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162 Terms
What is quantum mechanics?
Quantum mechanics is the framework for explaining the behavior of matter and energy at the atomic and subatomic levels, where classical mechanics fails.
Why is quantum mechanics important?
Understanding the structure of atoms, properties of solids, interactions with light, nuclear fission and fusion, semiconductors, LEDs, microscopy, and computing.
What did classical physics explain?
Newton’s laws explained motion and matter. Maxwell’s equations explained radiant energy (electromagnetism).
What is the UV Catastrophe?
The UV catastrophe refers to the contradiction between classical physics predictions (continuous emission of energy at shorter wavelengths) and experimental observations of black body radiation.
What was Planck's Quantum Theory about?
Planck proposed that electromagnetic waves are quantized, meaning energy is emitted and absorbed in discrete packets (quanta) rather than continuously.
According to Planck's Quantum Theory, how does matter absorb light?
Matter can only absorb light of frequency in discrete quanta, which we now call photons. E=hv
What is the Photoelectric Effect?
When light of variable frequency is shone on a metal surface, electrons are only emitted at particular frequencies. This is the photoelectric effect.
According to classical theory, what should control light energy in the photoelectric effect?
Classical theory suggested that light intensity should control light energy, meaning electron emission should occur irrespective of frequency.
What was observed in the Photoelectric Effect experiment?
Electron emission depended on the frequency rather than intensity. A certain threshold frequency was required for emission.
How does light behave in the Photoelectric Effect?
Light behaves as a particle (photons), transferring energy to electrons. The work function is the minimum energy required to release an electron.
How is kinetic energy and threshold frequency related in the Photoelectric Effect?
The electron released has a kinetic energy = 1/2mv^2. The threshold frequency (v0), must be exceeded to give photons enough energy to enable electrons to escape from the surface: hv0 = (M), so 0 = (M)/h
How is the Photoelectric Effect experiment performed?
Variable frequency light source, shine light onto a metal surface. Determine the light frequency which causes electrons to be emitted. Measure the energy of the emitted electrons.
What happens during Photoelectron Spectroscopy?
EM radiation (typically X-Ray) is directed onto a molecule/material, and the energy of the electrons emitted is measured: ½ mev2 = h - I (where I is the ionisation energy, instead of the work function).
What is XPS used for?
It can determine composition, and chemical properties of surfaces. Can be used for molecules!
What happens during Compton Scattering?
If light can be described as photons, if they collide with other particles, there should be a change in their momentum (= mass x velocity).
What were Compton's results?
The incident wavelength peak was always present, but also observed a peak at different wavelengths. The shift in 𝝀 varies with the angle
How can the photon model explain Compton Scattering?
The photon model explains the change in energy/momentum of photons scattered by individual electrons. ∆ = (2h/mec) sin2 (½)
What do electrons act like, in addition to particles?
Electrons can also act like waves.
What do diffraction and interference patterns indicate about electrons?
Diffraction and interference patterns indicate wave-like behavior.
What does it mean to say that ligh and electrons exhibit wave-particle duality?
Light behaves as a particle at the atomic scale. The electron can also behave like a wave. This leads to the concept of wave-particle duality
What is wave particle duality?
That subatomic molecules behave in both ways as waves, but also as particles at the same time.
What scale is classical mechanics good at describing?
Macroscale. So understanding how big objects move.
What is quantum chemistry important for?
Understanding what an atom looks like. Understanding how bonding works and understanding how molecules interact with each other.
Who derived a mathematical explanation for some phenomena that were previously unknown, marking the beginning of quantum theory?
Max Planck in the 1900s.
What work did Einstein win the Nobel prize for?
Einstein's explanation of the photoelectric effect.
Who derived mathematical descriptions of quantum applied to an electron in atoms?
Heisenberg and Schrodinger.
What do the Schrodinger and Heisenberg equations do?
They encompass everything that can possibly happen to an atom or to a subatomic molecule.
What did Maxwell accurately describe?
Electromagnetic radiation works.
How does quantum theory explain the blackbody radiation spectrum?
It treats the system as quantised states rather than a continuum, explaining the UV catastrophe.
What is threshold frequency in the context of the photoelectric effect?
The minimum energy required to remove an electron from a metal surface.
How does the photoelectric effect experiment work with a detector or photocell?
