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Aiden's Chemistry Notes

created: 2025-10-15; modified: 2025-10-15

Topic 1A: Investigating Atoms & Topic 1B: Quantum Theory

  1. Electromagnetic Radiation

Light is a form of ER; ER is a type of energy that travels through space; has the form
\[ \lambda \, \nu = c \] where $c$ is $3.0 \times 10^{8}\ \mathrm{m\ s^{-1}}$

  1. Electromagnetic Spectrum

The range of all possible frequencies of ER, from high to low frequency: $\gamma$-rays, X-ray, Ultraviolet, Visble, Infraed, Microwave, Radio
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  1. Atomic Spectra

When atoms absorb energy, their electrons move to a higher $n$ level (excited state), they gain $hv$ energy. When they fall back to a lower $n$ level (ground state), they emit energy in the form of light.
\[ E_{\text{photon}} = hv = \frac{hc}{\lambda} = E_{\text{higher}} - E_{\text{lower}} \] This light can be passed through a prism to produce an atomic emission spectrum; this is unique to each element. Likewise, when white light passes through a cool gas, the gas absorbs certain wavelengths of light, producing an atomic absorption spectrum.
\[ v = cR_H \left( \frac{1}{n_{\text{1}}^2} - \frac{1}{n_{\text{2}}^2} \right) \] The names of the different series of lines in the hydrogen atomic emission spectrum are:
Lyman ($n_1=1$), Balmer ($n_1=2$), Paschen ($n_1=3$), Brackett ($n_1=4$), Pfund ($n_1=5$).
The Planck Equation only came to light because of the photoelectric effect, where light of a certain frequency can eject electrons from a metal surface.
It's important to note that intensity of radiation is the number of photons, not the energy of each photon: a dim light has fewer photons than a bright light but each still carries the same energy.

  1. Work Function
The work function $\boldsymbol{\phi}$ is the minimum energy required to remove an electron from a metal surface. If an electron is being removed from an atom or molecule, it can be though as the photoionization, or the ionization energy.
\[ KE_{\text{ejected electron, max}} + \phi = E_{\text{photon}} \Rightarrow \tfrac{1}{2} m v^{2} + \phi = h \nu \]
  1. De Broglie Relation
De Broglie proposed that particles can have wave-like properties through this relation:
\[ \lambda = \frac{h}{mv} = \frac{h}{p} \]

Topic 1D: The Hydrogen Atom

  1. Energy Levels

The energy of an electron in a hydrogen atom (or a hydrogen-like atom) is given by:
\[ E_n = - \frac{Z^2hR}{n^2} \] From this, one can derive the Rydberg formula:
\[ E_{\text{photon}} = \Delta E_{\text{electron}} = R_{\infty} \cdot hc \left| \frac{1}{n_1^2} - \frac{1}{n_2^2} \right| \]

  1. Quantum Numbers

Topic 1 Formulas and Constants

  1. Formulas
\[ \lambda \, \nu = c \] \[ E_{\text{photon}} = hv = \frac{hc}{\lambda} = E_{\text{higher}} - E_{\text{lower}} \] \[ KE_{\text{ejected electron, max}} + \phi = E_{\text{photon}} \Rightarrow \tfrac{1}{2} m v^{2} + \phi = h \nu \] \[ \lambda = \frac{h}{mv} = \frac{h}{p} \] \[ E_n = - \frac{Z^2hR}{n^2} \] \[ E_{\text{photon}} = \Delta E_{\text{electron}} = R_{\infty} \cdot hc \left| \frac{1}{n_1^2} - \frac{1}{n_2^2} \right| (n_2 > n_1) \]
  1. Constants
  1. Speed of light, $c = 3.0 \times 10 ^{8}\ \mathrm{m\ s^{-1}}$
  2. Planck's constant, $h = 6.626 \times 10^{-34}\ \mathrm{J\ s}$
  3. Rydberg constant, $R_{\infty} = 1.097 \times 10^{7}\ \mathrm{m^{-1}}$
  4. Rydberg energy, $R = 2.178 \times 10^{-18}\ \mathrm{J}$
  5. Electron mass, $m_e = 9.109 \times 10^{-31}\ \mathrm{kg}$

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