Atomic structure, spectroscopy, and quantum mechanics

1
Atomic structure, spectroscopy, and quantum
mechanics

• Chapter 5

2
Key concepts

• Know the general concepts behind the experiments
  leading to the discovery of the electron and the
  proton.
• Understand the general character of the atomic
  nucleus.
• Know the relationship between wavelength and
  frequency of electromagnetic radiation (light)
  ??c
• Understand the term quantum of energy, and the
  quantum nature of light Eh?
• Describe the photoelectric effect.
• Understand how the line spectra of atoms led to
  Bohrs model of the atom. Also understand the
  drawbacks of Bohrs model.
• Understand the wave nature of matter use the
  DeBroglie formula for calculating the wavelength
  of matter waves.
• Explain the Heisenberg uncertainty principle, and
  know how it affects our understanding of the
  atom.
• Know that Schrodingers equation H?E? leads to
  the atomic orbital. Know the four quantum
  numbers used to describe an electron in any
  atomic orbital.
• Be able to recognize the spatial representation
  of s, p, or d orbitals.
• Understand how Paulis exclusion principle
  affects the population of electrons in any atomic
  orbital.
• Know how to write electronic configurations, and
  know what these represent.
• Understand the reasoning behind the shape of the
  periodic table.

3
Gods view of the world vs. our view of the world

• Mos. 49. Believe in God believe that he is,
  and that he created all things, both in heaven
  and in earth believe that he has all wisdom, and
  all power, both in heaven and in earth believe
  that man doth not comprehend all the things which
  the Lord can comprehend.
• D C 13019. And if a person gains more
  knowledge and intelligence in this life through
  his diligence and obedience than another, he will
  have so much the advantage in the world to come.
• While we may not comprehend all the things which
  the Lord can comprehend, we are encouraged to
  obtain knowledge on all subjects, including the
  workings of creation. This is where the
  scientific method comes into play.

4
Models and the scientific method

• There is always a model that will explain any
  related set of bona fide experiments.
• Models should always start out simple and
  definite enough that predictions can be made.
• A model is of limited value except as it
  correlates a substantial body of observable
  material.
• Models that suggest important new experiments can
  be useful, even if the theory must be modified.
• Henry Eyring, Ann. Rev. Phys. Chem. 28, 1 (1977)
• It is important to remember that we will be
  discussing a series of experiments, data, and
  models. Models are meant to describe nature, not
  the other way around. We change the model in
  order to better fit new experimental evidence.
• Models help us understand processes and
  mechanisms (how). Scientific models rarely, if
  ever, help us understand the underlying purposes
  of Nature (why). Increasing our understanding of
  our relationship to God will help in that area

5
The electron (e-)

• Electric charge investigated from the 1800s, but
  detailed characteristics first outilined by J. J.
  Thomson
• Thomson used a cathode ray tube to examine the
  electrons properties

6
Cathode ray tube Cathode rays radiation
produced in vacuum tubes that travels from the
cathode ( - lead) to the anode ( lead)
7
Thomsons discoveries

• Nature of the cathode ray is independent of the
  cathode material.
• A magnet can alter the path of the cathode ray
• Electron charge to mass ratio
• 1.76 ? 108 coulombs/gram
• (Coulomb unit of charge)

8

• Thomsons experiment is the forerunner of the
  mass spectrometer (more on that in a minute).
  Mass spectrometer measures the mass-to-charge
  ratio of particles.
• With the mass/charge ratio known, something
  needed to be learned about the mass or charge of
  the particle in order to determine the remaining
  property.

9
Millikan oil-drop experiment
Produces Small oil drops
Used to Measure oil-drop size
Removes electrons From atoms in air
Attracts free electrons oil drop suspended
when Plate voltage is sufficient.
Fig. 5-2, p.177
10
Millikans observations

• Charges on oil-drops are integral multiple of
  some factor that is the fundamental charge of an
  electron.
• What if you were working in Millikans lab? (5)

13.45810-19 C 17.30810-19 C
15.37310-19 C 28.84410-19 C
17.30310-19 C 11.54510-19 C
15.37810-19 C 19.21410-19 C
11
Electron mass

• Fundamental electron charge 1.602 ? 10-19 C
• With Millikans results, we can now find the mass
  of an electron. How?

12
Canal rays Protons

• A protons mass is 1836 times larger than an
  electron. Thus, its charge-to-mass ratio is
  __________ than the z/m for an electron.

