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Quizlet

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average was about a 68% for test 1

Ch 3 - part 3

Phet simulation

standing waves
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Applying Wave Theory

Why is e- energy quantized?

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De Broglie (1924) reasoned that e- is both particle and wave.
- Electron is a particle but has wave properties
- Particles therefore must have both wave and particle properties
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Schrodinger Wave Equation

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- - Don’t have to know this
  - H is an operator
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In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e
H is called an “operator”: in this case taking the second derivative with respect to x, y, and z. E is the energy
Solution is a wave function: Ψ
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1. energy of e- is given by Ψ
2. Ψ2 is the probability of finding e- in a volume of space
A simple example of a wavefunction is:
- Ψ=Asin(x)
energy of e- is given by Ψ
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Ψ^2 is the probability of finding e- in a volume of space
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Schrodinger’s equation can only be solved exactly for simple systems (H atom). Must approximate its solution for multi- electron systems.
- Our approximations though are good enough to work in practical application
- Horizon made it to Pluto for example

Quantum Numbers: The Solutions from the Wave Function, ψ

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Calculations show that the size, shape, and orientation in space of an orbital are determined by three integer terms in the wave function.
- Quantize the energy of the electron
These integers (solutions) are called quantum numbers.
- There are four quantum numbers:
  - Principal quantum number,n
    - Energy level
- Angular momentum quantum number, l
  - Orbital type
Magnetic quantum number, ml
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- Position of orbital in an X-Y-Z plot
Spin quantum number, ms
- Orientation of the spin of the electron
These quantum numbers control how electrons are distributed in an atom

Principal Quantum Number, n: The Energy Level

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It characterizes the energy of the electron in a particular orbital.
- It is Bohr’s energy level.
Values of n can be any whole number integer >= 1.
It determines the size (overall) and energy of an orbital.
The larger the value of n, the more energy the orbital has.
The larger the value of n, the larger the orbital.
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Energies are defined as being “negative.”
- An electron’s energy is lowered (made more negative) as a result of its interaction with the nucleus of the atom.
  - An electron would have E = 0 when it escapes the atom.
- As n gets larger, the following occurs:
  - The amount of energy between orbitals gets smaller.
  - The energy of the orbital becomes greater (less negative).
- Won’t have to memorize this, but will need to know the energy is about 1/n^2
Rydberg constant for hydrogen (R_h) is 2.10 * 10^-8 J

Principal Energy Level in

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Angular Momentum Quantum Number, l: The Orbital Quantum Number

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The angular momentum quantum number determines the shape of the orbital.
- l can have integer values from 0 to (n – 1).
  - Ex n = 1
    - Only l=0 is allowed
  - n = 2
    - l = 0 or l = 1 are allowed
Each value of l is designated by a particular letter that designates the shape of the orbital.
- s orbitals are spherical.
- p orbitals are like two balloons tied at the knots (dumbbell shape).
- d orbitals are mainly like four balloons tied at the knots.
- f orbitals are mainly like eight balloons tied at the knots.

Magnetic Quantum Number, ml: The Position or Orientation Quantum Number

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The magnetic quantum number is an integer that specifies the orientation of the orbital.
- The direction in space the orbital is aligned relative to the other orbitals
Values are integers from −l to +l.
- Including zero
- Gives the number of orbitals of a particular shape
  - When l=2,the values of ml are−2,−1,0,+1,+2, which means there are five orbitals with l = 2.

Describing an Orbital

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Each set of n, l, and ml describes one orbital.
Orbitals with the same value of n are in the same principal energy level.
- Also called the principal shell
Orbitals with the same values of n and l are said to be in the same sublevel.
- Also called a subshell

Illustration of Energy Levels and Sublevels

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Energy Levels and Sublevels

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In general:
- The number of sublevels within a level = n
- the number of orbitals within a level = 2l + 1
- The number of orbitals in a level = n^2

Quantum Leaps

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- When an electron falls from a higher to lower energy level, light is emitted
  - An unstable state is when an electron is sitting in a state greater than 1

How Does the Quantum Mechanical Model of an Atom Explain Atomic Spectra?

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Each wavelength in the spectrum of an atom corresponds to an electron transition between orbitals.
When an electron is excited, it transitions from an orbital in a lower energy level to an orbital in a higher energy level.
When an electron relaxes, it transitions from an orbital in a higher energy level to an orbital in a lower energy level.
When an electron relaxes, a photon of light is released whose energy equals the energy difference between the orbitals.

It Explains Electron Transitions

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To transition to a higher energy state, the electron must gain the correct amount of energy corresponding to the difference in energy between the final and initial states.
Electrons in high energy states are unstable and tend to lose energy and transition to lower energy states.
Each line in the emission spectrum corresponds to the difference in energy between two energy states.

It Predicts the Spectrum of Hydrogen

Audio 0:31:35.930644 • For an electron in an energy state n, there are (n–1) energy states it can transition to. Therefore, it can generate (n – 1) lines.

Energy Transitions in Hydrogen

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The energy of a photon released is equal to the difference in energy between the two levels the electron is jumping between.
It can be calculated by subtracting the energy of the initial state from the energy of the final state.
- Don’t have to memorize this, just remember the 1/n^2 part

Transitions

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Example problem

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Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state.
Calculate the wavelength of the light emitted by a hydrogen atom during a transition of its electron from the n = 4 to the n = 1 principal energy level. Recall that for hydrogen En = -2.18 * 10-18 J*(1/n2)
Audio 0:44:32.880831 A) 97.3 nm B) 82.6 nm C) 365 nm D) 0.612 nm E) 6.8 * 10-18 nm
A
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It is possible to determine the ionization energy for hydrogen using the Bohr equation. Calculate the ionization energy for an atom of hydrogen, making the assumption that ionization is the transition from n=1 to n=infinity (RH=2.18 x 10-18 J) A) -2.18 × 10-18 J B) +2.18 × 10-18 J C) +4.59 × 10-18 J D) -4.59 × 10-18 J E) +4.36 × 10-18 J
B

Vocab

Term	Definition
quantum numbers	integer solutions to the wave functions (energy level n, orbital level l, magnetic quantum number m_l, and spin quantum number m_s)
(quantum number) n	quantum number which controls the size and energy of an orbital
(quantum number) l	quantum number which controls the shape of the orbital
s orbital shape	spherical
p orbital shape	like two balloons tied at the knots
d orbital shape	like four balloons tied together
f orbital shape	like eight balloons tied together at the knots
m_l (quantum number)	quantum number which controls the position or orientation of orbitals
sublevel (subshell)	orbitals with the same values of n and l are said to be in the same _
excited	An electron is said to be this when it transitions from an orbital of lower energy to an orbital of higher energy
relaxes	An electron is said to do this when it transitions from an orbital of higher to lower energy