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  • Understanding Root Mean Square Speed: Particle Motion in Substances
    The average amount of motion of each particle in a substance is called the root mean square (rms) speed. It is a measure of the average kinetic energy of the particles in a substance. The rms speed can be calculated by taking the square root of the mean of the squares of the speeds of all the particles in the substance.

    $$v_{rms}=\sqrt{\frac{3RT}{M}}$$

    where:

    - \(v_{rms}\) is the root mean square speed in m/s.

    - \(R\) is the ideal gas constant \(R=8.314\ J/K\cdot mol\).

    - \(T\) is the absolute temperature in Kelvin.

    - \(M\) is the molar mass of the substance in kg/mol.

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