Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases
Determine the average magnitude of linear momentum for a helium molecule in a sample of helium gas at 0^ C . The mass of a helium molecule is 6.64 10⁻²⁷ kg and the Boltzmann constant is 1.38 10⁻²³ J K ⁻¹ .
Options
- A8.0 10⁻²⁴ kg m s ⁻¹
- B7.1 10⁻²⁴ kg m s ⁻¹
- C4.0 10⁻²⁴ kg m s ⁻¹
- D8.7 10⁻²⁴ kg m s ⁻¹
Correct answer
A. 8.0 10⁻²⁴ kg m s ⁻¹
Step-by-step solution
The average magnitude of linear momentum of a gas molecule is given by: p = m v where v is the average speed of the molecule. The formula for average speed from the kinetic theory of gases is: v = 8kT m Thus, the average magnitude of linear momentum is: p = m 8kT m = 8mkT Given values: Mass of helium molecule, m = 6.64 10⁻²⁷ kg Boltzmann constant, k = 1.38 10⁻²³ J K ⁻¹ Temperature, T = 0^ C = 273 K Substituting these values into the expression: p = 8 6.64 10⁻²⁷ 1.38 10⁻²³ 273 p = 20012.4 10⁻⁵⁰ 3.1416 p = 6370.15 10