Dust particles in a grain elevator frequently have masses of the order of 1.0 × 10^-9 kg.If,to a first approximation,we model the dust particles as an ideal gas,what would be the rms speed of such a particle in air at 27°C? The Boltzmann constant is 1.38 × 10^-23 J/K . A)3.5 × 10^-6 m/s B)5.6 × 10^-5 m/s C)7.8 × 10^-4 m/s D)5.2 × 10^-3 m/s E)4.9 × 10^-2 m/s

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Quizplus · Accepted Answer

The rms speed of an ideal gas particle is given by the formula:$$v_{rms}=\sqrt{\frac{3kT}{m}}$$where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the particle.Plugging in the given values, we get:$$v_{rms}=\sqrt{\frac{3(1.38 	imes 10^{-23} 	ext{ J/K})(300 	ext{ K})}{1.0 	imes 10^{-9} 	ext{ kg}}}=3.5 	imes 10^{-6} 	ext{ m/s}$$Therefore, the correct answer is A.

Dust Particles in a Grain Elevator Frequently Have Masses of the Order