A gas eventually will escape from a planet's atmosphere if the average velocity of the atoms exceeds 1/6 times the escape velocity of the planet.If the average velocity of water vapor in Venus's atmosphere is 0.9 km/s, would it eventually escape into outer space? Note that Venus's mass is 5 *10²⁴ kg, its radius is 6,050 km, and G = 6.67 *10 ^- ¹¹ N m ² /kg ² . A) Water vapor would escape because 1/6 times the escape velocity is 0.51 km/s. B) Water vapor would not escape because 1/6 times the escape velocity is 1.7 km/s. C) Water vapor would escape because 1/6 times the escape velocity is 0.42 km/s. D) Water vapor would not escape because 1/6 times the escape velocity is 2.6 km/s. E) Water vapor would escape because 1/6 times the escape velocity is 1.3 km/s.

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Quizplus · Accepted Answer

The escape velocity $ v_e $ can be calculated using the formula $ v_e = \sqrt{\frac{2GM}{R}} $. Substituting the given values for Venus, the escape velocity is approximately 10.36 km/s. Therefore, 1/6 of the escape velocity is approximately 1.73 km/s. Since the average velocity of water vapor (0.9 km/s) is less than 1/6 of the escape velocity, the water vapor would not escape.

A Gas Eventually Will Escape from a Planet's Atmosphere If