unit 5 & 6: astro 355

what do atomic processes describe? list the four types of atomic processes. which ones can be either radiative or collisional?

they describe how and why an atom changes physically.

1. Excitation

2. De-excitation

3.Ionization

4.Recombination

The first three (excitation, de-excitation, ionization) can be either radiative or collisional.

explain both: radiative processes and collisional processes.

radiative - involves an atom gaining or losing energy radiatively through an interaction with a photon

collisional - involves an atom gaining or losing energy non-radiatively through a collision with another particle, such as an electron, ion, or atom.

explain radiative excitation (photon pov vs atom pov). how would this be represented symbolically? how is energy conserved?

absorption is from the photon’s POV. radiative excitation is from the atom’s POV. it is when a photon gets absorbed into an atom, causing the atom to become excited and reach a higher n energy level.

the radiative energy from the photon is converted into atomic potential energy stored in the now excited atom, since it now holds more energy.

explain collisional excitation (how does it happen with stars). how is this represented symbolically? explain the ideal assumption and how energy is conserved.

In stars, collisions are typically with fast-moving, free electrons. When a free particle with an initial KE (initial velocity) collides with an atom, it excites the atom into a higher n energy level, with the particle leaving with a final KE (final velocity).

Perfectly elastic collision such that no KE from the colliding particle is transferred into changing the KE of the atom. Energy is conserved, but kinetic energy can be converted into atomic potential energy during excitation.

explain radiative ionization and how it is represented symbolically

if the incoming photon’s energy is greater than the binding energy of the atom, then the atom is ionized.

explain collisional ionization and how it is represented symbolically. what is the ideal assumption?

occurs when a free electron with a kinetic energy greater than the ionization potential of the atom, collides with the atom.

Perfectly elastic collision such that no KE from the colliding particle is transferred into changing the KE of the ion.

explain recombination and the two ways that it can occur for a H atom. in both cases, what happens (also in eq form for total energy of system)

Occurs when a free electron is captured by an ion, with a photon carrying away the excess energy (it’s the real deal for hydrogen).

direct recombination: A free electron recombines with a proton (H+) and goes directly into the ground state (n = 1).

multi-step recombination: A free electron recombines with a proton into an excited state (n > 1). Multiple photons can be emitted as the atom eventually reaches n = 1 through spontaneous emission.

in both cases, the H atom ends up in ground state with:

Erad, tot = 13.6 eV +1/2 (m_ev_e²)

what is the ideal assumption for recombination? and how is energy conserved?

Perfectly inelastic collision. Total particle momentum is conserved (not KE) but the free electron’s initial KE contributes fully to the spontaneous emission.

(The electron's initial KE and the energy released by becoming bound contribute to the emitted photon, while the H atom retains some KE from the collision)

what are all stellar photospheres mostly made of

H & He

using the simplified gas model with gas as a collection of freely moving particles placed in a box, explain the main concepts of foundational gas physics (macroscopic). (particles in photospheres, physical properties, motion relations)

atoms, free subatomic particles, ions, and molecules are found in stellar photospheres.

gas is described by three interrelated physical properties: T = temperature, n = N/V = number density, P = pressure.

key: temperature and pressure are related to the motion of gas particles. Temperature is related to the velocities of individual gas particles, while pressure is related to the forces exerted by individual gas particles on the walls of the container.

recall ideal gas law, define pressure

P = nkT. relates the three physical properties of a gas. also called the “pressure equation of state” for an ideal gas.

recall kinetic theory of gases (what does it model, what occurs due to its motion)

microscopic gas physics, models a gas as a large collection of tiny particles in constant, random motion. The motions and interactions (like collisions) of the individual gas particles give rise to the macroscopic properties.

the quantity kt is called _________

characteristic thermal energy

What is the ideal case of thermodynamic equilibrium?

A state where temperature, pressure, and chemical composition are balanced throughout the system. There are no net flows of heat, matter, or chemical change, and macroscopic properties remain constant over time. Particles still move and interact, but the system's overall properties remain unchanged.

explain what the Maxwell-Boltzmann Velocity Distribution gives us, when a gas obeys the distribution, what is at the tail of each distribution, and what the increasing / decreasing curves represent.

key: The M-B velocity distribution gives the probability of finding a gas particle with a particular velocity in a gas with temperature T.

Under ideal case of thermodynamic equilibrium, a gas can be described by a single temperature, and particles in the gas obey a Maxwell-Boltzmann velocity distribution.

Each M-B distribution has a tail of very high-speed particles.

f(v) ∝ v²exp(-mv²/2kT). increasing parabola (v²), decreasing exponential (e^-v²)

for M-B distribution, the area under the curve is _________ for different curves of the same atom

the same

explain temperature dependence from M-B distribution (a higher temp gas has..)

larger average & peak particle velocity, a wider distribution of gas particle velocities. (compared to lower temperature gas).

key: Higher T_photosphere means what (in terms of KE)

greater KE available to collisionally excite and ionize photospheric atoms.

The most probable (i.e., peak) velocity equation is?

interpret the M-B graph (what it shows, peak, area, shaded, symmetry). how could we find the area of the shaded region?

• Shows how particles are distributed among different speeds.

• Peak: Most probable speed (the speed possessed by the largest number of particles).

• Area under the curve: Represents the total fraction of particles.

• Shaded area: Represents the fraction of particles within a particular speed range.

• The curve is asymmetric, with a tail extending toward higher speeds.

draw a rectangle with shaded region and find the area. (A = bh = Δv x nv/v)