: 1s2
The four quantum numbers of each of the 2 electrons are {n,l,ml,ms}
{1,0,0,½}, {1,0,0,-½}

30. Aufbau Principle Aufbau is German for building up.
As the protons are added one by one, the electrons fill up hydrogen-like orbitals.
Fill up in order of energy levels.

31. Increasing energy He with 2 electrons 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p3d 4d 5d 7p 6d 4f 5f
He with 2 electrons

33. Details
Valence electrons- the electrons in the outermost energy levels (not d).
Core electrons- the inner electrons.
Hund’s Rule- The lowest energy configuration for an atom is the one with the maximum number of unpaired electrons in the orbital.
C 1s2 2s2 2p2

34. Pauli Exclusion principle
no two electrons within a particular atom can have all four identical quantum numbers.
this principle means that if two electrons occupy the same energy level, same orbital and same orientation they must have opposite spin.
Eg, He: {1,0,0,½} and {1,0,0,-½}

35. Fill from the bottom up following the arrows
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
1s2
2s2
2p6
3s2
3p6
4s2
3d10
4p6
5s2
4d10
5p6
6s2
56 electrons

37. Details
Elements in the same column have the same electron configuration.
Put in columns because of similar properties.
Similar properties because of electron configuration.
Noble gases have filled energy levels.
Transition metals are filling the d orbitals

38. Examples
1. Write the electronic configuration of the first 37 atoms H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb 2. Write the condensed electronic configuration of the atoms from sodium to rubidium 3. Write the four quantum numbers for all of the electrons of the atom boron.

39. Exceptions Ti = [Ar] 4s2 3d2 V = [Ar] 4s2 3d3 Cr = [Ar] 4s1 3d5
Mn = [Ar] 4s2 3d5
Half filled orbitals.
Scientists aren’t sure of why it happens
same for Cu [Ar] 4s1 3d10
Irregular pattern repeats for the other atoms in the same group as Cr and Cu

40. Quantum Theory - summary
Quantum theory explains the wave-like nature of eֿ and the quantization of energy in the atom.
Distinct energy levels can be identified by the principal quantum number, n
The 2n² rule can still be applied. (max electrons per shell)
Experimental data (ionization energies) show that eֿ in the same energy level do not possess the same energy. (i.e subshells exist)
Evidence points to energy sublevel the number of different kinds of energy sublevel in principal level = n.
The energy sublevels are designated in order of increasing energy, s, p, d, f.

41. Some General Trends in the Periodic System
The last digit of the group number is indicative of the # of eֿ in highest energy level. (# valence electrons)
The atoms of group 18 have completely filled s and p orbitals.
The number of the period (row) is also the number of the highest energy levels occupied by electrons in the ground state. (row # is equal to the number of energy levels)
The first, second, and third transition series elements correspond to 3d, 4d and 5d orbital being filled.
Lanthanoids and actinoids are formed by filling the 4f and 5f orbitals.
Atoms of the elements in group 1 and 17 have one more and one less electron than its nearest noble gas. These are extremely reactive.

42. Periodic Table Alkali metals Noble Gases S S Halogens n=1
Alkaline Earth metals
p p p
n=2
Transition metals
n=3 d
n=4 3d
n=5 4d
n=6 5d
n=7 6d
Inner transition elements 4f 5f

43. Periodicity in outer energy-level electron configuration
Transition elements – fill orbitals 3d, 4d , 5d , 6d
Lanthanide Series – 4f orbitals
Actinicide Series - 5f orbitals (inner transition elements)
Group 1 elements → 1eֿ in outer s orbital - one more eֿ than noble gas proceeding it very reactive. metals (inert gases)
Atoms in group 2 have 2eֿ in s orbital of highest energy level. S orbitals are filled.
Group 17 elements → 2eֿ in s and 5eֿ in p at highest level one eֿ short of a noble gas configuration. → are very reactive
Last digit of group # = # of eֿ in outer energy levels. Eg: Group 16 S, O, etc) have 6eֿ at outer level s²p4 .
Group 18 have 8eֿ or completely filled s and p orbitals. → This makes them chemically inactive. s and p at highest energy level which matches row they belong to.

44. Conclusion:
1. Similarities in chemistry and physics properties are paralleled by and reflect similarities in eֿ configurations.
2. High stability when s and p orbitals are filled.
3. Chemical behaviour is related to the eֿ configuration of the highest energy level.