At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth'

Question

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given: Mass of oxygen molecule (m) = $2.76 	imes 10^{-26} 	ext{ kg}$, Boltzmann's constant $k_B = 1.38 	imes 10^{-23} 	ext{ JK}^{-1}$)

Accepted Answer

The escape velocity $V_{escape} = 11200 	ext{ m/s}$. The rms speed is given by $\sqrt{\frac{3k_B T}{m}} = 11200 	ext{ m/s}$. Solving for T gives $T = 8.360 	imes 10^4 	ext{ K}$.

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