Less massive molecules tend to escape from an atmosphere more often than more massive molecules because a. the gravitational force on them is less. b. they are moving faster. c. they are more buoyant. d. they are smaller and so experience fewer collisions on their way out.

Kinetic energy is the energy an object possesses due to its motion. In the context of molecules in an atmosphere, kinetic energy is critical. The key idea is that molecules move at different speeds depending on various factors. Temperature is one primary factor. As temperature increases, molecules move faster because they gain more kinetic energy.
This relationship is described by the equation: \( KE = \frac{1}{2}mv^2 \)
In this equation, \( KE \) stands for kinetic energy, \( m \) is the mass of the molecule, and \( v \) is its velocity. Notice how the kinetic energy is directly proportional to the mass of the molecule and the square of its velocity.

• Less massive molecules tend to move faster if the temperature is constant.
• This increased velocity translates into more kinetic energy.

The faster a molecule moves, the more likely it is to overcome the gravitational pull of a planet and escape into space. This is why less massive molecules with higher velocities are more likely to escape an atmosphere.
Understanding kinetic energy helps explain why step 3 of the solution emphasizes that less massive molecules escape more due to their higher velocities.

Atmospheric composition refers to the different gases that make up an atmosphere. Earth's atmosphere, for instance, is composed mainly of nitrogen (78%) and oxygen (21%), with trace amounts of other gases like argon and carbon dioxide.
The mass of these gases is a critical factor. Less massive gas molecules, such as hydrogen or helium, have higher average speeds at a given temperature due to their lower mass.

• These lighter gases are more prone to reach the escape velocity needed to leave the atmosphere.
• Heavier gases, like carbon dioxide, tend to remain in the atmosphere due to their slower speeds.

Over time, lighter gases can be depleted from the atmosphere because they continually escape into space. This process influences the planet's climate and the types of life that can thrive there. A planet's size and gravitational force also play a role in determining which gases remain. More massive planets with stronger gravitational forces can retain lighter gases more effectively.Understanding atmospheric composition provides context to the problem by highlighting why some molecules are more likely to escape.

Gravitational force is the attractive force between two masses. In the context of a planet and its atmosphere, it's the force that pulls gas molecules toward the planet's center. The gravitational force is a key player in determining which molecules can escape an atmosphere.
This force is described by Newton's law of universal gravitation: \[ F = G \frac{m_1 m_2}{r^2} \]
In this equation, \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between their centers. A few key points about gravitational force:

• It's stronger for more massive planets.
• It decreases with distance.

On Earth, the gravitational force is strong enough to retain heavier gas molecules. However, lighter molecules like hydrogen and helium, which move faster due to their lower mass, are more likely to reach escape velocity and leave the atmosphere. While the gravitational force on less massive molecules is indeed smaller (as mentioned in step 2 of the solution), it isn't the only reason they escape more easily. The molecule's velocity, driven by kinetic energy, plays a bigger role.
Understanding gravitational force clarifies why step 6 concludes that the higher velocity of less massive molecules is the main factor in their escape from an atmosphere.