At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from earth ?

Q: At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from earth ? (ve = 11.2 km/s, m = 2.76 × 10-26e kg and k = 1.38 × 10-23 J/K)

Sol: If the temperature is T, according to kinetic theory of gases ,

Translational KE $\large = \frac{3}{2} k_B T$

The oxygen molecule will escape from earth if

$\large \frac{3}{2} k T > \frac{1}{2} m v_e^2$

$\large T > \frac{m v_e^2}{3 k}$

$\large T > \frac{2.76 \times 10^{-26} \times (11.2 \times 10^3)^2}{3 \times 1.38 \times 10^{-23}}$

T > 8.36 × 104 K