at room temperature a diatomic is found to have an r.m.s speed of 1930 m/s the gas is;

We know that,
$$\begin{gathered} {v_{rms}}^2=\frac{3RT}{M} \\ Where, M =molar mass \\ So, \\ M=\frac{3RT}{{v_{rms}}^2} \end{gathered}$$
Now, at room temperature (298 K), R = 8.314 kg m² s^-1
Putting the values we get:

$M=\frac{3\times 8.314\times 298}{(1930{)}^2}=0.002 Kg = 2g$
So, the gas is hydrogen (H₂) with molar mass 2 g.