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 k_B = 1.38 × 10⁻²³ JK⁻¹)

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Accepted Answer

2.508 × 10⁴ K. The escape speed from Earth is approximately 11.2 km/s. Using the formula for rms speed, v_rms = sqrt(3k_B T / m), and equating it to the escape speed, we solve for T: T = (m * v_escape²) / (3 * k_B). Substituting the given values, T = (2.76 × 10⁻²⁶ * (11.2 × 10³)²) / (3 * 1.38 × 10⁻²³) ≈ 2.508 × 10⁴ K.

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 k_B = 1.38 × 10⁻²³ JK⁻¹)

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