# Useful Constants, Units, and Approximations

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 | \(\mu_0\) | \(4 \pi \times 10^{-7} \text{ N s}^2 \text{/C}^2\) |

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 m |

## 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 |