The root-mean-square speed of a gas particle can be calculated using the equation:
v_rms = (3kT/m)^(1/2)
where v_rms is the root-mean-square speed, k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and m is the mass of the gas particle.
For SF6, the molar mass is 146 g/mol, so the mass of one SF6 molecule is 146 g/mol / 6 = 24.33 g/mol.
Substituting the values into the equation, we get:
v_rms = (3 * 1.38 x 10^-23 J/K * 295 K / 24.33 x 10^-23 g)^(1/2) = 384 m/s
Therefore, the root-mean-square speed of SF6 at room temperature (295 K) is 384 m/s.