Midterm 2011 Solutions

# 6 ev for hydrogen maxwellboltzmann distribution nv is

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Unformatted text preview: ation (AU) / distance (pc) For radians, separation and distance must be in same units Parallax: π(“) = 1/d(pc) Tangential speed: Vtan (km/s) = 4.74 µ (“/yr) d(pc) µ is the magnitude of proper motion Doppler shift: λ0 is the rest frame wavelength, Vrad is the radial motion, positive for motion away from observer ∆λ = λ 0 Stefan ­Boltzmann Law: F = σ T 4 L = 4π R2 σ T 4 F is the flux, T the temperature, L the luminosity and R the radius Blackbody distribution: B(T) is a spectral radiance: energy per unit time per unit area per unit wavelength per unit angular area Wein’s Displacement Law: Vrad c Bλ (T ) = 2hc2 1 5 ehc/λkT − 1 λ λpeak is the peak wavelength of the blackbody distribution λpeakT = 2898 µm K Potential energy for e ­ orbital state n in a Hydrogen ­like atom: En = −χi /n2 Degeneracy for orbital state n: gn = 2n2 χi = 13.6 eV for Hydrogen Maxwell ­Boltzmann Distribution: n(v) is the number density of particles with velocity v, n is the total number density, m is the particle mass n(v )dv = n Ideal gas pressure law: n and ρ are the number and mass densities, m = µmH is the individual mass M ≈ uNnucleon is the molar mass P = nkT = Page 18 of 19 m 2π kT 3/2 e−mv ρRT ρkT = µmH M 2 /2kT 4π v 2 dv Physics 160 Fall 2011 Radiation Pressure Law Mean molecular weight: Aj = mj/mH, Nj is the number density and zj is the proton number of species j P= Boltzmann equation: Ni is the number of atoms in a given orbital state i Midterm Exam 14 aT 3 j µn = Nj Aj j Nj for neutrals Nj Aj j 1+zj µi = j Nj for ionized gas Ni gi = e−(Ei −Ej )/kT Nj gj ∞ Partition function: gi e−(Ei −E1 )/kT Z1 (T ) = i=1 Saha equation: Nm...
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## This document was uploaded on 02/26/2014 for the course PHYS 160 at UCSD.

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