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Atomic structure, spectroscopy, and quantum mechanics

Chapter 5

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Key concepts

1. Know the general concepts behind the experiments leading to the discovery of the electron and the proton.

2. Understand the general character of the atomic nucleus.3. Know the relationship between wavelength and frequency of electromagnetic radiation (light):

=c4. Understand the term quantum of energy, and the quantum nature of light: E=h5. Describe the photoelectric effect.6. Understand how the line spectra of atoms led to Bohr’s model of the atom. Also understand

the drawbacks of Bohr’s model.7. Understand the wave nature of matter; use the DeBroglie formula for calculating the

wavelength of matter waves.8. Explain the Heisenberg uncertainty principle, and know how it affects our understanding of the

atom.9. Know that Schrodinger’s equation H=E leads to the atomic orbital. Know the four quantum

numbers used to describe an electron in any atomic orbital.10. Be able to recognize the spatial representation of s, p, or d orbitals.11. Understand how Pauli’s exclusion principle affects the population of electrons in any atomic

orbital.12. Know how to write electronic configurations, and know what these represent.13. Understand the reasoning behind the shape of the periodic table.

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God’s view of the world vs. our view of the world

• Mos. 4:9. 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 130:19. 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.

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Models and the scientific method

a) There is always a model that will explain any related set of bona fide experiments.

b) Models should always start out simple and definite enough that predictions can be made.

c) A model is of limited value except as it correlates a substantial body of observable material.

d) 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…

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The electron (e-)

• Electric charge investigated from the 1800’s, but detailed characteristics first outilined by J. J. Thomson

• Thomson used a cathode ray tube to examine the electron’s properties

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Cathode ray tube

Cathode rays: radiation produced in vacuum tubes that travels from the cathode ( - lead) to the anode (+ lead)

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Thomson’s discoveries

1. Nature of the cathode ray is independent of the cathode material.

2. A magnet can alter the path of the cathode ray

3. Electron charge to mass ratio—

1.76 108 coulombs/gram (Coulomb = unit of charge)

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• Thomson’s 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.

9Fig. 5-2, p.177

Millikan oil-drop experiment

Removes electrons From atoms in air

ProducesSmall oil drops

Used toMeasure oil-drop size

Attracts free electrons;oil drop suspended whenPlate voltage is sufficient.

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Millikan’s 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 Millikan’s lab? (#5)

13.458×10-19 C 17.308×10-19 C

15.373×10-19 C 28.844×10-19 C

17.303×10-19 C 11.545×10-19 C

15.378×10-19 C 19.214×10-19 C

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Electron mass

• Fundamental electron charge: 1.602 10-19 C• With Millikan’s results, we can now find the mass

of an electron. How?

eee

e mzz

m

12Fig. 5-3, p.178

Canal rays: Protons

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

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Nature of the nucleus

• First model: “Plum pudding” model (or the gumdrop-popcorn-ball model)

• Electrons are held close to nucleus in a “blob”.

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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…

15Fig. 5-4, p.179

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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.

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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).

18Table 5-1, p.175

19Fig. 5-8, p.184

Mass spectrometer

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Factors affecting ion deflection

1. Magnitude of accelerating voltage

2. Magnetic field strength

3. Particle mass

4. Particle charge

21Fig. 5-9, p.185

22Fig. 5-10a, p.185

23Fig. 5-10b, p.185

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Electromagnetic

spectrum

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= c

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

• Some examples

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Planck’s constant

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

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• Planck’s 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 Planck’s constant

• Released or absorbed energy at frequency in whole multiples of h (h, 2h, 3h, etc.)

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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/166/170213/Media_Portfolio/PhotoelectricEffect/PhotoelectricEffect.MOV

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Einstein’s deduction

• light is made of photons (light particles, quanta).

• Light has both wave properties and particle properties

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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

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21

111

nnR

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Bohr’s 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, E=h

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• 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. Bohr’s model failed, but led to development

of the next step

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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

mv

h

So….why do we not exhibit waves?

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• 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)

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Experimental evidence of matter waves

http://www.mos.org/sln/SEM/gallery/guessit/7a.htmlScanning electron microscope image of leafcutter ant head

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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.

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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.

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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 (we’ll talk more about spin later) ms +1/2, -1/2

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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)

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Representations of orbitals

• There are two components of an orbital, its radial distribution and its angular distribution.

• Angular distribution is commonly called the orbital’s “shape”.

42http://www.shef.ac.uk/chemistry/orbitron/AOs/1s/index.html

s, p, and d orbital shapes

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• Radial distribution: An atom with n > 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/166/170213/RadialElectronDistribution.html

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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/166/170213/EnergyOrbitalsElectron.html

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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)

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Number of….

• Orbitals in a shell• Electrons in a shell

• Orbitals in a subshell

• Electrons in a subshell

• n2

• 2n2

• s=1; p=3; d=5• - l to + l• s?; p?; d?

MAXIMUM NUMBER OF ELECTRONS IN ANY SINGLE ORBITAL IS ____!!!

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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.

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Hund’s rule

• For degenerate orbitals, lowest energy is obtained when spin is maximized. this means…

1. Electrons will fill the subshell orbitals, one at a time, until each orbital has one electron.

2. All electrons will have the same spin (either up or down, or either +1/2 or –1/2)

3. Only then will electrons be paired.

What is degenerate?

http://wps.prenhall.com/wps/media/objects/166/170213/ElectronConfigurations.html

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• Condensed electronic configurations– A “shorthand” for writing complete electronic

configurations.

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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

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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.

52Fig. 5-31, p.219

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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.

54Table 5-5, p.220