1. ELECTRONIC STRUCTURE OF ATOMS
Chapter 6
ELECTRONIC STRUCTURE OF ATOMS

2. Electronic Structure
Much of what we know about the energy of electrons and their arrangement around the nucleus of an atom comes from analysis of light emitted or absorbed by matter.

3. The Wave Nature of Light

4. The Electromagnetic Spectrum
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c = l . n

5. Electromagnetic Radiation
Relating frequency and wavelength
c = l . n
c = l . f
c = speed of light = 3.00 x 108 m/s
n or f = frequency in cycle per second or Hertz
= wavelength in meters
(1 nm = 1 x 10-9 m)
Note: As wavelength increases, frequency (& energy) will decrease.

6. Limitations of the Wave Model of Light
The prevailing laws of physics couldn’t explain:
Blackbody Radiation – emission of light from hot objects
Photoelectric Effect – emission of electrons from metal surfaces on which light strikes
Emission Spectra – emission of light from excited gas atoms
*Couldn’t relate temperature , intensity, & wavelength of light

7. Max Planck 1900
Solved problem by stating energy can only be released or absorbed in discrete ‘chunks’ of some minimum size.
He named this smallest quantity of energy a ‘quantum’.
He said the minimum amount of energy that an object can gain or lose is related to its frequency.
E = h . f
E = Energy in Joules
h = Planck’s Constant = x Joule-second
f = frequency in cycles per second or Hertz

8. Albert Einstein 1905
Used Planck’s Quantum Theory to explain the photoelectric effect.
Photoelectric Effect - light shining on a clean metal surface causes the surface to emit electrons if the light is of a certain minimum frequency .
He said light energy hitting a metal surface is not like a wave but like a stream of tiny energy packets called ‘photons’.
He said the energy of a photon can also be found by:
E = h * f
6. No matter the intensity, if the photons don’t have enough energy, no electrons are emitted.

9. Dual Nature of Light
Planck & Einstein are describing light as behaving like tiny particles of energy – just like matter is made of particles!
We theorize light has both a wave like and a particle like nature.
We refer to this as the DUAL NATURE OF LIGHT.

10. Bohr Model of the Atom
Ground State = when electrons are in the lowest energy state
Excited State – when electrons absorb energy & move to a higher energy state
Spectra – light energy given off when electrons return to lower energy states
LIMITATION: Bohr couldn’t explain spectra of multi-electron atoms.

11. Red, Orange, Yellow, Green, Blue, Indigo, Violet
Recall
Hot objects give off light.
When the light from a light bulb passes through a prism, a RAINBOW or CONTINUOUS SPECTRUM forms.
Remember ROY G. BIV?
Red, Orange, Yellow, Green, Blue, Indigo, Violet

12. When the light from an element gas tube passes through a prism, only some colors are seen – called a BRIGHT-LINE SPECTRUM or LINE SPECTRA.
Gas Tube
Hydrogen gas gives off pink light
Power Supply
Hydrogen’s Bright Line Spectrum as viewed through a prism 

13. This site shows the Line Spectra of Various Elements
Often Shown This Way
This site shows the Line Spectra of Various Elements

14. 1/l = (RH)( 1/n12 - 1/n22 ) Johann Balmer
Showed that the wavelengths of the four visible
lines of hydrogen fit the following formula:
1/l = (RH)( 1/n /n22 )
Where RH = Rydberg Constant
RH = x 107 m-1
n = energy level
(n2 bigger than n1)

15. Niels Bohr explains Hydrogen’s Line Specta
Bohr’s Postulates
Electrons must be in specific energy levels
An electron in an allowed energy state will not radiate energy & spiral into the nucleus
Energy is emitted or absorbed by electrons as they move from one allowed energy state to another.
The amount of energy: E = h . f

16. n is the energy level or principal quantum number
How much energy?
Bohr calculated the energy an electron possesses when in each energy state.
E = (-2.18 x J) (1/n2)
where n = 1, 2, 3, etc.
n is the energy level or principal quantum number
Note that the values are negative. The energy is lowest (most negative) for n = 1.
When the electron is completely removed and an ion forms the energy = zero.

17. E = (-2.18 x J) (1/n2)

18. And the Energy Change? DE = (-2.18 x 10-18 J) (1/nf2 - 1/ni2)
Where the initial energy state = ni
Where the final energy state = nf

19. Dual Nature of Light & Matter!
Light has both particle (photon) & wavelike properties.
Louis de Broglie suggested that matter is the same – called the de Broglie’s hypothesis.
Matter has both particle like & wave like properties.

20. De Broglie’s Hypothesis
For matter waves:
= h / (m . v)
Where: l = wavelength (meters)
m v = momentum
m = mass (kg)
v = velocity (m/s)
h = x Joule-second
Recall: Joule = 1 kg-m2/s2
This wavelength only becomes significant when dealing with tiny high velocity particles such as electrons.

21. Heisenberg’s Uncertainty Principle
Heisenberg’s Uncertainty Principle: It is inherently impossible for us to know simultaneously both the exact momentum of an object and its exact location in space.
This becomes significant when dealing with the position of electrons within an atom.

