In the realms of classical and quantum mechanics, precise measurements and calculations are pivotal. This requires the use of standardized units and universally accepted physical constants. Below, we outline the key units and constants employed throughout this document, ensuring clarity and consistency in our discussions and analyses.
We adhere to the International System of Units (SI) for all measurements, which includes meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, amperes (A) for electric current, kelvin (K) for temperature, mole (mol) for the amount of substance, and candela (cd) for luminous intensity.
The following are the fundamental physical constants used:
| Name | Symbol | Value | Units |
|---|---|---|---|
| Speed of Light | c | 299,792,458 | \left(\frac{m}{s}\right) |
| Gravitational Constant | G | 6.67430 \times 10^{-11} | \left(\frac{m^3}{kg \cdot s^2}\right) |
| Vacuum Permittivity | \varepsilon_0 | 8.854187817 \times 10^{-12} | \left(\frac{F}{m}\right) |
| Planck Constant | h | 6.62607015 \times 10^{-34} | \left(\frac{m^2 \cdot kg}{s}\right) |
| Reduced Planck Constant | \hbar | 1.0545718 \times 10^{-34} | \left(\frac{m^2 \cdot kg}{s}\right) |
| Electron Charge | e | 1.602176634 \times 10^{-19} | C |
| Electron Mass | m_e | 9.10938356 \times 10^{-31} | kg |
| Proton Mass | m_p | 1.67262192369 \times 10^{-27} | kg |
| Neutron Mass | m_n | 1.67492749804 \times 10^{-27} | kg |
| Avogadro's Number | N_A | 6.02214076 \times 10^{23} | mol^{-1} |
| Boltzmann Constant | k_B | 1.380649 \times 10^{-23} | \left(\frac{J}{K}\right) |
These constants form the foundation upon which the principles of physics are understood and applied in both classical and quantum mechanical contexts.
The following Python code can be copied and immediately be used:
# Physical Constants
SPEED_OF_LIGHT = 299792458 # m/s
GRAVITATIONAL_CONSTANT = 6.67430e-11 # m^3/kg/s^2
VACUUM_PERMITTIVITY = 8.854187817e-12 # F/m
PLANCK_CONSTANT = 6.62607015e-34 # m^2 kg / s
REDUCED_PLANCK_CONSTANT = 1.0545718e-34 # m^2 kg / s
ELECTRON_CHARGE = 1.602176634e-19 # C
ELECTRON_MASS = 9.10938356e-31 # kg
PROTON_MASS = 1.67262192369e-27 # kg
NEUTRON_MASS = 1.67492749804e-27 # kg
ELECTRON_MASS = 9.10938356e-31 # kg
AVOGADRO_NUMBER = 6.02214076e23 # 1/mol
BOLTZMANN_CONSTANT = 1.380649e-23 # J/K