1. Chapter 5 Periodicity and the Electronic Structure of Atoms

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. The Nature of Light its Wave Nature
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. 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 l 

8. 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

9. 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

10. 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

11. Particlelike Properties of Radiant Energy: The Photoelectric Effect and Planck’s Postulate
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.

12. 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

13. 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

14. The Bohr Model of the Atom: Quantized Energy
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

15. 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 −
Line Spectrum: A series of discrete lines on an otherwise dark background as a result of light emitted by an excited atom

16. The Bohr Model of the Atom: Quantized Energy
Johannes Rydberg later modified the equation to fit every line in the entire spectrum of hydrogen.
m: shell the transition
is to (inner shell) l 1
= R n2 m2 −
n: shell the transition
is from (outer shell)

17. Wavelike Properties of Matter
Chapter 5: Periodicity and Atomic Structure
Wavelike Properties of Matter
1/13/2019
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 =
Copyright © 2008 Pearson Prentice Hall, Inc.

18. 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)

19. 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

20. The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers
electron energy and position are complimentary
because KE = ½mv2
for an electron with a given energy, the best we can do is describe a region in the atom of high probability of finding it – called an orbital
a probability distribution map of a region where the electron is likely to be found
distance vs. y2 (wave function)
many of the properties of atoms are related to the energies of the electrons
Probability of finding
electron in a region
of space (Y 2)
Solve
Wave
equation
Wave function
or orbital (Y)
calculations show that the size, shape and orientation in space of an orbital are determined be three integer terms in the wave function
added to quantize the energy of the electron
these integers are called quantum numbers
principal quantum number, n
angular momentum quantum number, l
magnetic quantum number, ml
Since we can’t ever be certain of the electron’s position, we work with probabilities.

21. The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers
Principal Quantum Number (n)
Describes the size and energy level of the orbital
Commonly called a shell
Positive integer (n = 1, 2, 3, 4, …)
As the value of n increases,
the energy increases.
the average distance of the e– from the nucleus increases.

22. The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers
Angular-Momentum Quantum Number (l)
Defines the three-dimensional shape of the orbital
Commonly called a subshell
There are n different shapes for orbitals.
If n = 1, then l = 0.
If n = 2, then l = 0 or 1.
If n = 3, then l = 0, 1, or 2.
Commonly referred to by letter (subshell notation)
l = 0 s (sharp)
l = 1 p (principal)
l = 2 d (diffuse)
l = 3 f (fundamental)
Scientists working in spectroscopy first used sharp, principal, diffuse, and fundamental with respect to atomic spectra.
After f, the series goes alphabetically (g, h, etc.).
the energy of the subshell increases with l (s < p < d < f).

23. The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers
Magnetic Quantum Number (ml )
Defines the spatial orientation of the orbital
There are 2l + 1 values of ml, and they can have any integral value from -l to +l.
If l = 0, then ml = 0.
If l = 1, then ml = –1, 0, or 1.
If l = 2, then ml = –2, –1, 0, 1, or 2.

24. The Quantum Mechanical Model of the Atom: Orbitals and Quantum Numbers

25. Examples
Give the possible combination of quantum numbers for the following orbitals
3s orbital 2 p orbitals
Give orbital notations for electrons in orbitals with the following quantum numbers:
n = 2, l = 1 ml = 1
n = 3, l = 2, ml = -1

26. The Shapes of Orbitals
Node: A surface of zero probability for finding the electron
s orbitals are spherical and penetrate closer to the nucleus.

27. The Shapes of Orbitals
p orbitals are dumbbell-shaped, with a nodal plane running through the nucleus.
Introductory Physical Chemistry courses often explore the mathematical relationships that define the regions of space (or shape).