Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $$v_{rms}$$ and choose the correct answer from the options given below:

The root mean square speed of gas molecules is given by:

$$v_{rms} = \sqrt{\frac{3RT}{M}}$$

where $$R$$ is the gas constant, $$T$$ is the temperature, and $$M$$ is the molar mass of the gas.

Since all three vessels are at the same temperature:

$$v_{rms} \propto \frac{1}{\sqrt{M}}$$

Molar masses:

Neon (monoatomic): $$M = 20$$ g/mol

Chlorine (diatomic, Cl$$_2$$): $$M = 71$$ g/mol

Uranium hexafluoride (polyatomic, UF$$_6$$): $$M = 238 + 6 \times 19 = 352$$ g/mol

Since $$v_{rms} \propto \frac{1}{\sqrt{M}}$$, the gas with the smallest molar mass has the highest $$v_{rms}$$:

$$M_{\text{Ne}} < M_{\text{Cl}_2} < M_{\text{UF}_6}$$

Therefore:

$$v_{rms}(\text{mono}) > v_{rms}(\text{dia}) > v_{rms}(\text{poly})$$