To calculate the root mean square (RMS) speed of a molecule in an ideal gas, we can use the equation:
v = √(3 * k * T / m)
Where: v is the RMS speed of the molecule. k is the Boltzmann constant (1.38 * 10^-23 J/K). T is the temperature in Kelvin. m is the mass of the molecule.
Let's plug in the given values:
T = 484 K m = 2 * 10^-26 kg
v = √(3 * (1.38 * 10^-23 J/K) * (484 K) / (2 * 10^-26 kg))
Calculating this equation gives us:
v ≈ 1261 m/s
Therefore, the root mean square speed of a molecule in the gas is approximately 1261 m/s.