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Physics · PYQ NEET UG 2018
हिन्दीAt what temperature will the r.m.s. speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given: Mass of oxygen molecule \( = 2.76 \times 10^{-26}\text{ kg} \), Boltzmann's constant \( k_{\text{B}} = 1.38 \times 10^{-23}\text{ J K}^{-1} \))
Correct answer · Option 2
\( 8.360 \times 10^4\text{ K} \)
Explanation
Escape velocity on Earth \( v_e \approx 11.2\text{ km/s} = 11.2 \times 10^3\text{ m/s} \). Equating \( v_{\text{rms}} = \sqrt{\frac{3k_{\text{B}}T}{m}} = v_e \), we get \( T = \frac{m v_e^2}{3k_{\text{B}}} = \frac{2.76 \times 10^{-26} \times (11.2 \times 10^3)^2}{3 \times 1.38 \times 10^{-23}} \approx 8.36 \times 10^4\text{ K} \).
