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Quantum Chemistry 0
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In quantum mechanics, the Schrödinger
equation is used to solve Newton's equations
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This course consists
of 120 videos that are organized into 10 chapters
and a course playlist, as well as various chapter
playlists
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On the
other hand, in quantum mechanics, the behavior
is probabilistic
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However, atoms and electrons behave
differently from these objects
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1 Introduction

2

Quantum Chemistry 0
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1 Blackbody Radiation
This discussion will focus on blackbody radiation and
the origins of early quantum theory
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The theory predicts that as the frequency of light
increases, the amount of radiation also increases with
the square of the frequency
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Planck proposed that the energy levels inside the black
box cannot have any possible level, as classical theory
suggests, but rather there exists a quantized set of
values
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Here are a few examples of this formula:




At a frequency of 1 Hz and temperature of 1000 K,
the density of radiation is 0
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At a frequency of 10 14 Hz and temperature of 300 K,
the density of radiation is 2
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Quantum Chemistry 1
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1 Blackbody Radiation

Quantum Chemistry 1
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This effect was solved by a quantum
hypothesis, providing an example of a quantum
solution to a classical physics problem
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Changing the frequency of
the light from red to green to blue would not change
the electrons that are ejected from the surface
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This means
that changing the intensity of the UV light will not
change the speed of the ejected electrons
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2 Photoelectric Effect

Quantum Chemistry 1
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3 Rydberg Formula
Rydberg Formula
In this article, we will discuss the Rydberg formula
and an example of when a quantization hypothesis
solved a problem that classical physics couldn't seem
to solve
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This radiation
occurs when transitioning from one energy level to
another
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6 inverse centimeters so wave numbers or ν
is equal to the frequency of the light divided by the
speed of light
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This number, 109
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Quantum Chemistry 1
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4 - Bohr Hydrogen Model
1: Radius
we will explore the Bohr model for the hydrogen
atom and calculate the radius of a hydrogen atom in
certain conditions
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General Physics Review

In physics, we have mass and the resistance to
acceleration is the moment of inertia
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This presents a situation
with two unknowns: v and r
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Niels Bohr had a hypothesis in 1911:
The Bohr radius is the radius at which n equals 1, and
then the radius goes up quadratically with n
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1 nanometers (nanometer being 10^-9
or 1 billionth of a meter)
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Quantum Chemistry 1
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We will start by using the
equation derived from Bohr's hypothesis:
r = (n^2 * h^2)/(4*pi^2 * me * k * e^2)
Where:



r = radius of the hydrogen atom
n = principal quantum number (for hydrogen, n
= 1)



h = Planck's constant (6
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109 x 10^-31 kg)





k = Coulomb's constant (8
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602 x 10^-19 C)

Plugging in the values, we get:
r = (1^2 * (6
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109 x 10^31 * 8
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602 x 10^-19)^2)
Simplifying and converting to nanometers, we get:
r = 0
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053 nanometers
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4 - Bohr Hydrogen Model
1: Radius

Quantum Chemistry 1
...
To determine the radius of the ground state of the atom, we looked at a
rotating reference frame and concluded that the Coulomb force attracting the electron
to the nucleus must be balanced by the centrifugal force keeping it rotating constantly
around the proton
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So, it starts at low energy and continuously goes up
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Jumps Between Two Energy Levels
We calculate the energy difference between two energy levels as delta E
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The
value of the Rydberg constant (Rh), or what we might refer to as R infinity, is
expressed analytically and is accurate to within 0
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Note that the
proton has finite mass, and the electron does not weigh infinitely more than the proton
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

Assumption: angular momentum of the electron is quantized
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Quantum Chemistry 1
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7 - Uncertainty Principle
in Measurement
Einstein, in 1906, described light as both a particle and a
wave with the photoelectric effect
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He suggested that matter is something that can have
a wavelength, which can be defined as the wavelength
equals Planck's constant divided by momentum of the
particle
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I
have set some integer n from 1 up to 12
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As long as n is some integer, you get a
case where the wave is a standing wave and can exist on
the circle, and the end meets up with the beginning
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7 - Uncertainty Principle
in Measurement

Quantum Chemistry 1
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





The uncertainty for where an electron is located is
related to the photon used to measure its position
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A smaller wavelength photon provides more accurate
information on the electron's position
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Developing a General Theory

The next chapter will begin with the classical wave
equation, which will allow us to start developing a more
general theory for waves that describe these small particles
and how we can derive a general equation
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7 - Uncertainty Principle
in Measurement

Quantum Chemistry 2
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It
involves second derivatives and partial derivatives, and is
an equation in which we need to solve using the
derivatives of a function for the function itself
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In the
next video, we will apply this specifically to the case of a
one-dimensional vibrating string
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General Solution:
Solution to the wave equation: $$\frac{\partial^2
u}{\partial t^2}= c^2 \frac{\partial^2 u}{\partial
x^2}$$Solution to the separation of variable:$$u(x,t) =
X(x)T(t)$$By substitution, we arrive at two ODEs:$$X''(x) +
kX(x) = 0$$$$T''(t) + c^2kT(t) = 0$$The solution to each
ODE is:$$X(x) = A\sin(kx) + B\cos(kx)$$$$T(t) = C\sin(ct) +
D\cos(ct)$$Therefore, the general solution to the wave
equation is:$$u(x,t) = \left(A\sin(kx) +
B\cos(kx)\right)\left(C\sin(ct) + D\cos(ct)\right)$$
The solution involves sines and cosines, which is taught in
an ordinary differential equations course to solve this
particular equation
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1 - Classical Wave
Equation

Quantum Chemistry 2
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The displacement at the value x equals zero for all values
of time is going to be equal to zero
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Beta l equals to some integer n times pi so that
is true at any integer times pi
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Beta equals n pi over l so this is equal to a different
constant times cosine of n pi v t over l plus phi which is
some phase factor some angle which is determined by the
relative ratios of c and d
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The next part will show how the
string vibrates over time in a general case
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Quantum Chemistry 2
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The animations will show how waves
vibrate and move through time
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As we
increase the value of n, the waves oscillate faster but the
amplitude remains constant
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Sub Waves

We can see various sub waves traveling back and forth
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Vibrating String
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