(a) Show that the speed distribution function can be written n(v) = 4 -1/2 (v/vm) 2 v -1 m e -(v/v m ) 2 ,

(a) Show that the speed distribution function can be written n(v) = 4π^-1/2 (v/vm)²v ^-1_m e^-(v/v_m)2, where v_m is the most probable speed. Consider 1 mole of molecules and approximate dv by Δv = 0.01 v_m. Find the number of molecules with speeds in dv at

(b) v = 0,

(c) v = v_m, 

(d) v = 2v_m, and 

(e) v = 8v_m.