Kinetic energy of electron gas. Show that the kinetic energy of a three-dimensional gas of N free electrons at 0 K is U, = N€p .
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- The most probable speed an atom/molecule in an ideal gas in thermodynamic equilibrium at temperatureT will have is vmp=(2kgT/M)/2. What is the most probable speed in a gas of hydrogen molecules (H2) at 77 °C? m,=1.67x10 27 kg, kg=1.38x10 23 J/K.Near the surface of a certain kind of star, approximately one hydrogen atom per 10 million is in the first excited level (n = 2). Assume that the other atoms are in the n = 1 level. Use this information to estimate the temperature there, assuming that Maxwell-Boltzmann statistics are valid.Atoms can be "cooled" to incredibly low temperatures by letting them interact with a laser beam. Various novel quantum phenomena appear at these temperatures. What is the rms speed of cesium atoms that have been cooled to a temperature of 100 nK ? Express your answer with the appropriate units.