The probability that a molecule in a gas will have a speed v is proportional to the

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The probability that a molecule in a gas will have a speed v is proportional to the function

3/2 —ту? т v? exp fv(v) = 2k в T 2πkp T

where m is the mass of the molecule, kB is Boltzmann€™s constant, and T is the temperature on the Kelvin scale. The most probable speed is the speed for which this function is at a maximum. Find the expression for the most probable speed and find its value for nitrogen molecules at T = 298 K. Remember to use the mass of a molecule, not the mass of a mole.

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