Problem 3+ For a monoatomic gas, one measure of the average speed of the atoms is the root mean square speed, defined as Vrms = V(12) = 3kBT , where k is the Boltzmann constant, T is the m temperature and m is the atomic mass. Calculate the de Broglie wavelength of He, Ar and iodine (12) at 300K and 1000K. +|_ lProbiem 7a Consider a particle moving in a illbox of length a. The wave functions are quantized and their general solution is given by the equationw n(x) = sinlrx} a] Calculate the ground state energy [71 = 1]. Why the energy of the ground state is not zero? What does it meanh b] Assume that the particle is in the ground state (in = 1). Caiculate the probability of nding the particle in the interval 2: s x :1 4?.0 c] Repeat the same calculation as [h] by assuming that the particle is in the excited state it = 3.4 .J