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  4. 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 × 10-26 kg Boltzmann’s constant kB = 1.38 × 10-23 J K-1)

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Q. 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 $k_B = 1.38 \times 10^{-23} J \, K^{-1}$)

NEETNEET 2018Kinetic Theory

Solution:

$V_{\text{escape }} = 11200\, m/s$
Say at temperature T it attains $V_{\text{escape}}$
So, $ \sqrt{\frac{3k_{B}T}{m_{o_2} }} =11200 \,m/s$
On solving,
$T = 8.360 \times 10^{4} \,K $