Question

Kinetic energy is defined as ½ mv2, where m is the mass of the object, and v is the velocity (or speed). Two gas molecules have the same kinetic energy, but molecule X has four times the mass of molecule Y. What can you say about their speeds?

Answer 1

The velocity of molecule Y is 2 times the velocity of molecule X

Step-by-step explanation:

Data provided in the question:

Formula for kinetic energy = ½ mv²

Let the mass of molecule X be 'm₁' and velocity 'v₁'

and mass of mass of molecule Y be 'm₂' and velocity 'v₂'

Thus,

According to the question

m₁ = 4m₂ ..............(1)

since the kinetic energy of both the molecules are equal

Therefore,

½ m₁v₁² = ½ m₂v₂²

or

m₁v₁² = m₂v₂²

from (1)

4m₂v₁² = m₂v₂²

or

4v₁² = v₂²

or

2v₁ = v₂

hence,

The velocity of molecule Y is 2 times the velocity of molecule X