289 Radiation

Radiation is the propagation of electromagnetic waves through space.

289.1 Energy Levels

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.