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The root mean square velocity of a gas particle is equal to the square root of (3RT/M), where R is the gas constant (in J K^-1 mol^-1), T is temperature in Kelvin (around 293 at room temperature) and M is molar mass (0.028 kg/mol for diatomic nitrogen, which makes up >50% of the atmosphere. Plugging in these values gives approximately 511 m/s.

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