If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum? a) 16b) 2^(1/2)
c) 2d) 2*2^(1/2)e) 4

The linear momentum is given by the following equation:

  (1)

Where is the mass and the velocity.

On the other hand, the kinetic energy is given by:

  (2)

Which is the same as:

Now, if we double the kinetic energy, equation (2) changes to:

  (3)

So, if we want to obtain the kinetic energy as shown in (3), the only option that works is increasing momentum by a factor of or :

Applying this in (2):

>>>As we can see, this equation is the same as equation (3)

Therefore, the correct answer is B