Answer
$$4.71
$$
Work Step by Step
$$v_{\text {arg }}=\sqrt{8 R T / \pi M}$$ and
$$v_{\text {rms }}=\sqrt{3 R T / M}$$, respectively. Thus,
$$
\frac{v_{\text {avg } 2}}{v_{\text {ms } 2}}=\frac{\sqrt{8 R T / \pi M_{2}}}{\sqrt{3 R T / M_{1}}}=\sqrt{\frac{8 M_{1}}{3 \pi M_{2}}}
$$
If $v_{\text {arg } 2}=2 v_{\text {mst }},$ then
$$
\frac{m_{1}}{m_{2}}=\frac{M_{1}}{M_{2}}=\frac{3 \pi}{8}\left(\frac{v_{\text {arg } 2}}{v_{\text {ms } 1}}\right)^{2}=\frac{3 \pi}{2}=4.71
$$
