289 Radiation
Radiation is the propagation of electromagnetic waves through space.
289.2 Notes
The following equations, formulas, and laws govern radiation, photon interactions, and electron transitions within an atom:
Planck’s Relation (\(E = hf\)): Relates a photon’s energy to its frequency through Planck’s constant.
Hydrogen Energy Levels (\(E_n = -13.6 \text{ eV}/n^2\)): Defines the quantized energy states of a hydrogen atom based on the principal quantum number.
Rydberg/Balmer Formula (\(\dfrac{1}{\lambda} = R(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2})\)): Predicts wavelengths of light emitted or absorbed as electrons transition between specific atomic orbitals.
Conservation of Energy Transition Law (\(E_{\text{photon}} = \Delta E_{\text{atom}}\)): Photons are absorbed or released only if their energy matches the difference between stationary states.
Photon Momentum (\(p = h/\lambda\)): Quantifies the momentum carried by a massless photon based on its wavelength.
Dipole Selection Rule (\(\Delta l = \pm 1\)): Law requiring orbital angular momentum to change by exactly one unit during a single-photon transition.
Pauli Exclusion Principle: Fundamental law stating no two electrons in an atom can occupy the identical quantum state simultaneously.
Einstein Coefficients (\(A = \dfrac{8\pi h \nu^3}{c^3} B\)): Relates the probabilities of spontaneous emission, stimulated emission, and photon absorption in a system.
Fermi’s Golden Rule (\(\dfrac{dP_b}{dt} = \dfrac{2\pi}{\hbar} |\langle b|H^{(1)}|a\rangle|^2 \rho(E_a)\)): Calculates the transition rate between quantum states under the influence of an electromagnetic perturbation.
Bohr Radius (\(a_0 = \dfrac{4\pi\epsilon_0\hbar^2}{me^2}\)): Establishes the physical distance scale characterizing the innermost electron orbit of the hydrogen atom.