Answer
a) $819\;\rm m/s$
b) $\approx 3660\;\rm m/s$
Work Step by Step
We know that the rms speed is given by
$$v_{\rm rms}=\sqrt{\dfrac{3k_BT}{m}}$$
We will use this formula for both cases.
a) For Argon atoms, the mass is given by $m=M_{Ar}(1.66\times 10^{-27})$ where $M$ is the atomic mass of the element.
Plugging in the first formula above;
$$(v_{\rm rms})_{Ar}=\sqrt{\dfrac{3k_BT}{M_{Ar}(1.66\times 10^{-27})}}$$
Plugging the known;
$$(v_{\rm rms})_{Ar}=\sqrt{\dfrac{3(1.38\times 10^{-23})(800+273)}{(39.9)(1.66\times 10^{-27})}}$$
$$(v_{\rm rms})_{Ar}=\color{red}{\bf 819}\;\rm m/s$$
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b) For hydrogen molecules, and by the same approach,
$$(v_{\rm rms})_{H_2}=\sqrt{\dfrac{3k_BT}{M_{H_2}(1.66\times 10^{-27})}}$$
Plugging the known;
$$(v_{\rm rms})_{H_2}=\sqrt{\dfrac{3(1.38\times 10^{-23})(800+273)}{(2)(1.66\times 10^{-27})}}$$
$$(v_{\rm rms})_{H_2}=\color{red}{\bf 3658}\;\rm m/s$$
