The escape speed from the Earth is 1.12 x 10⁴ m/s (Section 8–7). So a gas molecule traveling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field and be lost to the atmosphere. Can you explain why our atmosphere contains oxygen but not helium?

검증된 단계별 안내

Understand the concept of escape speed: Escape speed is the minimum speed an object must have to escape the gravitational pull of a planet without further propulsion. For Earth, this speed is approximately 1.12 × 10⁴ m/s.

Relate escape speed to the kinetic energy of gas molecules: The kinetic energy of a gas molecule is given by the equation \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the molecule and \( v \) is its speed. The average speed of gas molecules is related to their temperature and mass through the Maxwell-Boltzmann distribution.

Compare the molecular speeds of oxygen and helium: Helium atoms are much lighter than oxygen molecules. According to the Maxwell-Boltzmann distribution, lighter molecules (like helium) move faster on average than heavier molecules (like oxygen) at the same temperature.

Determine the likelihood of escape: Since helium atoms move faster on average, a significant fraction of them can reach or exceed the escape speed of Earth, allowing them to escape Earth's gravitational field. In contrast, oxygen molecules, being heavier, have lower average speeds and are less likely to reach escape velocity.

Conclude why Earth's atmosphere retains oxygen but not helium: Over time, helium atoms escape into space due to their higher speeds, while oxygen molecules remain bound to Earth's atmosphere because their speeds are generally insufficient to overcome Earth's gravitational pull.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

주요 개념

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Escape Velocity

Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without further propulsion. For Earth, this speed is approximately 11.2 km/s. If an object, such as a gas molecule, exceeds this speed, it can escape into space, which is crucial for understanding why lighter gases like helium can be lost from the atmosphere.

Molecular Mass and Kinetic Energy

The kinetic energy of a gas molecule is directly related to its temperature and mass. Lighter molecules, such as helium, have higher average speeds at a given temperature compared to heavier molecules like oxygen. This means that helium molecules can reach escape velocity more easily, leading to their gradual loss from the atmosphere over time.

Atmospheric Retention

Atmospheric retention refers to the ability of a planet to hold onto its gases. Factors influencing this include the planet's gravity and the temperature of the atmosphere. Earth’s gravity is sufficient to retain heavier gases like oxygen, while lighter gases like helium can escape more readily, resulting in a composition that favors heavier elements in the atmosphere.