Bombarding a metal with light and measuring the emitted electrons to understand surface properties, with a voltmeter indicating electron velocity and energy.
What did Compton observe in his scattering experiment?
The change in wavelength of scattered X-rays varies with the scattering angle, indicating a change in momentum.
What did Davisson and Girmer's experiment demonstrate?
Electrons, when diffracted through nickel foil, create concentric rings, indicating they behave as waves.
What is wave particle duality?
That subatomic molecules behave in both ways as waves, but also as particles at the same time.
What scale is classical mechanics good at describing?
Macroscale. So understanding how big objects move.
What is quantum chemistry important for?
Understanding what an atom looks like. Understanding how bonding works and understanding how molecules interact with each other.
Who derived a mathematical explanation for some phenomena that were previously unknown, marking the beginning of quantum theory?
Max Planck in the 1900s.
What work did Einstein win the Nobel prize for?
Einstein's explanation of the photoelectric effect.
Who derived mathematical descriptions of quantum applied to an electron in atoms?
Heisenberg and Schrodinger.
What do the Schrodinger and Heisenberg equations do?
They encompass everything that can possibly happen to an atom or to a subatomic molecule.
What did Maxwell accurately describe?
Electromagnetic radiation works.
How does quantum theory explain the blackbody radiation spectrum?
It treats the system as quantised states rather than a continuum, explaining the UV catastrophe.
What is threshold frequency in the context of the photoelectric effect?
The minimum energy required to remove an electron from a metal surface.
How does the photoelectric effect experiment work with a detector or photocell?
Bombarding a metal with light and measuring the emitted electrons to understand surface properties, with a voltmeter indicating electron velocity and energy.
What did Compton observe in his scattering experiment?
The change in wavelength of scattered X-rays varies with the scattering angle, indicating a change in momentum.
What did Davisson and Girmer's experiment demonstrate?
Electrons, when diffracted through nickel foil, create concentric rings, indicating they behave as waves.
What did classical physics explain?
Newton’s laws explained motion and matter. Maxwell’s equations explained radiant energy (electromagnetism).
What is the UV Catastrophe?
The UV catastrophe refers to the contradiction between classical physics predictions (continuous emission of energy at shorter wavelengths) and experimental observations of black body radiation.
What was Planck's Quantum Theory about?
Planck proposed that electromagnetic waves are quantized, meaning energy is emitted and absorbed in discrete packets (quanta) rather than continuously.
According to Planck's Quantum Theory, how does matter absorb light?
Matter can only absorb light of frequency in discrete quanta, which we now call photons. E=hv
What is the Photoelectric Effect?
When light of variable frequency is shone on a metal surface, electrons are only emitted at particular frequencies. This is the photoelectric effect.
According to classical theory, what should control light energy in the photoelectric effect?
Classical theory suggested that light intensity should control light energy, meaning electron emission should occur irrespective of frequency.
What was observed in the Photoelectric Effect experiment?
Electron emission depended on the frequency rather than intensity. A certain threshold frequency was required for emission.
How does light behave in the Photoelectric Effect?
Light behaves as a particle (photons), transferring energy to electrons. The work function is the minimum energy required to release an electron.
How is kinetic energy and threshold frequency related in the Photoelectric Effect?
The electron released has a kinetic energy = 1/2mv^2. The threshold frequency (v0), must be exceeded to give photons enough energy to enable electrons to escape from the surface: hv0 = (M), so 0 = (M)/h
How is the Photoelectric Effect experiment performed?
Variable frequency light source, shine light onto a metal surface. Determine the light frequency which causes electrons to be emitted. Measure the energy of the emitted electrons.
What happens during Photoelectron Spectroscopy?
EM radiation (typically X-Ray) is directed onto a molecule/material, and the energy of the electrons emitted is measured: ½ mev2 = h - I (where I is the ionisation energy, instead of the work function).
What is XPS used for?
It can determine composition, and chemical properties of surfaces. Can be used for molecules!
What happens during Compton Scattering?
If light can be described as photons, if they collide with other particles, there should be a change in their momentum (= mass x velocity).
What were Compton's results?
The incident wavelength peak was always present, but also observed a peak at different wavelengths. The shift in 𝝀 varies with the angle
How can the photon model explain Compton Scattering?
The photon model explains the change in energy/momentum of photons scattered by individual electrons. ∆ = (2h/mec) sin2 (½)
What do electrons act like, in addition to particles?
