Question

The speed of molecules of gas in a cubical vessel of side 5 m is 15 $m{s}^{-1}$. This molecule is constantly colliding with the walls of the container the collision frequency will be
A) 0.2 per second
B) 1.5 per second
C) 2.5 per second
D) 5 per second

Answer 1

Hint
As we have to find the frequency of the molecule so it totally means that firstly we have to find the time taken by the particle between the successive collisions.
Mathematically it can be expressed as
T = $\dfrac{1}{f}$

Complete step-by-step answer:
As in the given question
Speed of the gas molecule = 15 m/s
And side of the vessel = 5 meter
So, distance travelled by the particle during the collision from the same wall of the distance
2 × 5 = 10 meter
So the time taken by the particles is given by
T = $\dfrac{d}{s}$
Here t = time
D = distance travelled by the object
S = speed of the particle
So putting the value in the equation
T = $\dfrac{{10}}{{15}}$
So the frequency is given by
F = $\dfrac{1}{t}$
So putting the value in the equation
F = $\dfrac{{15}}{{10}}$
Or it can be also written as
F = 1.5
Option (B) is the correct answer.

Note
According to the kinetic theory of the gas
The gas equation is given by
PV = NRT
P = represent the pressure by the gas in the container
V = volume of the container
N = Number of molecule
R = represent the gas constant