1. For a gas at the same temperature, the r.m.s. speed is

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

So, at constant temperature,

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

where $M$ is the molar mass.

2. Hence, for chlorine and argon,

$\frac{v_{\text{Ar}}}{v_{\text{Cl}_2}}=\sqrt{\frac{M_{\text{Cl}_2}}{M_{\text{Ar}}}}$

Given:

• $v_{\text{Cl}_2}=490\ \text{m/s}$
• $M_{\text{Cl}_2}=70.9\ \text{u}$
• $M_{\text{Ar}}=39.9\ \text{u}$

So,

$v_{\text{Ar}}=490\sqrt{\frac{70.9}{39.9}}$

3. Calculate the ratio:

$\frac{70.9}{39.9} \approx 1.7769$

$\sqrt{1.7769} \approx 1.333$

Therefore,

$v_{\text{Ar}} \approx 490 \times 1.333$

$v_{\text{Ar}} \approx 653\ \text{m/s}$

This is closest to option $D$.

4. Checking options:

• A: $451.7\ \text{m/s}$ — too small
• B: $751.7\ \text{m/s}$ — too large
• C: $551.7\ \text{m/s}$ — too small
• D: $651.7\ \text{m/s}$ — matches best

Therefore, the correct answer is:

$\boxed{D\; (651.7\ \text{m/s})}$