1. Chapter 7 The Quantum-Mechanical Model of the Atom

2. A Theory that Explains Electron Behavior
the quantum-mechanical model explains the manner electrons exist and behave in atoms
helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons
why some elements are metals while others are nonmetals
why some elements gain 1 electron when forming an anion, while others gain 2
why some elements are very reactive while others are practically inert
and other Periodic patterns we see in the properties of the elements

3. One of the ways that energy travels through space:
– Light from sun; microwave oven; radiowaves for MRI mapping
• Exhibit the same type of wavelike behavior and
travel at the speed of light in a vacuum
• It has electric and magnetic fields that
simultaneously oscillate in planes mutually
perpendicular to each other and to the direction
of propagation through space.
Electromagnetic radiation has oscillating electric (E) and magnetic (H) fields in planes

4. The Nature of Light its Wave Nature
light is a form of electromagnetic radiation
composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field
an electric field is a region where an electrically charged particle experiences a force
a magnetic field is a region where an magnetized particle experiences a force
all electromagnetic waves move through space at the same, constant speed
3.00 x 108 m/s in a vacuum = the speed of light, c

5. Characterizing Waves the number of waves = number of cycles
Waves are characterized by wavelength, frequency, and speed.
– wavelength (λ) is the distance between two
consecutive peaks or troughs in a wave.
– frequency (ν) is defined as the number of waves (cycles) per second
- is a measure of the distance covered by the wave
the distance from one crest to the next
the number of waves = number of cycles
units are hertz, (Hz) or cycles/s = s-1
1 Hz = 1 s-1
the amplitude is the height of the waVe
the distance from node to crest
or node to trough
the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light

6. Amplitude & Wavelength
Dim light
Bright light

7. Interference the interaction between waves is called interference
when waves interact so that they add to make a larger wave it is called constructive interference
waves are in-phase
when waves interact so they cancel each other it is called destructive interference
waves are out-of-phase

8. Diffraction
when traveling waves encounter an obstacle or opening in a barrier that is about the same size as the wavelength, they bend around it – this is called diffraction
traveling particles do not diffract
the diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves
an interference pattern is a characteristic of all light waves

9. The Electromagnetic Spectrum
visible light comprises only a small fraction of all the wavelengths of light – called the electromagnetic spectrum
short wavelength (high frequency) light has high energy
radiowave light has the lowest energy
gamma ray light has the highest energy
high energy electromagnetic radiation can potentially damage biological molecules
ionizing radiation

10. Color the color of light is determined by its wavelength or frequency
white light is a mixture of all the colors of visible light
a spectrum
RedOrangeYellowGreenBlueViolet
when an object absorbs some of the wavelengths of white light while reflecting others, it appears colored
the observed color is predominantly the colors reflected

11. The Relationship Between Wavelength and Frequency
for waves traveling at the same speed, the shorter the wavelength, the more frequently they pass
this means that the wavelength and frequency of electromagnetic waves are inversely proportional
since the speed of light is constant, if we know wavelength we can find the frequency, and visa versa
c = v x λ
c is defined to be the rate of travel of all electromagnetic energy in a vacuum and is a constant value—speed of light.
c= 3.00 x 108 m/s

12. Example
Calculate the wavelength of red light with a frequency of 4.62 x 1014 s-1
A laser dazzels the audience in a rock concert by emitting green light with a wave length of 515 nm. Calculate the frequency of the light

13. Particlelike Properties of Radiant Energy: The Photoelectric Effect and Planck’s Postulate
it was observed that many metals emit electrons when a light shines on their surface
this is called the Photoelectric Effect
classic wave theory attributed this effect to the light energy being transferred to the electron
according to this theory, if the wavelength of light is made shorter, or the light waves intensity made brighter, more electrons should be ejected
the frequency of the light used for the irradiation must be above some threshold value, which is different for every metal called the threshold frequency
regardless of the intensity
it was also observed that high frequency light with a dim source caused electron emission without any lag time

14. Particlelike Properties of Electromagnetic Energy
Refers to the phenomenon in which electrons are emitted from the surface of a metal when light strikes it:
– No electrons are emitted by a given metal below a specific threshold frequency νo.
– For light with frequency lower than the threshold frequency, no electrons are emitted regardless of the intensity of the light.
– For light with frequency greater than the threshold frequency, the number of electrons emitted increases with the intensity of the light.
– For light with frequency greater than the threshold frequency, the kinetic energy of the emitted electrons increases linearly with the frequency of the light.

