Electronic Structure of Atoms

1
Electronic Structure of Atoms

• Chapter 6 in Brown LeMay

2
The Physics of Light

• Until 1900s light was considered a wave
• During the 1900s, light is considered a particle
  also

3
Electromagnetic Wave
4
General Wave Characteristics

• Amplitude height from origin to peak
• This is intensity for light and loudness for sound

5
Wavelength

• Distance from one point to the next identical
  point (could be peak to peak for example)
• Units are meters/cycle
• Symbol ?
• Called lambda

6
Frequency

• Speed of oscillation
• Example how many water waves pass your eye per
  second
• Unit is cycles/second, also called hertz
• 1 hertz 1 cycle per second 1/seconds
• Symbol f or nu

7
Speed (v)

• Speed of a wave is the rate that it travels
  through space
• Speed of all EM waves c
• C 3.00 X 108 m/s
• V wavelength X frequency ?f
• Units meters X cycles
• --------------------- m/s
• cycles X second

8
Animation

• http//www.surendranath.org/Applets/Waves/Twave01/
  Twave01Applet.html

9
EM Spectrum

• If speed is constant, than all EM waves must have
  varying wavelengths and frequencies
• As wavelength goes up, frequency must go down.

10
Visible Light
11
Why does white light show colors in a prism?

• Different wavelengths are affected differently
• Red is spread the least largest wavelength
• Purple is spread the most smallest wavelength

12
Light Through a Prism
13
Continuous Spectrum

• The kind of spectrum shown when light passes
  through a prism is called a continuous spectrum
• All wavelengths of visible light are represented
• Rainbows are continuous

14
Exceptions

• There were some phenomena of light that could not
  be explained by waves
• Black-body radiation heated object glowed
  several different colors ( orange to blue to
  white)

15
Max Planck

• First associated color with a certain frequency,
  and therefore amount of energy
• Energy can be absorbed by atoms in discrete
  chunks called quanta (bundle in Latin
• E hf
• h 6.626 X 10-34 J-s
• Nobel Prize in 1918

16
Einsteins Contribution - 1905

• Solar cell electrons on a metallic surface are
  removed by light and a current flows
• A certain frequency (or higher) is needed
• Higher intensity of a lower frequency does not
  work
• Connects this to Planck photons are bundles of
  light energy.
• You need a threshold frequency and everything
  else higher works
• This is called the photoelectric effect
• His only Nobel Prize

17
Quanta and the Hydrogen Atom

• Elements that were heated (flame tests) or
  electrified (discharge tubes) gave line spectra
  (not continuous spectra like rainbows)
• Balmer and Rydberg did calculations to get
  wavelength (and therefore color) of each line on
  hydrogen line spectrum 9late 1800s)
• 1/? (on board)
• Rydbergs constant 1.096776 X 107 1/m
• They had no clue what this meant!

18
Bohrs Explanation

• 1. Only orbits of certain radii with definite
  enrgies are allowed
• 2. Circular motion does not radiate enrgy and
  therefore remains stable
• 3. Energy permitted to be absorbed or emitted is
  equal to hf.
• Nobel Prize in 1922

19
Details

• Energy allowed for each orbit
• E (-2.18 X 10-18 J)(1/n2)
• n 1, 2, 3
• n is called principal quantum number
• As n increases, orbit gets larger
• Most negative energy for n 1 (called ground
  state), therefore most stable
• Derive equation for a jump
• Try http//www.mhhe.com/physsci/astronomy/applet
  s/Bohr/applet_files/Bohr.html

20
Problems

• Only works for 1-electron atoms hydrogen!
  Actually, simply a mental exercise.
• Language remains
• Ground state
• Jumping up and down
• Energy is quantized

21
More Pieces to the Puzzle

• All matter can behave as a wave or a particle!
• de Broglie (1897 1987)
• ? h/mv (mv is momentum)
• Calaulate wavelength of a person
• Calculate wavelength of an electron
• (m 9.11 X 10-28 g, v 5.97 X 106 m/s)

22
Uncertainty Principle

• It is inherently impossible to know both the
  exact momentum and location of an electron at the
  same time.
• (?x) x (?mv) or h/4pi
• If you calculate the location of an electron
  using known m and v, the error is larger than the
  size of the electron.
• Photon explanation is simpler.
• Location is best described as probability.

23
Quantum Mechanics

• Schrödinger (1887 1961) equation which deals
  with both particle and wave behavior of the
  electron
• Based upon wave functions which describes the
  place in space where electron is most likely to
  be probability density
• Wave function is called an orbital a specific
  distribution in space

24
Quantum Mechanical Model First quantum number

• Three numbers are used in the equations to
  describe this n,l,m
• n is the principle quantum number
• 1,2,3, etc.
• Larger the n, further from the nucleus, larger
  the E value will take less to remove the
  electron.

25
Second quantum number

• Called l
• Values are 0 to n-1
• Defines shape
• This is where we get s,p,d,f
• S 0 p 1 d 2 f 3
• For example, how many l values for n 3?
• What are they?

26
Third Quantum Number

• Called m
• This is the magnetic quantum number, which
  describes the orientation in space
• Values are between L and L, including 0
• For a p sublevel, what is the L?
• What are the possible m values?

27
Continued

• Collection of all orbitals make the electron
  shell
• Subshell or sublevel same n and l
• Total number of orbitals in n is n2
• Orbitals are like nodes in wave
• S 1
• P 3
• D 5
• F 7

28
Energy within one level

• Increases with value of L
• All orbitals within the same L (like all d
  orbitals have equal energy
• The term is degenerate for this
• The last quantum number is ms or spin number
• Pauli Exclusion Principle no two electrons can
  have the same 4 quantum numbers
• or (½)
• If orbital has two electrons, they have opposite
  spin.
• Try a few

29
Electron Configuration

• This is the distribution of electrons in various
  orbitals
• Ground state all electrons are in lowest
  possible state
• Simple configuration does not show orbitals
• Try carbon

30
Orbital Diagram

• This shows how degenerate orbitals fill also
• Follow Hunds Rule for degenerate orbitals, the
  lowest energy is obtained when the number of
  electrons with the same spin is maximized.
• Show carbon
• Try iron to show order of filling
• Read across table

31
Condensed version

• For convenience, indicate nearest noble gas in
  brackets and continue on with the configuration
• This clearly shows core and valence (outer)
  electrons
• Try gold
• Exceptions are not interesting chemically
• Lanthanum, chromium, copper