Question

The speed of a molecule of gas in a cubical vessel of side $4\text{m}$ is $16\text{m/s}$. This molecule is constantly colliding with the wall of the container. The collision frequency will be

• A. $2{\text{s}}^{-1}$
• B. $4{\text{s}}^{-1}$
• C. $6{\text{s}}^{-1}$
• D. $1{\text{s}}^{-1}$

Answer 1

The correct option is A $2{\text{s}}^{-1}$

Given:
Speed of the gas molecule $=16\text{m/s}$
Side of the cubical vessel $=4\text{m}$
$\therefore$ Between two collisions with the same wall, distance travelled $=2\times L$
$=2\times 4\text{m}$
$=8\text{m}$
$\therefore$ Time between successive collisions $=\frac{8\text{m}}{16\text{m/s}}=0.5\text{s}$
So, collision frequency $=\frac{1}{T}=2{\text{s}}^{-1}$