Question

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

Answer 1

Answer:
`√(2)`

The linear momentum
`p` is given by the following equation:

`p=m.v` (1)

Where
`m` is the mass and
`v` the velocity.

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

`K=(p^(2))/(2m)` (2)

Which is the same as:

`K=(1)/(2)m.v^(2)`

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

`2K=2(p^(2))/(2m)`

`2K=(p^(2))/(m)` (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
`√(2)` or
`2^(1/2)`:

Applying this in (2):

`K=((√(2)p)^(2))/(2m)`

`K=((2p)^(2))/(2m)`

`K=(p^(2))/(m)`>>>As we can see, this equation is the same as equation (3)

Therefore, the correct answer is B