NST II Formulae and Physical Constants (Cambridge)

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NATURAL SCIENCES TRIPOS ASTROPHYSICS

Part II

Examinations: 6, 8, 9 & 10 June, 2011

Astrophysics Constants and Formulae Available for examinations in the Natural Sciences Tripos Part II – Astrophysics Physical Constants velocity of light Newtonian gravitational constant Planck’s constant

c = 2.998 × 108 ms−1

G = 6.673 × 10−11 m3 kg−1 s−2 h = 6.626 × 10−34 Js

¯h = 1.055 × 10−34 Js = h/2π

Stefan – Boltzmann constant gas constant Avogadro’s number Boltzmann’s constant atomic mass unit

σ = 5.671 × 10−8 Wm−2 K−4 = ac/4

R∗ = 103 R

R = 8.314 Jmol−1 K−1

NA = 6.022 × 1023 mol−1

k = 1.381 × 10−23 JK−1 = R/NA

mu = 1.661 × 10−27 kg

proton rest mass

mp = 1.673 × 10−27 kg = 938 MeV

neutron rest mass

mn = 1.675×10−27 kg (mn −mp = 1.29 MeV) = 939 MeV

electron rest mass

me = 9.109 × 10−31 kg = 0.511 MeV

classical electron radius

re = 2.818 × 10−15 m

Compton wavelength Thomson cross section

(mp /me = 1836)

λC = 2.426 × 10−12 m = h/me c

σT = 6.652 × 10−29 m2 = (8π/3)re2

inverse fine-structure constant

α−1 = 137.0

radiation density constant

a = 7.566 × 10−16 Jm−3 K−4 = 8π 5 k 4 /15c3 h3

electronic charge Bohr radius

e = 1.602 × 10−19 C

a0 = 5.292 × 10−11 m = h2 /πµ0 c2 me e2

temperature of triple point of water Ttr = 273.16K vacuum magnetic permeability

µ0 = 4π × 10−7 Hm−1 (exact)

vacuum electrical permittivity

ǫ0 = 8.854 × 10−12 Fm−1 = c−2 µ−1 0

ionization potential of hydrogen

χH = 13.598 eV 1


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