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The MOT cloud is loaded from a background of thermal vapour, or from an atomic beam, usually slowed down to the capture velocity using a Zeeman slower. However, the trapping potential in a magneto-optical trap is small in comparison to thermal energies of atoms and most collisions between trapped atoms and the background gas supply enough ...
The two particles of the same energy have spin 1 ⁄ 2 (spin up) or − 1 ⁄ 2 (spin down), leading to two states for each energy level. In the configuration for which the total energy is lowest (the ground state), all the energy levels up to n = N/2 are occupied and all the higher levels are empty.
Maxwell–Boltzmann distribution is a specific application of Maxwell–Boltzmann statistics to the kinetic energies of gas particles. The distribution of velocities (or speeds) of particles in an ideal gas follows from the statistical assumption that the energy levels of a gas molecule are given by its kinetic energy:
For a supersonic flow in an expanding conduit (M > 1 and dA > 0), the flow is accelerating (dV > 0). For a supersonic flow in a converging conduit (M > 1 and dA < 0), the flow is decelerating (dV < 0). At a throat where dA = 0, either M = 1 or dV = 0 (the flow could be accelerating through M = 1, or it may reach a velocity such that dV = 0).
By the equipartition theorem, internal energy per mole of gas equals c v T, where T is absolute temperature and the specific heat at constant volume is c v = (f)(R/2). R = 8.314 J/(K mol) is the universal gas constant, and "f" is the number of thermodynamic (quadratic) degrees of freedom, counting the number of ways in which energy can occur.
Therefore, the kinetic energy per kelvin of one mole of monatomic ideal gas (D = 3) is = =, where is the Avogadro constant, and R is the ideal gas constant. Thus, the ratio of the kinetic energy to the absolute temperature of an ideal monatomic gas can be calculated easily:
As a simple approximate equation, the physical value of is usually very close to 1/3 of the detonation velocity of the explosive material for standard explosives. [1] For a typical set of military explosives, the value of D 2 E {\displaystyle {\frac {D}{\sqrt {2E}}}} ranges from between 2.32 for Tritonal and 3.16 for PAX-29n.
Gas flow can be grouped in four regimes: For Kn≤0.001, flow is continuous, and the Navier–Stokes equations are applicable, from 0.001<Kn<0.1, slip flow occurs, from 0.1≤Kn<10, transitional flow occurs and for Kn≥10, free molecular flow occurs. [6] In free molecular flow, the pressure of the remaining gas can be considered as effectively ...