Waves

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Spectra (How do we know what the universe if made out of?)

\large Multi-messenger astronomy

• Electromagnetic radiation
• cosmic rays
• meteorites
• neutrinos
• gravitational waves

Atoms and spectra

Hydrogen gas exhibits emission lines at discrete visible wavelengths, fit by empirical relation by Balmer in 1885 $\frac{1}{\lambda }=R(1/4-1/n^2)$ $n=integer>2$

Bohrs model

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Because orbital angular momentum is quantized, so is $r_n$ and $E_n$ $\to$ discrete orbtial levels

Atomic transition processes

• Transitions to free unbounded states behave similarly, however, they have diff names
• ionization and recombination
• photoionization (electron is knocked free). photon knocks electron free
• collisional ionization (electron becomes free). any other particle knocks electron free
• a positively charged ion may combine with a free leectron, and atom emits radiation (photons) as the electrons drop to lower levels. called recombination

Kirchoff’s Laws

• blackbody
• emission lines
• absorption lines

Tempature affects internal states of atoms and molecules

• temp of gas dermines the kinetic energies of the colliding particles
• and the incoming photons
• we observe outgoing photons

Temperature vs velocity

• Thermal motions: emitted or absorbed photos inherent their energy from the doppler velocites of the thermal motions of particles/atoms
• equilibrium distribution of particles speeds in an ideal gas is given by the Maxwell-Boltzmann distribution

mean free path and opt depth

• mean free path $x_m$. Distance which intensity decrease by a factor of 1/e
• optical depth $\tau =x/x_m$. Thickness of slab in units of mean free path $x_m$
• column density, $N(x)$: total number of absorbing particle sin a column with cross-section area 1 $m^2$ and length $x$