The root mean square (rms) speed of X$$_2$$ gas is x m/s at a given temperature. When the temperature is doubled, the X$$_2$$ molecules dissociated completely into atoms. The root mean square speed of the sample of gas then becomes (in m/s)

Case - 1 : An ideal gas of molecular weight M at temperature T.

Case - 2 : Another ideal gas of molecular weight 2M at temperature T/2.

Identify the correct statement in context of above two cases.

The average speed of H₂ at T₁K is equal to that of O₂ at T₂K. The ratio T₁ : T₂ is

Avogadro's law is valid for