STANDARD Physics Root Mean Square Speed MCQ Question
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping the Earth's atmosphere? (Given : Mass of oxygen molecule (m) = 2.76 × 10⁻²⁶ kg, Boltzmann constant k_B = 1.38 × 10⁻²³ J K⁻¹)
2.508 × 10⁴ K
8.360 × 10⁴ K
5.016 × 10⁴ K
1.254 × 10⁴ K
Correct Answer
Detailed Explanation
Escape velocity from the Earth's surface is v_escape = 11200 m s⁻¹. At temperature T, the oxygen molecule attains escape velocity. Using the formula v_escape = √(3kT/m), we solve for T to find T = 8.360 × 10⁴ K.
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