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Physics LibreTexts

Useful Constants, Units, and Approximations

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    2558
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    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 = 103 m
    mega M \(\times 10^{6}\) 1 Mm = 106 m
    giga G \(\times 10^{9}\) 1 Gm = 109 m
    tera T \(\times 10^{12}\) 1 Tm = 1012 m
    peta P \(\times 10^{15}\) 1 Pm = 1015 m

    Fundamental Constants

    Quantity Symbol Value
    Magnetic permeability of a vacuum

    \(\mu_0\)

    \(4 \pi \times 10^{-7} \text{ N s}^2 \text{/C}^2\)
    Stephan-Boltzman 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 Lennard-Jones 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 620-750 700 4.3 1.8
    Orange 590-620 600 5.0 2.0
    Yellow 570-590 580 5.1 2.1
    Green 495-570 540 5.5 2.3
    Blue 450-495 470 6.4 2.6
    Violet 380-450 400 7.5 3.1