21. From Maxwell Boltzmann distribution it seems the average speed is proportional to the square root of the temperature. 22. Here, the Maxwell Boltzmann distribution of energies must be considered, which leads to the modified expression, 23. We can model the electrons at the sheath edge with a Maxwell Boltzmann distribution , i . e ., 24. The Maxwell Boltzmann distribution also requires low density, implying that g _ i \ gg N _ i. 25. These fluctuations happen on time scales which are much larger than the microscopic relaxation times to the Boltzmann distribution . 26. Fluorescence is most effective when there is a larger ratio of atoms at lower energy levels in a Boltzmann distribution . 27. Since at temperature " T " the molecules have energies given by a Boltzmann distribution , frequency factor. 28. The " configuration probability " is given by the Boltzmann distribution with inverse temperature ? e " 0: 29. The fraction of molecules occupying a given vibrational mode at a given temperature can be calculated using the Boltzmann distribution . 30. :: : Depending on your mathematical background, the OP may want to consider looking into Maxwell Boltzmann distribution .