Chapter 9: Problem 16
Less massive molecules tend to escape from an atmosphere more often than more massive ones 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.
Short Answer
Expert verified
b. they are moving faster.
Step by step solution
01
Understand the Problem
Identify why less massive molecules escape from an atmosphere more than more massive ones.
02
Consider the Gravitational Force
Evaluate whether the gravitational force is less significant on less massive molecules (Option a). Gravitational force depends on mass; less massive molecules experience less force, but this doesn't explain increased escape rates.
03
Analyze Molecular Speed
Determine if less massive molecules are indeed moving faster (Option b). According to the kinetic theory of gases, lighter molecules move faster at a given temperature.
04
Assess Buoyancy
Check if buoyancy is a factor (Option c). Buoyancy is related to the density of the medium and does not significantly affect individual molecules escaping an atmosphere.
05
Evaluate Collisions
Consider if being smaller and experiencing fewer collisions affects escape rates (Option d). Collisions do happen in the atmosphere, but they mainly depend on the density of gases rather than molecule size.
06
Conclusion
The primary factor for less massive molecules escaping more frequently is that they move faster at a given temperature.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Kinetic Theory of Gases
The kinetic theory of gases is a fundamental theory in physics that explains the behavior of gases based on the idea that they are made up of a large number of small particles, usually atoms or molecules. These particles are in constant, random motion, colliding elastically with each other and the walls of their container. This constant motion is what gives gases their pressure and temperature properties.
- The theory helps explain why gases fill the volume of any container they are in.
- It also explains why gases can be compressed much more easily than liquids or solids.
Molecular Speed
Molecular speed is crucial in understanding why less massive molecules escape from an atmosphere more easily. According to the kinetic theory of gases, the average speed of gas molecules is given by the equation: \( v = \sqrt{\frac{3kT}{m}} \), where \( v \) is the molecular speed, \( k \) is the Boltzmann constant, \( T \) is the absolute temperature, and \( m \) is the mass of the molecule.
- Lighter molecules (\( m \) is smaller) have higher speeds at the same temperature.
- This higher speed makes it easier for less massive molecules to reach the escape velocity of a planet or star.
Gravitational Force on Molecules
Gravitational force is an attractive force that pulls objects towards the center of a mass, like a planet. The force is given by Newton's law of gravitation: \( F = \frac{G m_1 m_2}{r^2} \), where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the objects, and \( r \) is the distance between their centers.
- Less massive molecules experience less gravitational pull than more massive molecules because \( m \) is smaller.
- However, this smaller gravitational force is not the primary reason for their increased escape rate.
Buoyancy in Gases
Buoyancy refers to the force that causes objects to float in a fluid. In gases, this is often less significant than in liquids. Buoyancy in the context of gases depends on the density differences between the gas and the object.
- Molecules themselves are so small that buoyancy has negligible effects on their ability to escape an atmosphere.
- It mostly influences macroscopic objects within the gas medium.
Collision Frequency of Molecules
Collision frequency refers to how often molecules in a gas collide with each other. This depends on the density of the gas and the average speed of the molecules.
- In a dense atmosphere, molecules collide more frequently.
- Although collisions affect the movement within the gas, they do not significantly deter escaping molecules.