15. No electrons would be ejected.
Suppose a Metal Will Eject Electrons from Its Surface When Struck by Yellow Light. What Will Happen If the Surface Is Struck with Ultraviolet Light?
No electrons would be ejected.
Electrons would be ejected, and they would have the same kinetic energy as those ejected by yellow light.
Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light.
Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light.
No electrons would be ejected.
Electrons would be ejected, and they would have the same kinetic energy as those ejected by yellow light.
Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light.
Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light.
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Spectra
When atoms or molecules absorb energy, that energy is often released as light energy,
Fireworks, neon lights, etc.
When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum.
Noncontinuous
Can be used to identify the material
Flame tests
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17. Einstein’s Explanation
Energy is in fact quantized and can be transferred only in discrete units of size hν.
A system can transfer energy only in whole quanta
Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons
the energy of a photon of light was directly proportional to its frequency
inversely proportional to it wavelength
the proportionality constant is called Planck’s Constant, (h) and has the value x J∙s

18. Kinetic Energy = Ephoton – Ebinding
Ejected Electrons
1 photon at the threshold frequency has just enough energy for an electron to escape the atom
binding energy, f
for higher frequencies, the electron absorbs more energy than is necessary to escape
this excess energy becomes kinetic energy of the ejected electron
Kinetic Energy = Ephoton – Ebinding
KE = hn - f

19. Examples
What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x 108 Hz?
Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 3.83 mJ

20. Examples
he blue color in fireworks is often achieved by heating copper(I) chloride (CuCl) to about 1200°C. The hot compound emits blue light having a wave- length of 450 nm. What is the increment of energy (the quantum) that is emitted at 450 nm by CuCl?
What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons?

21. Spectra
when atoms or molecules absorb energy, that energy is often released as light energy
fireworks, neon lights, etc.
when that light is passed through a prism, a pattern is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum
non-continuous
can be used to identify the material
Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers
However, his equation gave little information into why atomic spectra were discrete, why atoms are stable, or why his equation worked

22. Exciting Gas Atoms to Emit Light with Electrical Energy
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23. Identifying Elements with Flame TestsNa K Li Ba
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24. Emission vs. Absorption Spectra
Spectra of Mercury

25. The Interaction of Radiant Energy with Atoms: Line Spectra
Line Spectrum: A series of discrete lines on an otherwise dark background as a result of light emitted by an excited atom
The Bunsen burner was used for elemental analysis.
Gas discharge tubes can be used along with inexpensive diffraction grating glasses (search on “rainbow glasses”) for a fun demonstration.

26. The Interaction of Radiant Energy with Atoms: Line Spectra
In 1885, Johann Balmer discovered a mathematical relationship for the four visible lines in the atomic line spectrum for hydrogen. l 1
= R n2 22 −
Johannes Rydberg later modified the equation to fit every line in the entire spectrum of hydrogen. l 1
= R n2 m2 −
R (Rydberg constant) = × 10–2 nm–1

27. Rutherford’s Nuclear Model
The atom contains a tiny dense center called the nucleus.
The volume is about 1/10 trillionth the volume of the atom.
The nucleus is essentially the entire mass of the atom.
The nucleus is positively charged .
The amount of positive charge balances the negative charge of the electrons.
The electrons move around in the empty space of the atom surrounding the nucleus.
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28. Problems with Rutherford’s Nuclear Model of the Atom
Electrons are moving charged particles.
According to classical physics, moving charged particles give off energy.
Therefore, electrons should constantly be giving off energy.
This should cause the atom to glow!
The electrons should lose energy, crash into the nucleus, and the atom should collapse!
But it doesn’t!
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29. Bohr’s Model
Neils Bohr proposed that the electrons could only have very specific amounts of energy
fixed amounts = quantized
the electrons traveled in orbits that were a fixed distance from the nucleus
stationary states
therefore the energy of the electron was proportional the distance the orbital was from the nucleus
electrons emitted radiation when they “jumped” from an orbit with higher energy down to an orbit with lower energy
the distance between the orbits determined the energy of the photon of light produced

30. Bohr Model of H Atoms

31. The Bohr Model of the Atom: Quantized Energy
m: shell the transition
is to (inner shell) l 1
= R n2 m2 −
n: shell the transition
is from (outer shell)

32. Wavelike Properties of Matter
Chapter 5: Periodicity and Atomic Structure
Wavelike Properties of Matter
11/19/2018
Energy is really a form of matter, and all matter exhibits both particulate and wave properties.
–Large “pieces” of matter, such as base balls, exhibit predominantly particulate properties
–Very small “pieces” of matter, such as photon, while showing some particulate properties through relativistic effects, exhibit dominantly wave properties
–“Pieces” of intermediate mass, such as electrons, show both the particulate and wave properties of matter
Louis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light.
In other words, perhaps matter is wavelike as well as particlelike. mv h
l =
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33. examples
What velocity would an electron (mass = 9.11 x 10-31kg) need for its de Broglie wavelength to be that of red light (750 nm)?
Determine the wavelength of a neutron traveling at 1.00 x 102 m/s (Massneutron = x g)

34. Quantum Mechanics and the Heisenberg Uncertainty Principle
Heisenberg Uncertainty Principle – both the position (Δx) and the momentum (Δmv) of an electron cannot be known beyond a certain level of precision
1. (Δx) (Δmv) > h 4π
2. Cannot know both the position and the momentum of an electron with a high degree of certainty
3. If the momentum is known with a high degree of certainty
i. Δmv is small
ii. Δ x (position of the electron) is large
4. If the exact position of the electron is known
i. Δmv is large
ii. Δ x (position of the electron) is small

35. Determinacy vs. Indeterminacy
according to classical physics, particles move in a path determined by the particle’s velocity, position, and forces acting on it
determinacy = definite, predictable future
because we cannot know both the position and velocity of an electron, we cannot predict the path it will follow
indeterminacy = indefinite future, can only predict probability
the best we can do is to describe the probability an electron will be found in a particular region using statistical functions

36. Trajectory versus Probability
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