Download 1. Thermodynamics Conduction

1.
Thermodynamics
Chapters 19, 20, 21 (HRW)
Conduction
Radiation
P-V Diagrams
1st Law of TD
Engines
Entropy
F-L Contraction
Time Dilation
Addition of Velocities
Rel. Doppler
Rel. Kinematics
PMT1.1, PF1
H1-19.62
MT1.3, PMT1.2
MT1.2, PF2
PMT1.3
H3-21.3
MT2.1
PMT2.1
PF3
H5-2.51
MT2.2
2.
Relativity
Chapter 2
3.
Photons
Chapters 1, 3, 5
X-rays
Photoelectric Effect
Compton Scattering
De Broglie
Bragg scattering
H6-3.43
MT2.3, PF4
PMT2.2
PMT2.4
H8-5.3
4.
Quantum Theory
Chapters 5, 6
5.
Atomic Theory
Chapters 4, 7, 8
6.
Nuclear Properties
Chapter 12
Planck
H6-3.33
Heisenberg
MT3.1
Schrödinger
H9-6.5
Square Well
MT3.2, PMT3.1, PF5
Simple Harm. Osc.
H9-6.37
Pot. barriers, Tunneling
H9-6.39
Bohr
H7-4.23
Rutherford
MT2.4, PMT2.3
Atomic Q numbers
PMT3.2
Zeeman effect
MT3.3
J = L+S, spect. Notation
MT3.4
Anom. Zeeman effect
PMT3.3
Nuclear composition
H12-12.4
Binding energy
H12-12.17
Sizes and shapes
H12-12.8
Radioactive decay
H12-12.50
Half lives
PF7
7.
Nuclear Reactions
Chapter 13
Reactions
Q-values
Fission
Fusion
8.
Elementary Particles
Chapter 14
Fundamental forces
Particle classification
Quark structure
PMT3.4
PF6
H13-13.30
PF8
Useful Constants:
1 calorie = 4.186 J
Latent heat of vaporization of water = 539 cal/g = 2256 kJ/kg
Latent heat of fusion of water = 79.5 cal/g = 333 kJ/kg
Specific heat of water = 1 cal/g = 4.19 kJ/kg
1 atmosphere = 1.01E5 Pa
Universal Gas Constant, R = 8.31 J/mol.K
Boltzmann’s constant, k = 1.38E-23 J/K
Stefan-Boltzmann constant, σ = 5.67E-8 W/m2K4
Avogadro’s number, NA = 6.02E23 mol-1
Coulomb’s constant, (1/4π ε 0) = 8.99E9 N.m2/C2
Speed of light, c = 3.00E8 m/s
Charge of an electron, -e = -1.6E-19 C
Mass of the electron, me = 9.1E-31 kg = 511 keV/c2 = 5.49E-4 u
Mass of the proton, mp = 1.67E-27 kg = 938.3 MeV/c2 = 1.00728 u
Mass of the neutron, mn = 1.675E-27 kg = 939.6 MeV/c2 = 1.00866 u
Mass of the α particle, mα = 3727.4 MeV/c2 = 4.00151 u
Planck’s constant, h = 6.63E-34 J.s = 4.14E-15 eV.s
Planck’s reduced constant, ħ = h/2π = 1.05E-34 J.s = 6.58E-16 eV.s
Compton Wavelength of the electron, λ c = h/mec = 2.4263E-12 m
The Bohr Magneton, µ B = 5.79E-5 eV/T
Atomic mass unit, u = 1.66E-27 kg = 931.5 MeV/c2
1 Curie = 3.7E10 Bq
Useful Formulae
ΔQ = mcΔT where m = mass, c = specific heat.
Heat conduction, I = ΔT/R in Watts where R = thermal resistance = Δx/kA and
Δx = thickness, A = area and k = thermal conductivity
of the material.
4
PRAD = σεAT where ε = emissivity and A = area.
1st Law of Thermodynamics:
ΔQ = ΔW + ΔU
Ideal gas law: PV = nRT
Work done, ΔW = ∫PdV vrms = √(3RT/M)
Molar specific heats: CV = ΔU/nΔT CP = ΔQ/nΔT CP = CV + R γ = CP/CV
Adiabatic ==> ΔQ = 0, and PVγ = constant. Entropy change: ΔS = ∫dQ/T
Carnot engine efficiency, εC = 1 – QC/QH = 1 – TC/TH
Pot. energy lost by a charge q in a potential difference of V is U = qV
Wave relation: v = ν λ where v = velocity, ν = frequency, λ = wavelength.
β = v/c
γ = 1/√(1 – β 2) Length Contr.: L′ = L/γ
Addition of Velocities: v′ = (v + u)/(1 + vu/c2)
Rel. Doppler Effect:
Time Dilation,T′ = γT
ν′ =
E2 = p2c2 + m2c4
E = γmc2 p = γmv
Momentum – Energy relations:
√(1 – β) ν
√(1 + β)
K = E – mc2
Planck’s Relation: E = hν Einstein’s Photoelectric Law: hν = K + φ
Compton Effect:
Δλ = λ’ – λ = (1 – cosθ)h/mec
Elec. potential at a distance R from a charge Q:
Bohr Quantization Relation:
V = (1/4π ε 0)Q/R
L = mvr = nħ
Atomic Radii: rn = n2a0/Z
where a0 = 5.29E-11 m
Atomic Energies:
En = -Z2E0/n2
where E0 = 13.6 eV
Impact parameter: b = Z1 Z2 e2 cot(θ/2)
8πε 0K
n = ρNA/A
f = πb2nt
Fraction of α’s scattered through θ or greater:
4
2
2
N(θ) = Ni n t e Z1 Z2 _____
16 (4πε 0)2 r2 K2 sin4(θ/2)
Rutherford Scattering:
de Broglie wavelength: λ = h/p
Bragg’s Law:
nλ = 2dsinθ
Heisenberg Uncertainty Principle:
ΔpxΔx ≥ ħ/2
ΔEΔt ≥ ħ/2
Probability = ψ2 Normalization condition: ∫ψ2dx = 1
En = n2π2ħ2/2mL2
Infinite Square Well Pot. in 1-dim: ψ = √2/L sin(nπx/L)
E = π2ħ2 (n12/L12 + n22/L22 + n32/L32)
2m
2
V = ½kx ω2 = k/m En = (n+½)ħω
Infinite Square Well Pot. in 3-dims:
Simple Harmonic Oscillator:
Q number relations: n > 0 l < n
s = ±½
S
L= 0
P
1
D
2
F
3
G
4
L = √l(l+1) ħ
S = √s(s+1) ħ
|ml| ≤ l
J=L+S
Lz = mlħ
j=l±s
Spectroscopic Notation:
n2s+1Lj
Zeeman Effect: VB = -µ.B = µ BBml or 2µ BBms
Anomalous Zeeman Effect:
VB = µ BBgmj
where g = Landé g-factor = 1 + J(J+1)+S(S+1)-L(L+1)
2J(J+1)
Radioactive decay law:
N = Noe-λt
Activity: R = λN
1 Becquerel (Bq) = 1 decay/s
Q-value:
Q = (Mx + MX – My – MY)c2
with t1/2 = 0.693/λ