Each type of molecule has the same average kinetic energy in a planetary atmosphere. As a result (and knowing that an oxygen [O₂] molecule has twice the mass of a methane [CH₄] molecule), we can say that in this atmosphere the average speed of an oxygen molecule is: A)1.4 times less than that of a methane molecule. B)half that of a methane molecule. C)twice that of a methane molecule. D)1.4 times greater than that of a methane molecule.

Question

Quizplus · Accepted Answer

The average kinetic energy of a molecule is given by $ \frac{1}{2}mv^2 $, where $ m $ is the mass and $ v $ is the speed of the molecule. Since the kinetic energy is the same for both types of molecules and the mass of an oxygen molecule is twice that of a methane molecule, the speed of an oxygen molecule must be $ \sqrt{1/2} $ times that of a methane molecule, which is approximately 1.4 times less.

Each Type of Molecule Has the Same Average Kinetic Energy