22. QUANTUM MECHANICS
LIMITATION: Bohr couldn’t explain spectra of multi-electron atoms.
It took Quantum Mechanics to explain the behavior of light emitted by multi-electron atoms.
Quantum Mechanics is one of the most revolutionary discoveries of the 20th century – the ‘new’ physics.

23. Quantum Mechanics
Heisenberg & de Broglie set the stage for a new model of the electron that would describe its location not precisely, but in terms of probabilities - called Quantum Mechanics or Wave Mechanics.

24. Erwin Schrodinger (1887 – 1961)
Proposed a Wave Equation (wave functions - y) that incorporates the dual nature of the electron.
Y2 provides info about the electron’s location.
In the Quantum Mechanical Model, we speak of the probability (Y2) that the electron will be in a certain region of space at a given instant.
We call it probability density or electron density.

25. Con’t
4) The wave functions are called orbitals. 5) Orbitals differ in energy, shape, and size. 6) An orbital can hold up to TWO electrons. 7) Four numbers can be used to describe the location of an electron in an orbital.

26. Four Quantum Numbers 1st Quantum Number =
The Principal Quantum Number (n)
2nd Quantum Number =
The Azimuthal Quantum Number or
The Angular Momentum Quantum Number (l)
3rd Quantum Number =
The Magnetic Quantum Number (ml)
4th Quantum Number =
The Spin Magnetic Quantum Number (ms)

27. Pauli Exclusion Principle
Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n, l, ml , ms )

28. 1st Quantum Number
It tells the principal energy level (shell) – ‘n’ n = 1 for the 1st PEL n = 2 for the 2nd PEL , etc. As the value of ‘n’ increases, the electron has more energy, is less tightly bound to the nucleus, and it spends more time further away from the nucleus.

29. 2nd Quantum Number
It tells the sublevel or subshell, which indicates the shape of the orbital – ‘l’
If ‘l’ = zero, the sublevel is s
If ‘l’ = 1, the sublevel is p
If ‘l’ = 2, the sublevel is d
If ‘l’ = 3, the sublevel is f
In terms of energy, s < p < d < f.
The value of ‘l’ is always at least one less than the value of ‘n’.

30. 3 rd Quantum Number ml ml ml ml ml
It tells the orientation of the orbital in the sublevel - For the s sublevel, there is only one orientation: = 0 For the p sublevel, there are 3 possible orientations: = +1, 0, -1 For the d sublevel, there are 5 possible orientations: = +2, +1, 0, -1, -2 For the f sublevel, there are 7 possible orientations: = +3, +2, +1, 0, -1, -2, -3 ml ml ml ml ml

31. 4th Quantum Number
It tells the electron spin within the orbital There are two possible values: + 1/2 or – 1/2 They indicate the two opposite directions of electron spin – which produce oppositely directed magnetic fields.
(ms)

32. Memorize

33. The “s” orbital

36. The “p” orbitals

40. The “d” orbitals

43. The “f” orbital

44. Atomic Orbitals: Putting Them Together

45. Be Able To:
Assign a set of four quantum number to each electron in an atom.
Recognize a valid set of quantum numbers
Describe atomic orbitals using quantum numbers.
Determine the # of orbitals and/or electrons in a given energy level or sublevel.
State the order of orbital energies from highest to lowest.

46. Writing Electron Configurations
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
4f14 5d10 6p6 7s2 5f14 6d10 7p6 6f14 7d10

48. Table 7-2:  Electron Configuration and Energy Levels for the Periodic Table of the Elements
Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Period
s-Orbitals
d-Orbitals
p-Orbitals
1s1
1s2
2s1
2s2
2p1
2p2
2p3
2p4
2p5
2p6
3s1
3s2
3p1
3p2
3p3
3p4
3p5
3p6
4s1
4s2
3d1
3d2
3d3
3d4
3d5
3d6
3d7
3d8
3d9
3d10
4p1
4p2
4p3
4p4
4p5
4p6
5s1
5s2
4d1
4d2
4d3
4d4
4d5
4d6
4d7
4d8
4d9
4d10
5p1
5p2
5p3
5p4
5p5
5p6
6s1
6s2 *
5d1
5d2
5d3
5d4
5d5
5d6
5d7
5d8
5d9
5d10
6p1
6p2
6p3
6p4
6p5
6p6
7s1
7s2 **
6d1
6d2
6d3
6d4
6d5
6d6
6d7
6d8
6d9
6d10
7p1
7p2
7p3
7p4
7p5
7p6
f-Orbitals
*  Lanthanoids
4f1
4f2
4f3
4f4
4f5
4f6
4f7
4f8
4f9
4f10
4f11
4f12
4f13
4f14
**   Actinoids   
5f1
5f2
5f3
5f4
5f5
5f6
5f7
5f8
5f9
5f10
5f11
5f12
5f13
5f14

49. Orbital Notation
One way: Nitrogen
Another way: Aluminum

50. Pauli Exclusion Principle
Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n, l, ml , ms ) NO! YES!

51. Hund’s Rule
Hund’s Rule – For degenerate orbitals, minimum energy is obtained when the number of electrons with the same spin is maximized.
Degenerate – means same sublevel