The Maxwell-Boltzmann probability density function f(v) is given by

where m (kg) is the mass of each molecule, v (m/s) is the speed, T(K) is the temperature, and k = 1.38 × 10-23 J/K is Boltzmann's constant. The most probable speed vP corresponds to the maximum value of f(v) and can be determined from Df(v)/dv = 0. Create a symbolic expression for f(v), differentiate it with respect to v and show that vP = ˆš2kt/m. Calculate vP for oxygen molecules (m = 5.3 × 10-26 kg) at T = 300 K (k = 1.38 × 10-23 J/K). Make a plot of f(v) versus v for 0

2( mm