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If the RMS speed of a gas is 300 m/s, what is the kinetic energy per molecule?

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Question: If the RMS speed of a gas is 300 m/s, what is the kinetic energy per molecule?

Options:

  1. 0.5 * m * (300)^2
  2. 0.5 * m * (150)^2
  3. 0.5 * m * (600)^2
  4. 0.5 * m * (100)^2

Correct Answer: 0.5 * m * (300)^2

Solution:

The kinetic energy per molecule is given by KE = 0.5 * m * v^2. Substituting v = 300 m/s gives the correct expression.

If the RMS speed of a gas is 300 m/s, what is the kinetic energy per molecule?

Practice Questions

Q1
If the RMS speed of a gas is 300 m/s, what is the kinetic energy per molecule?
  1. 0.5 * m * (300)^2
  2. 0.5 * m * (150)^2
  3. 0.5 * m * (600)^2
  4. 0.5 * m * (100)^2

Questions & Step-by-Step Solutions

If the RMS speed of a gas is 300 m/s, what is the kinetic energy per molecule?
  • Step 1: Understand that the kinetic energy (KE) of a molecule is calculated using the formula KE = 0.5 * m * v^2.
  • Step 2: Identify the variables in the formula: 'm' is the mass of the molecule and 'v' is the speed of the molecule.
  • Step 3: Note that the problem gives us the RMS speed (v) of the gas, which is 300 m/s.
  • Step 4: To find the kinetic energy per molecule, we need the mass (m) of one molecule of the gas. This information is not provided in the question.
  • Step 5: If we had the mass of the molecule, we would substitute v = 300 m/s into the formula KE = 0.5 * m * (300)^2 to calculate the kinetic energy.
  • Kinetic Energy – The kinetic energy of an object is the energy it possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2.
  • RMS Speed – RMS (Root Mean Square) speed is a statistical measure of the speed of particles in a gas, which can be used to calculate kinetic energy.
  • Molecular Mass – The mass of a single molecule is required to calculate the kinetic energy per molecule, which may not be provided in the question.
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