Answer:
457.8394 K
Explanation:
[tex]v_e[/tex] = Escape velocity = 2.38 km/s
T = Temperature
R = Gas constant = 8.314 J/mol K
M = Molar mass = 2.016 g/mol
The rms velocity of a molecule is given by
[tex]v_r=\sqrt{\frac{3RT}{M}}\\\Rightarrow v_r^2=\frac{3RT}{M}\\\Rightarrow T=\frac{v_r^2M}{3R}[/tex]
Here, [tex]v_r=v_e=2.38\ km/s[/tex]
[tex]T=\frac{v_e^2M}{3R}\\\Rightarrow T=\frac{(2.38\times 10^3)^2\times 2.016\times 10^{-3}}{3\times 8.314}\\\Rightarrow T=457.8394\ K[/tex]
The temperature of the hydrogen molecule would be 457.8394 K