Fig. 5-3, p.178
13
Nature of the nucleus

• First model Plum pudding model (or the
  gumdrop-popcorn-ball model)
• Electrons are held close to nucleus in a blob.

14
Rutherford gold foil experiment

• Utilized work of Madame Curie on radioactive
  particles
• ? -- high speed electrons
• ?-- gamma-rays (light), no charge
• ?--alpha-rays 2 charge ? charged nucleus of
  He atom
• Rutherford used ?? rays in his experiment, firing
  them at a piece of gold foil.
• Predict what will happen in the experiment

15
Fig. 5-4, p.179
16
At the molecular level

• Most alpha particles pass straight through
• Some are deflected at very steep angles
• This can only occur if the alpha particle is
  repelled at close range by a positively charged
  particle.

17
The nucleus

• Nucleus is very small, dense, highly charged
  center of the atom. Electrons spaced relatively
  widely about the nucleus.
• Diameter of nucleus ? 10-14 m
• Diameter of H atom ? 10-10 m 1 Å (Angström)
• If H nucleus was 1 m in diameter, electron would
  be 10 km away (6.2 miles).

18
Table 5-1, p.175
19
Mass spectrometer
Fig. 5-8, p.184
20
Factors affecting ion deflection

1. Magnitude of accelerating voltage
2. Magnetic field strength
3. Particle mass
4. Particle charge

21
Fig. 5-9, p.185
22
Fig. 5-10a, p.185
23
Fig. 5-10b, p.185
24
Electromagnetic spectrum
25
?? c

• as wavelength (?) increases, frequency (?)
  decreases. Product equal to speed of light in
  vacuum (c).
• Some examples

26
Plancks constant

• Blackbodies emit energy at all frequencies
• Behavior of blackbodies could not be explained by
  classical physics

27

• Plancks hypothesis Energy is released or
  absorbed from atoms in chunks, or quanta.
• A quantum of energy E h?.
• h 6.626 ? 10-34 J-s ? Plancks constant
• Released or absorbed energy at frequency ? in
  whole multiples of h? (h?, 2h?, 3h?, etc.)

28
Photoelectric effect--Einstein

• To remove an electron from a metal surface, a
  minimum energy (h?) is required.
• Shining more light does NOT increase the
  energy, just the intensity of the light.
• Below minimum energy (frequency), nothing
  happens.
• http//wps.prenhall.com/wps/media/objects/166/1702
  13/Media_Portfolio/PhotoelectricEffect/Photoelectr
  icEffect.MOV

29
Einsteins deduction

• light is made of photons (light particles,
  quanta).
• Light has both wave properties and particle
  properties

30
Bohr model of the atom

• Line spectrum of atoms discrete lines vs.
  rainbow.
• Rydberg series empirically determined
  mathematical series that describes hydrogen line
  spectrum.
• R 1.097 ? 107 m-1

31
Bohrs description of the atom

• 1. Electrons travel in orbits around nucleus.
  Only certain orbits, corresponding to certain
  definite energies, are allowed.
• 2. An electron in a permitted orbit has a
  specific energy in an allowed state. An electron
  in an allowed state will not radiate energy.
• 3. Energy is only emitted or absorbed when
  electrons move from one orbit to another. Energy
  is emitted or absorbed as a photon, Eh?

32

• Advantages
• Explains observed line spectrum of hydrogen.
• Explains quantized absorbtion and emission of
  energy
• Disadvantage
• Model works only for hydrogen or other 1-electron
  atoms.
• Bohrs model failed, but led to development of
  the next step

33
Dual nature of matter

• DeBroglie Matter, like light, exhibits both
  wave properties and particle properties.
• DeBroglie wavelength (matter waves)
• Example of matter waves Scanning electron
  microscope

So.why do we not exhibit waves?
34

• Examples
• 0.25 kg ball moving at 90 mph. What is the
  DeBroglie wavelength?
• What is the DeBroglie wavelength of a helium atom
  (4.0 amu) moving 1000 m s-1?
• Matter waves are observable only with very small,
  very fast particles. (atoms and electrons)

35
Experimental evidence of matter waves
Scanning electron microscope image of leafcutter
ant head
http//www.mos.org/sln/SEM/gallery/guessit/7a.html
36
Heisenberg uncertainty principle

• Because electrons are constantly moving very
  fast, it is impossible to know precisely both the
  position and momentum of an electron. (billiards
• The nature of an electron is probed by using
  photons. But, the interaction of the photon with
  the electron changes the nature of the electron.
• A well defined orbit of an electron around a
  nucleus cannot be defined. The precise behavior
  of an electron in an atom cannot be directly
  determined.

