Kelvi

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 $(m) = 2.76 \times 10^{-26}$ kg $,$ Boltzmann's constant $k_B = 1.38 \times 10^{-23}$ J K $^{-1}$

hard

Kinetic Theory

2018

physics

$5.016 \times 10^4$ K

$8.360 \times 10^4$ K

$2.508 \times 10^4$

Explanation

To solve this problem, we need to find the temperature at which the root mean square (rms) speed of oxygen molecules is equal to the escape velocity from Earth. $\\$ The escape velocity $v_{escape}$ from Earth is given by: $\\ v_{escape} = \sqrt{\frac{2GM}{R}} \\$

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