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

• A. $1.254 \times 10^4 K $
• B. $2.508 \times 10^4 K $
• C. $5.016 \times 10^4 K $
• D. $8.360 \times 10^4 K $

Answer 1

The Correct Option is D

$V_{\text{escape }} = 11200\, m/s$
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 $