Quantum Model of Atom. Kim Shih Ph.D. The Behavior of the Electrons. Electrons are incredibly small a single speck of dust has more electrons than the number of people who have ever lived on earth Electron behavior determines much of the behavior of atoms
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Kim Shih
A Theory that Explains Electron Behavior
Kim Shih
The Nature of Light:Its Wave Nature
Kim Shih
Kim Shih
The Relationship Between Wavelength and Frequency
Kim Shih
Calculate the wavelength of red light with a frequency of 4.62 x 1014 s−1
Calculate the wavelength of a radio signal with a frequency of 100.7 MHz. 1MHz= 106 s1
Kim Shih
Color 4.62 x 10
Kim Shih
Amplitude & Wavelength 4.62 x 10
Kim Shih
Electromagnetic Spectrum 4.62 x 10
Kim Shih
Interference 4.62 x 10
Kim Shih
Interference 4.62 x 10
Kim Shih
Diffraction 4.62 x 10
Kim Shih
Diffraction 4.62 x 10
Kim Shih
2Slit Interference 4.62 x 10
Kim Shih
The Photoelectric Effect 4.62 x 10
Many metals emit electrons when a light shines on their surface
Kim Shih
Photoelectric Effect 4.62 x 10
Photoelectric Effect: Irradiation of clean metal surface with light causes electrons to be ejected from the metal. Furthermore, the frequency of the light used for the irradiation must be above some threshold value, which is different for every metal.
Kim Shih
Photoelectric Effect: 4.62 x 10The Problem
Kim Shih
Einstein’s Explanation 4.62 x 10
Kim Shih
Exercise 4.62 x 10
Kim Shih
Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 3.83 mJ
Hint:
Step 1: Convert all the units
Step 2: Find out individual photon energy
Step 3: Total energy /individual energy = total photon
Kim Shih
What is the frequency of radiation required to supply wavelength 337 nm and total energy 3.83
1.0 x 102 J of energy from 8.5 x 1027 photons?
Kim Shih
Spectra wavelength 337 nm and total energy 3.83
Kim Shih
Emission Spectra wavelength 337 nm and total energy 3.83
Kim Shih
Examples of Spectra wavelength 337 nm and total energy 3.83
Kim Shih
= wavelength 337 nm and total energy 3.83 R∞
= R∞
1
1
1
1
1
1
λ
λ


m2
22
n2
n2
Electromagnetic Energy and Atomic Line Spectra
Johann Balmer in 1885 discovered a mathematical relationship for the four visible lines in the atomic line spectra for hydrogen.
Johannes Rydberg later modified the equation to fit every line in the entire spectrum of hydrogen.
R (Rydberg Constant) = 1.097 x 102 nm1
Kim Shih
Rutherford’s Nuclear Model wavelength 337 nm and total energy 3.83
Kim Shih
Problems with Rutherford’s Nuclear Model of the Atom wavelength 337 nm and total energy 3.83
Kim Shih
The Bohr Model of the Atom wavelength 337 nm and total energy 3.83
Neils Bohr (1885–1962)
Kim Shih
Kim Shih wavelength 337 nm and total energy 3.83
Bohr Model of H Atoms wavelength 337 nm and total energy 3.83
Kim Shih
Wave Behavior of Electrons wavelength 337 nm and total energy 3.83
Louis de Broglie (1892–1987)
Kim Shih
Exercise wavelength 337 nm and total energy 3.83
Kim Shih
Calculate the wavelength of an electron traveling at 2.65 x 106 m/s
Hint: v = 2.65 x 106 m/s, m = 9.11 x 10−31 kg
h= 6.626 x 10−34 J∙s, J = kg m2 /s2
l=h/mv
Determine the wavelength of a neutron traveling at 1.00 x 102 m/s (Massneutron = 1.675 x 10−24 g)
Kim Shih
Kim Shih
Quantum Mechanics and the Heisenberg Uncertainty Principle 10
In 1926 Erwin Schrödinger proposed the quantum mechanical model of the atom which focuses on the wavelike properties of the electron.
In 1927 Werner Heisenberg stated that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle.
Kim Shih
Kim Shih
Heisenberg Uncertainty Principle 10
Based on de Broglie equation, electron velocity
related to λ.
Electron has both wave and particle properties called
Duality
It means we can not measure its position and velocity
at the same time.
Kim Shih
Determinacy vs. Indeterminacy 10
Kim Shih
Kim Shih
Kim Shih
Solutions to the Wave Function, 10Y
Kim Shih
electron in a region
of space (Y2)
solve
Wave
equation
Wave function
or orbital (Y)
Wave Functions and Quantum Numbers
A wave function is characterized by three parameters called quantum numbers, n, l, ml.
Kim Shih
Principal Quantum Number ( 10n)
Kim Shih
Principal Energy Levels in Hydrogen 10
Kim Shih
AngularMomentum Quantum Number ( 10l)
Kim Shih
Magnetic Quantum Number ( 10ml )
Kim Shih
Energy Shells and Subshells 10
Kim Shih
Wave Functions and Quantum Numbers 10
Kim Shih
Number of Electrons in Electron Shells and Subshells 10
Orbitals
Available
(2l + 1)
Number of Electrons
Possible in Subshell
[2(2l+1)]
Maximun Electrons
Possible for nth
Shell (2n2)
Subshells
Available
Shell
1
s 1 2 2
s 1 2 8
2
p 3 6
s 1 2 18
3
p 3 6
d 5 10
s 1 2 32
4
p 3 6
d 5 10
f 7 14
Kim Shih
Exercise 10
Kim Shih
What are the quantum numbers and names (for example, 2 10s, 2p) of the orbitals in then = 4principal level? How many orbitals exist?
n = 4
l = 0, 1, 2, 3
total of 16 orbitals: 1 + 3 + 5 + 7 = 42 = n2
Kim Shih
1. Identify the shell and subshell when n = 3 10l = 1 ml = 1
2. What are the possible quantum numbers for 4p?
3. Which of the following is not correct?
a. n = 3 l = 0 ml = 0
b. n = 2 l = 1 ml = 1
c. n = 1 l = 0 ml = 0
d. n = 4 l = 1 ml = 2
Kim Shih
Quantum Mechanical Explanation of Atomic Spectra 10
Kim Shih
Kim Shih
Kim Shih
Predicting the Spectrum of Hydrogen 10
Kim Shih
Hydrogen Energy Transitions 10
Kim Shih
Kim Shih 10
Exercise 10
Kim Shih
= 10R∞
= R∞
1
1
1
1
λ
1
1
λ


m2
n2
22
n2
Please identify all 4 lines(wavelength) in hydrogen
spectrum.
Rydberg Equation:
R (Rydberg Constant) = 1.097 x 102 nm1
Johann Balmer Equation:
Kim Shih
1 10
1
1
λ

m2
n2
Calculate the wavelength of light emitted when the hydrogen electron transitions from n = 6 to n = 5, E = hc/l
Rydberg Equation:
E
= R∞
=
hc
R (Rydberg Constant) = 1.097 x 102 nm1
h (Planck’s constant) = 6.626 x 1034 J s
Kim Shih
Kim Shih
Phases 10
Kim Shih
Probability Density Function 10
The probability density function represents the total probability of finding an electron at a particular point in space
Kim Shih
Node: A surface of zero probability for finding the electron.
Number of nodes = (n – 1)
Kim Shih
l 10= 1, p orbitals
Kim Shih
Kim Shih
l 10= 2, d orbitals
Kim Shih
d 10 orbitals
Kim Shih
l 10= 3, f orbitals
Kim Shih
f 10 orbitals
Kim Shih
Kim Shih