Atomic Structure, Electromagnetic Radiation

• The atom consists of protons, electrons, and neutrons.

Nuclear Model

• J.J. Thomson discovered the negatively charged electron
• The fundamental charge magnitude was found with the Millikan oil drop experiment.
• The Geiger-Marsden experiment disproved this by demonstrating a positive charge located in the nucleus comprised of protons and neutrons.

Electromagnetic Radiation

• Spectroscopy is the analysis of emitted or absorbed light by substances
• Electromagnetic radiation features oscillating electric and magnetic fields that travel at the speed of light.
• Wavelength (λ) represents the distance between two closest peaks of the wave.
• Amplitude (A) represents the height of the wave from centerline.
• The brightness of radiation, intensity, is the square of the amplitude.
• Frequency (𝜈) is the number of cycles of radiation per second
• The frequency to wavelength relationship: λ × ν = 𝑐
• White light is a mixture of all wavelengths of light between 420-700 nm.

Atomic Spectra

• Hydrogen gas emits electromagnetic radiation when a high current is passed through it, which “excites” electrons
• Transition is the movement from one energy level to another
• A continuous spectrum emerges when white light passes through a prism
• Emission lines appear when electromagnetic radiation emitted from hydrogen gas passes through prism exposing differing wavelengths of light that hydrogen gas emits
• Electrons can exist within discrete energy levels and the frequency of emitted light is 𝜈 = ℜ(1/𝑛1제곱−1/𝑛2제곱)
• Lyman series occurs if n1 = 1
• Balmer series occurs if n1 = 2
• Paschen series occurs if n1 = 3
• Absorption lines appear if white light is passed through hydrogen gas and a prism

Quantum Theory

• Two scientific findings led to the transition from classical to quantum physics: experiments showing differing wavelengths emitted by blackbody radiation and the photoelectric effect
• Incandescence is when a heated object begins to glow, caused by intensity radiation increases, and color changes
• A blackbody does not favor absorbing or emitting a specific wavelength
• Blackbody radiation has two defining laws, its intensity is defined by the Stefan-Boltzmann Law: σ × 𝑇4

Blackbody Radiation

• Wien's Law states, constant = 𝜆max × 𝑇
• Classical physics was unable to properly explain the experimental results
• Classical mechanics assumes a specific amount of energy for electromagnetic radiation can oscillate at any wavelength, which leads to the Ultraviolet catastrophe

Quanta and Photoelectric Effect

• Quantas are packets of energy where energy exchanged between matter and radiation occurs
• Energy itself can only be transferred in specific amounts: E = h𝜈
• The UV catastrophe can be avoided at low temperatures as there will not be enough energy to oscillate at a lower frequency
• Photons confirm the quanta concept: radiation will be above or below a certain threshold frequency known as its "work function" (𝜙)
• Electrons can be ejected immediately regardless of intensity
• Intensity is not equivalent to energy, it is the number of photons at a specific instance
• Kinetic energy of the ejected electron(s) increases linearly with the radiation frequency, mev제곱 = hv – Φ
• Bohr frequency conditions: hv = Eupper − Elower
• The All particles possess both wave and particle properties

Duality of Matter

• Blackbody radiation is wave property, it has frequency and amplitude
• The photoelectric effect is a particle property complete with mass and speed
• Diffraction in a pattern of high and low intensities generated by an object in the path of a ray of light that produces light and dark spots
• Constructive interference happens when peaks coincide, enhancing the amplitude of the wave
• Destructive interference happens when peaks and troughs coincide, which diminishes the wave to form a node

The Uncertainty Principle

• There will be an unknown due to the wave nature of an object, as a definite trajectory to preduct locations does not exist
• Heisenberg's Uncertainty Principle says the complementarity of location and momentum of a particle

Wave Functions and Energy Levels

• Wavefunction(𝛹) is a mathematical function with values that changes position, and is found via Schrodinger Equation

Quantization of Energy

• A particle is confined to a simple one-dimensional box, can only can be half-periods
• Walls of boxes have infinite potential energy
• Its wave function for this particle: Ψ𝑛(x) = (2/𝐿)1/2sin(𝑛π𝑥/𝐿)

Hydrogen Atoms

• Hydrogen is similar to a particle-in-a-box but the attraction of the nucleus confines the electron
• Energies are quantized

One electron species

• The Rydberg constant measured spectroscopically from the hydrogen emission spectrum is equivalent to the Rydberg's constant from fundamental constants
• Nuclear charge determines the number of protons in an atom
• Ionization energy completely extracts the attractive force in an atom with its single electron

Atomic Orbitals

• Are electron clouds centered around the nucleus where cloud density shows electron location
• Spherical polar coordinates (r,θ,ϕ): is used to define the location of a point around a nucleus
• Radial and angular wave functions express how the wave function changes with parameters
• Atomic Surface can have zero electron density if one or both the functions are zero

Quantum Numbers, Shells, and Subshells

Three quantum numbers express energy within an atom n, l, ml

• The first number is roughly equivalent with energy and size of the orbital
• One-electron atoms exhibit orbitals that have the same number that degenerate
• Orbitals with the same number belong to the same atomic shell
• Orbital angular momentum quantum number determines shape and not as important to energy
• Each has "n" number of subshells that have I's of the same value for its specific orbital shell principal number
• I is used to describe momentum in an electron

Shape of Orbitals

ns-orbital

• S orbitals in its shell have principal number, independent of the other angles , and are spherically symmetrical
• The probability density approaches zero going outwards of nucleus
• Instead of drawing it as an electron cloud, a boundary defines most area where that electron is found
• Having no angular momentum means it cannot fling away from nucleus, meaning there is a non-zero potential for it to be around nucleus

Distributions

• It is a probability for finding an electron at all values defined by θ,ϕ
• For orbitals: P(r) = r^2R^2(r)
• For an s orbital, it is spherically symmetrical
• It is the radial that changes with a specific amount from surface where that potential is equal to the kinetic