Chapter 6
Quantum Mechanics - Developed to help describe atoms correctly.
Quantum Theory - Describes the arrangement of electrons in an atom, or the electronic structure.
• Number of electrons
• Distribution of electrons around the nucleus
• Energy of each electron
Electromagnetic Radiation
• Light is energy in the form of electromagnetic radiation. All electromagnetic radiation transmits energy in the form of waves and consists of an electric field and a magnetic field.
• Also known as radiant energy, which is the energy in the form of light.
• Travels through space at a velocity of 3.00 x 108 m/s (speed of light)
Wavelength (λ)
• The distance on a wave between 2 equivalent points.
• Units: meters or nm (Nanometer: 10-9)
Frequency (ν)
• The number of complete waves passing any point per second.
• Cycles per second.
1
• Units: or s-1 or Hertz (Hz)
s
Wavelength and Frequency are inversely proportional.
Example 1: What is the frequency (in Hz) of a gold vapor laser light with a wavelength of 627 nm?
m 𝑐
c = 3.00 x 108 s , c = λ ν (rearrange to find frequency, ν = 𝜆 )
10 −9 𝑚
λ = 627 nm = 1 𝑛𝑚
= 6.27 x 10-7 m
𝑐 3.00 𝑥 108 𝑚/𝑠
ν =λ= 6.27 𝑥 10−7 𝑚
= 4.78 x 1014 s-1
(this is the same as 4.78 x 1014 Hz)
Example 2: What is the wavelength (in pm) of an X-ray with a frequency of 5.0 x 1018 Hz?
m 𝑐
c = 3.00 x 108 , c = λ ν (rearrange to find the wavelength, λ = )
s ν
v = 5.0 x 1018 Hz
𝑚
3.00 𝑥 1018 𝑠 1 𝑝𝑚
= 6.0 x 10-11m x −12 = 60pm
5.0 𝑥 1018 𝑠−1 10 𝑚
Quantized Energy and Photons
• Planck’s Theory
o E = (n)hv h = Planck’s constant = 6.626 x 10-34 J•s
o Einstein deduced that ONE photon must have an energy equal to the Planck constant times the frequency of light…
▪ Ephoton = hν
hc
• Ephoton = hv = λ
• Ephoton = KEe- + BEe- (kinetic energy + binding energy)
• Every material has a threshold frequency, v0, below which electrons will not be ejected from the metal.
o 1 eV = 1.602 x 10-19 J
Example: What is the energy of a photon (in eV) from a green laser that has a wavelength of 532nm?
To find energy: Ephoton = hν
𝑐 1𝑚
c = λ ν (rearrange to find frequency, ν = 𝜆 ) convert nm to m » 532nm x 10 −9 𝑛𝑚 = 5.32 x 10-7m
𝑚
hc (6.626 𝑥 10 −34 𝐽•𝑠)(3.00 𝑥 108 𝑠 ) 1 𝑒𝑉
Ephoton = = = 3.73 x 10-19J x 1.602 𝑥 10−19 𝐽 = 2.33eV
λ 5.32 𝑥 10−7 𝑚
Rydberg Equation
1 1 1
= (RH)(Z2)((𝑛 )2 − (𝑛2 )2
)
λ 1
Rydberg constant, RH = 1.097 x 107 m-1
Z = 1 (atomic number for hydrogen)
n = 1, 2, 3…. where n2 is larger than n1
1 1 1
= (RH)((𝑛 )2 − (𝑛 )2 )
λ 1 2
Example: What wavelength of light (in nm) is emitted when an electron in a hydrogen atom moves from n=5 to n=2?
1 1 1 1 1
= (RH)((𝑛 )2 − (𝑛 )2 ) = (1.097 x 107 m-1)(22 − 52 ) = 4.34 x 10-7m = 434 nm
λ 1 2
The Energy States of the Hydrogen Atom
Only transitions from n = 3, 4, 5, and 6 to n = 2 produce visible wavelengths.
Example: Which electronic transition in a hydrogen atom will result in the emission of light with the longest wavelength?
n = 3 to n =2
Orbitals and Quantum Numbers
Value of l 0 1 2 3
Type of orbital s p d f
Representation of Orbitals
Subshell Type s subshell p subshell d subshell f subshell
Spherical in shape Dumbbell in shape (2 lobes) Four-leaf clover in shape (4 lobes) Most have 6-8 lobes
Orbital One orientation (ml = 0) Three orientations (ml = -1, 0, +1) Five orientations (ml = -2, -1, 0, 1, Seven orientations (m1 = -3, -2, -1,
2) 0, 1, 2, 3)
l = 0 for s subshell l = 1 for p subshell l = 2 for d subshell l = 3 for f subshell
Subshell One s orbital per s subshell Three p orbitals per p subshell Five d orbitals per d subshell Seven f orbitals per f subshell
Can hold 2 electrons Can hold 6 electrons (2 per orbital) Can hold 10 electrons (2 per Can hold 14 electrons (2 per
orbital) orbital)
Electron Configuration
• An electron configuration is a shorthand notation which shows the distribution of electrons among subshells.
o The number of principal energy level is followed by a letter symbol for the subshell (1s).
o A superscript to each subshell symbol designates the number of electrons in that subshell (1s 2).
▪ Example: Orbital diagram for Carbon
Valence Electrons
• Electrons in the outermost shell OR electrons with the highest principal quantum number, n.
• Will be in s or p subshells (in s and d subshells for transition metals).
Core Electrons
• Electrons in the full shells between the nucleus and the valence shell.
• Will have the same electron arrangement as a noble gas.
