1. The Pilot Waves of de Broglie (3 marks) According to statistical mechanics, the average kinetic energy of a particle at tem- perature T is K = 3kBT/2, where kB = 8.617 x 10-BeV/K is Boltzmann's constant. Start by writing an expression for the de Broglie wavelength as a function of kinetic energy and then use this to calculate the average de Broglie wavelength of nitrogen molecules at room temperature. (Notes: As usual, it's better to work with he and me to simplify calculations. The value of kBT in mev near room temperature is another value that comes in handy in a lot of real-life science situations.)