An incandescent lamp of wattage W is filled with argon gas and has a tungsten filament. The collision frequency of evaporated tungsten atoms with the argon atoms is found to be proportional to W^ . The most reasonable value of is

Step-by-step solution

According to the Stefan-Boltzmann law, the power or wattage W radiated by the tungsten filament is proportional to the fourth power of its absolute temperature T : W T^4 T W^ 1/4 The collision frequency f of an evaporated tungsten atom with argon atoms in the bulb is given by the kinetic theory of gases: f = 2 d^2 n v_ rel Since the bulb is a sealed container, the volume is constant, meaning the number density n of argon atoms remains constant. The mean relative speed v_ rel of the atoms is proportional to the squa