NEET 2018 · PhysicsRMS speedPrevious Year Question
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given: mass of an oxygen molecule m = 2.76 × 10⁻²⁶ kg, Boltzmann constant k_B = 1.38 × 10⁻²³ J K⁻¹, escape speed = 11200 ms⁻¹)
Answer: (B) 8.360 × 10⁴ K. Correct Answer (B): 8.360 × 10⁴ K The molecule escapes when its rms speed equals the escape speed (≈ 11.2 km s⁻¹).
- A.5.016 × 10⁴ K
- B.8.360 × 10⁴ K✓
- C.2.508 × 10⁴ K
- D.1.254 × 10⁴ K
Correct Answer
(B) 8.360 × 10⁴ K
Solution & Explanation
Correct Answer (B): 8.360 × 10⁴ K The molecule escapes when its rms speed equals the escape speed (≈ 11.2 km s⁻¹). Setting v_rms = √(3k_BT/m) equal to v_escape and solving for T gives T = m v²_escape / (3k_B). Substituting the molecular mass and Boltzmann constant yields about 8.36 × 10⁴ K — extremely hot, which is why oxygen does not normally escape Earth.
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