Useful Constants, Units, and Approximations
 Page ID
 2558
These constants are provided for your convenience. You should know the SI unit conversions and SI prefixes, as well as be familiar with approximate values of common units. Do not memorize anything else; physics is not rote memorization (important values of constants will be given to you for quizzes and tests). Instead, engage with these values by practicing problems that use them, like in your DL or on your homework.
SI Prefixes
Name  Symbol  Meaning  Example 

femto 
f 
\(\times 10^{15}\)  1 fm = 10^{15} m 
pico  p  \(\times 10^{12}\)  1 pm = 10^{12} m 
nano  n  \(\times 10^{9}\)  1 nm = 10^{9} m 
micro  µ  \(\times 10^{6}\)  1 µm = 10^{6} m 
milli  m  \(\times 10^{3}\)  1 mm = 10^{3} m 
kilo  k  \(\times 10^{3}\)  1 km = 10^{3} m 
mega  M  \(\times 10^{6}\)  1 Mm = 10^{6} m 
giga  G  \(\times 10^{9}\)  1 Gm = 10^{9 m} 
tera  T  \(\times 10^{12}\)  1 Tm = 10^{12} m 
peta  P  \(\times 10^{15}\)  1 Pm = 10^{15} m 
Fundamental Constants
Quantity  Symbol  Value 

Magnetic permeability of a vacuum 
\(\mu_0\) 
\(4 \pi \times 10^{7} \text{ N s}^2 \text{/C}^2\) 
StephanBoltzman constant  \(\sigma\)  \(5.67 \times 10^{8} \text{ W m}^{2} \text{K}^{4}\) 
Speed of light (in a vacuum)  \(c\)  \(3.00 \times 10^8 \text{ m/s}\) 
Fundamental (electron or proton) charge  \(e\)  \(1.602 \times 10^{19} \text{ C}\) 
Gravitational constant  \(G\) 
\(6.67 \times 10^{11} \text{ N m}^2/\text{kg}^2\) 
Planck's constant 
\(h\) 
\(6.63 \times 10^{34} \text{ J s}\) \(4.14 \times 10^{15} \text{ eV s}\) 
Boltzmann's constant 
\(k_B\) 
\(1.38 \times 10^{23} \text{ J/K}\) 
Coloumb's constant  \(k\)  \(9 \times 10^9 \text{ N m}^2 \text{/C}^2\) 
Avagadro's number  \(N_A\)  \(6.02 \times 10^{23} \text{ atoms/mole}\) 
Refraction Indices (Optics)
Different frequencies of light have different refractive indices. This table gives the approximate value of the refractive index for light in the visible part of the spectrum. The exact values depend on the sample used and the frequency of light.
Medium  \(n=c/v_{medium}\) 

Vacuum  1.0 (exactly) 
Air  1.0003 
Water  1.33 
Glass (crown)  1.50  1.62 
Glass (flint)  1.57  1.75 
Silicon  3.5 
Germanium  4.0 
Diamond  2.42 
Eye  1.33 
Eye Lens  1.41 
Particles
Particle  Mass  Charge 

Proton 
\(1.67 \times 10^{27} \text{ kg}\) 
\(1.602 \times 10^{19} \text{ C}\) 
Electron  \(1.67 \times 10^{27} \text{ kg}\)  \(1.602 \times 10^{19} \text{ C}\) 
Neutron  \(9.11 \times 10^{31} \text{ kg}\)  \(0 \text{ C}\) 
Approximate Values
These figures provide a rough approximation for the value of various common physical quantities.
Quantity  Approximate Values  

Mass of an atom  between \(10^{27}\) and \(10^{25} \text{ kg}\)  between 1 and 200 atomic mass units (amu) 
Size of an atom  \(\sim 10^{10} \text{ m}\)  1 Å 
Depth of the LennardJones potential energy well  \(10^{21} \text{ J}\)  \(10^{3} \text{ eV}\) 
Ionization energy 
between \(10^{−20}\) and \(10^{−18} \text{ J}\) 
between 0.1 and 10 eV 
Frequency of visible light 
\(\sim 6 \times 10^{14} \text{ Hz}\) 

Energy of one photon in the visible spectrum  \(\sim 3 \times 10^{19} \text{ J}\)  ~2 eV 
Tallest building  829.8 m  
Height of Mt. Everest  8850 m  
Radius of the Earth  6380 km  
Circumference of the Earth  40,000 km 
Electromagnetic Spectrum
The electromagnetic spectrum, partitioned into different types of light based on frequency, is presented below:
Light is often characterized by wavelength, but as we learned in 7C the wavelength of light depends on the medium it travels through. However, the frequency does not; red light for example always has the same frequency. When someone says that “red light has a wavelength of 700 nm” this is understood by convention to mean the wavelength in a vacuum.
Color  \(\lambda\) range (nm)  \(\lambda\) midpoint (nm)  Frequency (\(10^{14} \text{ Hz}\))  Energy of one photon (eV) 

Red  620750  700  4.3  1.8 
Orange  590620  600  5.0  2.0 
Yellow  570590  580  5.1  2.1 
Green  495570  540  5.5  2.3 
Blue  450495  470  6.4  2.6 
Violet  380450  400  7.5  3.1 