37
Schrodinger equation H? E?

• ? a wave function (from standing waves). Wave
  functions define a region of space where it is
  most likely to find the electron in an atom. The
  square of the wavefunction, ?2, represents the
  electron density of that wavefunction.
• Orbitals Wave functions giving solutions to the
  Schrodinger equation. Orbitals are defined by
  three quantum numbers. Electrons in an orbital
  are defined using these numbers, plus one other.

38
Four quantum numbers used to define electrons in
orbitals
Quantum number name symbol values
Principal n 1,2,3,
Angular momentum l 0,(n-1)
Magnetic m l - l, l
Spin (well talk more about spin later) ms 1/2, -1/2
39
(No Transcript)
40
Electron shells and subshells

• Electron shell Orbitals that have the same
  principal quantum number
• (same n).
• Subshell Orbitals have the same principal and
  orbital angular momentum quantum numbers
• (same n and l)

41
Representations of orbitals

• There are two components of an orbital, its
  radial distribution and its angular distribution.
• Angular distribution is commonly called the
  orbitals shape.

42
s, p, and d orbital shapes
http//www.shef.ac.uk/chemistry/orbitron/AOs/1s/in
dex.html
43

• Radial distribution An atom with n gt 1 has at
  least one node (an area where the electron
  density is 0).
• As n increases, the number of nodes increases,
  and the distance from the nucleus to the highest
  electron density region also increases.
• Lower energy regions are forced closer to nucleus
  
• p. 208 209 in text give representations of s
  and p orbitals. You should know these. You
  should also be aware of the shapes of d orbitals
  (p. 209). f orbitals are shown on p 210, but
  they are rarely (never) encountered in this
  course.

http//wps.prenhall.com/wps/media/objects/166/1702
13/RadialElectronDistribution.html
44
Electron-electron repulsion

• In the hydrogen atom, all orbitals with the same
  n have the same energy. However, in
  many-electron orbitals, repulsions between the
  electrons cause differences in energy between
  orbitals of the same n, but different l.

http//wps.prenhall.com/wps/media/objects/166/1702
13/EnergyOrbitalsElectron.html
45
Pauli exclusion principle

• no two electrons in an atom can have the same
  four quantum numbers.
• ?The maximum number of electrons in any orbital
  is two. The maximum number of electrons in a
  shell (or subshell) is 2x the number of orbitals
  in the shell (or subshell).
• ms 1/2 or 1/2 (up or down)

46
Number of.

• Orbitals in a shell
• Electrons in a shell
• Orbitals in a subshell
• Electrons in a subshell

• n2
• 2n2
• s1 p3 d5
• - l to l
• s? p? d?

MAXIMUM NUMBER OF ELECTRONS IN ANY SINGLE
ORBITAL IS ____!!!
47
writing electronic configurations

• Electronic configurations a method of
  describing the orbital arrangement of electrons
  in an atom.
• orbital notation pictorially represents
  electron positions in orbitals.
• Simplified notation notes the number of
  electrons in each subshell.

48
Hunds rule
What is degenerate?

• For degenerate orbitals, lowest energy is
  obtained when spin is maximized. this means
• Electrons will fill the subshell orbitals, one at
  a time, until each orbital has one electron.
• All electrons will have the same spin (either up
  or down, or either 1/2 or 1/2)
• Only then will electrons be paired.

http//wps.prenhall.com/wps/media/objects/166/1702
13/ElectronConfigurations.html
49

• Condensed electronic configurations
• A shorthand for writing complete electronic
  configurations.

50
Aufbau principle

• Describes the order in which subshells are
  filled. this order is
• 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s,
  4f, 5d, 6p, 7s, 5f, 6d, 7p
• The ordering is due to electron repulsions in the
  higher orbitals

51
The periodic table

• The shape of the table is a result of the order
  in which the orbitals in the atoms are filled
  with electrons
• Different areas of the table indicate which
  subshell contains the valence (highest energy)
  electrons.
• s-block
• p-block
• d-block
• using the periodic table is an excellent way to
  remember the Aufbau principle.

52
Fig. 5-31, p.219
53
Exceptions to the rule in transition metals

• p. 220, text.
• These exceptions are due to the closeness in
  energy of higher number orbitals, and have to do
  with a balance between electron promotion and
  electron repulsion.

54
Table 5-5, p.220