Quantum Mechanics - Developed to help describe atoms correctly.
Quantum Theory - Describes the arrangement of electrons in an atom, or the electronic structure.
• Number of electrons
• Distribution of electrons around the nucleus
• Energy of each electron
Electromagnetic Radiation
• Light is energy in the form of electromagnetic radiation. All electromagnetic radiation transmits energy in the form of waves and consists of an electric field and a magnetic field.
• Also known as radiant energy, which is the energy in the form of light.
• Travels through space at a velocity of 3.00 x 108 m/s (speed of light)
Wavelength (λ)
• The distance on a wave between 2 equivalent points.
• Units: meters or nm (Nanometer: 10-9)
Frequency (ν)
• The number of complete waves passing any point per second.
• Cycles per second.
1
• Units: or s-1 or Hertz (Hz)
s
Wavelength and Frequency are inversely proportional.
Example 1: What is the frequency (in Hz) of a gold vapor laser light with a wavelength of 627 nm?
m 𝑐
c = 3.00 x 108 s , c = λ ν (rearrange to find frequency, ν = 𝜆 )
10 −9 𝑚
λ = 627 nm = 1 𝑛𝑚
= 6.27 x 10-7 m
𝑐 3.00 𝑥 108 𝑚/𝑠
ν =λ= 6.27 𝑥 10−7 𝑚
= 4.78 x 1014 s-1
(this is the same as 4.78 x 1014 Hz)
Example 2: What is the wavelength (in pm) of an X-ray with a frequency of 5.0 x 1018 Hz?
m 𝑐
c = 3.00 x 108 , c = λ ν (rearrange to find the wavelength, λ = )
s ν
v = 5.0 x 1018 Hz
𝑚
3.00 𝑥 1018 𝑠 1 𝑝𝑚
= 6.0 x 10-11m x −12 = 60pm
5.0 𝑥 1018 𝑠−1 10 𝑚
Quantized Energy and Photons
• Planck’s Theory
o E = (n)hv h = Planck’s constant = 6.626 x 10-34 J•s
o Einstein deduced that ONE photon must have an energy equal to the Planck constant times the frequency of light…
▪ Ephoton = hν
hc
• Ephoton = hv = λ
• Ephoton = KEe- + BEe- (kinetic energy + binding energy)
• Every material has a threshold frequency, v0, below which electrons will not be ejected from the metal.
o 1 eV = 1.602 x 10-19 J
Example: What is the energy of a photon (in eV) from a green laser that has a wavelength of 532nm?
To find energy: Ephoton = hν
𝑐 1𝑚
c = λ ν (rearrange to find frequency, ν = 𝜆 ) convert nm to m » 532nm x 10 −9 𝑛𝑚 = 5.32 x 10-7m
𝑚
hc (6.626 𝑥 10 −34 𝐽•𝑠)(3.00 𝑥 108 𝑠 ) 1 𝑒𝑉
Ephoton = = = 3.73 x 10-19J x 1.602 𝑥 10−19 𝐽 = 2.33eV
λ 5.32 𝑥 10−7 𝑚
Rydberg Equation
1 1 1
= (RH)(Z2)((𝑛 )2 − (𝑛2 )2
)
λ 1
Rydberg constant, RH = 1.097 x 107 m-1
Z = 1 (atomic number for hydrogen)
n = 1, 2, 3…. where n2 is larger than n1
1 1 1
= (RH)((𝑛 )2 − (𝑛 )2 )
λ 1 2
Example: What wavelength of light (in nm) is emitted when an electron in a hydrogen atom moves from n=5 to n=2?
1 1 1 1 1
= (RH)((𝑛 )2 − (𝑛 )2 ) = (1.097 x 107 m-1)(22 − 52 ) = 4.34 x 10-7m = 434 nm
λ 1 2
The Energy States of the Hydrogen Atom
Only transitions from n = 3, 4, 5, and 6 to n = 2 produce visible wavelengths.
Example: Which electronic transition in a hydrogen atom will result in the emission of light with the longest wavelength?
n = 3 to n =2
Orbitals and Quantum Numbers
Value of l 0 1 2 3
Type of orbital s p d f
Representation of Orbitals
Subshell Type s subshell p subshell d subshell f subshell
Spherical in shape Dumbbell in shape (2 lobes) Four-leaf clover in shape (4 lobes) Most have 6-8 lobes
Orbital One orientation (ml = 0) Three orientations (ml = -1, 0, +1) Five orientations (ml = -2, -1, 0, 1, Seven orientations (m1 = -3, -2, -1,
2) 0, 1, 2, 3)
l = 0 for s subshell l = 1 for p subshell l = 2 for d subshell l = 3 for f subshell
Subshell One s orbital per s subshell Three p orbitals per p subshell Five d orbitals per d subshell Seven f orbitals per f subshell
Can hold 2 electrons Can hold 6 electrons (2 per orbital) Can hold 10 electrons (2 per Can hold 14 electrons (2 per
orbital) orbital)
Electron Configuration
• An electron configuration is a shorthand notation which shows the distribution of electrons among subshells.
o The number of principal energy level is followed by a letter symbol for the subshell (1s).
o A superscript to each subshell symbol designates the number of electrons in that subshell (1s 2).
▪ Example: Orbital diagram for Carbon
Valence Electrons
• Electrons in the outermost shell OR electrons with the highest principal quantum number, n.
• Will be in s or p subshells (in s and d subshells for transition metals).
Core Electrons
• Electrons in the full shells between the nucleus and the valence shell.
• Will have the same electron arrangement as a noble gas.
