A

For two different gases at the same temperature with equal root mean square (RMS) velocities, we can use the formula for RMS speed given by:
$$ v_{rms} = \sqrt{\frac{3kT}{m}} $$
Here, \( v_{rms} \) is the root mean square velocity, \( k \) is the Boltzmann constant, \( T \) is the temperature in Kelvin, and \( m \) is the mass of the gas molecule.
Since the gases have equal RMS velocities at the same temperature:
If gas 1 has a mass \( m_1 \) and gas 2 has a mass \( m_2 \), then we have:
$$ v_{rms1} = v_{rms2} $$
which implies:
$$ \sqrt{\frac{3kT}{m_1}} = \sqrt{\frac{3kT}{m_2}} $$
Squaring both sides and cancelling common terms, we get:
$$ \frac{1}{m_1} = \frac{1}{m_2} $$
Therefore, \( m_1 = m_2 \). This means that if the two gases have the same RMS velocity at the same temperature, their masses must also be equal.