Electrons can also act like waves.
What do diffraction and interference patterns indicate about electrons?
Diffraction and interference patterns indicate wave-like behavior.
What does it mean to say that ligh and electrons exhibit wave-particle duality?
Light behaves as a particle at the atomic scale. The electron can also behave like a wave. This leads to the concept of wave-particle duality
How do electrons behave at the atomic level?
Electrons behave as waves at an atomic level; their wavelength is comparable to the distances between atoms in a crystal.
What information can be obtained from the distances between rings in electron diffraction?
The distances between the rings in the diffraction pattern can provide structural information, and they can reveal surface information because they do not penetrate far into the crystal.
What is Low Energy Electron Diffraction (LEED) used for?
Low Energy Electron Diffraction (LEED) is used to detect surface features like adsorbed molecules when the energies are low enough (20-200 eV).
According to wave-particle duality, how do electrons behave?
Electrons behave as both waves and particles.
What is the de Broglie equation?
λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum.
What does Heisenberg's Uncertainty Principle state?
The more precisely you know the position of a quantum particle, the less precisely you can know its momentum, and vice versa.
What is Zero Point Energy?
There is never a state with zero energy at the atomic level due to the uncertainty principle.
Why does the Bohr electron model not work with quantum theory?
Because it would be possible to know the trajectory (position and momentum), which is not allowed by the uncertainty principle.
What do orbitals describe?
Orbitals describe the location of electrons.
What is a wavefunction (Ψ)?
The mathematical function that, when plotted, gives the shape of the orbital (e.g., 1s orbital).
What is the Schrödinger equation?
HΨ = EΨ, where H is an operator, Ψ is the wavefunction, and E is the energy.
Give the general form of the equation used to represent orbitals
Ψ = exp (-ζr) Y (θ, φ), where r, θ, φ are coordinates.
What does the Schrodinger equation relate?
The wave function to the energy of any system.
What information does the wave function contain?
All the available information about what it is describing, e.g. a 1s electron in hydrogen.
What two energy terms does the Schrodinger equation divide energy into?
Kinetic and potential energy.
What is the Hamiltonian operator?
The sum of kinetic and potential energy operators that acts on the wavefunction.
How is kinetic energy altered in the context of the Schrodinger equation?
It must account for quantum effects on momentum.
What is the condition for a particle trapped in a box at the edges of the box?
The wavefunction must equal zero (the particle cannot escape).
What do the solutions for a particle in a box represent?
Standing waves, where more energy equals more nodes.
What equation relates angular wavenumber, k, to wavelength?
k = 2π / 𝜆
What is the general form of a wavefunction?
(x) = Asin(kx) + Bcos(kx)
What is the value of B in the general wavefunction form given the boundary conditions?
B = 0
What is the condition for kL based on the boundary condition (L) = 0?
kL = nπ
How are quantum dots related to the particle in a box model?
Electrons in bands behave like particles in a box, and emission is tuned by size.
In conjugated molecules, what are the delocalized 𝜋 electrons free to do?
Move over the length of the molecule chain.
What kind of force does a diatomic molecule experience when one atom is displaced from its position in the harmonic oscillator model?
A restoring force, opposite to the displacement (F = -kx).
What is the potential energy V(x) for a harmonic oscillator?
V(x) = (1/2)kx^2
What is the formula for allowed energies En for a harmonic oscillator?
En = (n + 1/2)ℏω, where n = 0, 1, 2, 3, 4…
What is the zero point energy?
The energy when n=0 E0 = 1/2 ℏω
Where are energy levels seen?
Vibrational spectroscopy and photochemistry
What terms are included in the Hamiltonian for the Hydrogen atom?
Kinetic energy of the electron and potential energy of attraction between the proton and the electron
What is the Born-Oppenheimer approximation?
The mass of the proton is so large that its kinetic energy can be ignored.
What is the formula of the potential energy term in the Hydrogen atom Hamiltonian?
Vne = −𝑒2 / (4𝜋𝜀0r)
What are the two terms included in the molecule Hamiltonian for H2+?
kinetic energy of the electron and the potential energy for the attraction for each proton
Why is the potential energy negative?
Due to the attraction between the electron and proton.
What is the main difference between the Hamiltonian of the H2+ and H2 molecules?
H2 molecule includes an electron repulsion term.