The Question is from neet-physics kinetic-theory-gases various-speeds-of-gas-molecules, and it was created by the author Mr. ANIL KUMAR.G

Question

Which of the following best describes the distribution of molecular speeds in a gas sample at a given temperature?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Kinetic Molecular Theory of Gases
 **Related Topics**: Maxwell-Boltzmann distribution, temperature and kinetic energy, root-mean-square speed
 **Prerequisites**: Understanding of gas molecules in constant random motion.
## SOLUTION PATHWAY
**Given Information**:
  Gas sample at a given temperature.
  Options describing the distribution of molecular speeds.
**Method & Steps**:
 1. Consider the Kinetic Molecular Theory of Gases. This theory states that gas particles are in constant, random motion.  The speeds of these particles are not uniform.
  Reasoning: The kinetic energy of a gas molecule is directly proportional to its temperature ($KE = \frac{3}{2}k_BT$, where $k_B$ is the Boltzmann constant and $T$ is the absolute temperature). However, this average kinetic energy doesn't imply that all molecules have the same speed.
  Formula/Rule: $KE = \frac{1}{2}mv^2$, where $m$ is the mass of the molecule and $v$ is its speed.
 2. Visualize the Maxwell-Boltzmann distribution. This distribution shows that the speeds of gas molecules follow a probability distribution, not a single value.  There's a range of speeds, with a most probable speed, an average speed, and a root-mean-square speed.
  Working: The Maxwell-Boltzmann distribution is a curve showing the probability of finding a molecule with a certain speed.  It's not a uniform distribution.
  Key Point: The distribution is temperature-dependent; higher temperatures lead to a broader distribution with higher average speeds.
 3. Analyze the options. Only option A accurately reflects the Maxwell-Boltzmann distribution.
  Result: Option A is the correct answer.
  Verification: The other options contradict the fundamental principles of the Kinetic Molecular Theory and the Maxwell-Boltzmann distribution.
 ## OPTION ANALYSIS
A ✓: A range of speeds, with some molecules moving faster and some slower. This is consistent with the Maxwell-Boltzmann distribution, where molecules have a range of speeds due to collisions and varying kinetic energies.
B :x: All molecules move at the same speed.  This is incorrect; the kinetic energies, and hence speeds, are distributed according to the Maxwell-Boltzmann distribution.
C :x: Most molecules move at a very low speed. This is incorrect; there is a distribution of speeds, with a most probable speed that's not necessarily very low.
D :x: Most molecules move at a very high speed.  This is incorrect;  while some molecules move at high speeds, the distribution peaks at a most probable speed that's lower than the average speed.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Assuming all molecules have the same speed at a given temperature: Remember the distribution of speeds.
  2.Confusing average speed with the most probable speed: The most probable speed is the speed at which the Maxwell-Boltzmann distribution curve peaks.
 **Quick Tips**:
  1.Visualize the Maxwell-Boltzmann distribution curve to understand the range of speeds.
  2.Remember that temperature is related to the *average* kinetic energy, not the speed of every single molecule.

Mr. ANIL KUMAR.G · Answer

The correct Option is "A range of speeds, with some molecules moving faster and some slower"

Mr. ANIL KUMAR.G · Answer

All molecules move at the same speed

Mr. ANIL KUMAR.G · Answer

Most molecules move at a very low speed

Mr. ANIL KUMAR.G · Answer

Most molecules move at a very high speed

NEET Physics Kinetic Theory of Gases Various Speeds Of Gas Molecules MCQs

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