If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum?
A) 16
B) 4
C) 2
D) $\sqrt { 2 }$
E) $2 \sqrt { 2 }$

Question

If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum? 
A) 16
B) 4
C) 2
D) $\sqrt { 2 }$
E) $2 \sqrt { 2 }$

Quizplus · Accepted Answer

The kinetic energy (KE) of a gas molecule is given by the equation $KE = \frac{p^2}{2m}$, where $p$ is the momentum and $m$ is the mass of the molecule. To double the kinetic energy, you need to double the value of $\frac{p^2}{2m}$, which means you need to make $p^2$ twice as large. If $p^2$ is doubled, then $p$ must be multiplied by $\sqrt{2}$ because $(\sqrt{2}p)^2 = 2p^2$.

If You Want to Double the Kinetic Energy of a Gas