Home
Class 11
PHYSICS
Estimate the mean free path and collisio...

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature `17 ^(@) C`. Take the radius of a nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of `N_(2)=28.0 u)`.

Text Solution

Verified by Experts

Mean free path
`lambda=(1)/(sqrt(2)pid^(2)lambda)implieslambda(K_(B)T)/(sqrt(2)pid^(2)p)(p=nK_(B)T)`
`lambda=((1.38xx10-23)(290))/((1.414)(2xx10^(-10))(2.026xx10^(5)))`
`1.1xx10^(-7)`
`V_(rms)=sqrt((3K_(B)T)/(m))=sqrt((3xx1.38xx10^(-23)xx290)/(28xx1.66xx10^(-27)))`
`=5.1xx10^(2)m//s`
`therefore` Collision frequency
`f=(V_(rms))/(lambda)=(5.1xx10^(2))/(1.1xx10^(-7))=4.6xx10_(s^(-1))^(9)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Estimate the mean free path and collison frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature 17^(@)C . Take the radius of a nitrogen molecule to be roughtly 1.0 Å . Compare the collision time with the time the molecule moves freely between two successive collision ( molecular mass of N_(2) = 28.0 ) . [Optional ]

Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2 atm and temperature 17^(@) C . Take the radius of a nitrogen molecule to be roughly 1.0 Å . Compare the collision time with the time the molecule moves freely between two successive collisions. (Molecular mass of nitrogen = 28.0 u).

Calculate the mean free path of nitogen at 27^(@)C when pressure is 1.0 atm. Given, diameter of nitogen molecule = 1.5 Å, k = 1.38 xx 10^(-23) JK^(-1) . If the average speed of nitrogen molecules is 675 ms^(-1) , find the time taken by the molecule between two successive collsions and the frequency of collisions.

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as :

An ideal gas is enclosed in a cylinder at pressure of 2atm and temperature, 300K. The mean time between two successive collisions is 6xx10^(-8) s. If the pressure is doubled and temperature is increased to 500K, the mean time between two successive collisions will be close to:

Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP.The mean free path (average distance covered by a molecule between successive collisions)=1.38xx10^(-5)cm.

Estimate the mean free path for a water molecule in water vapour at 373 K. Given diameter of water molecule = 2 Å and number density of water molecule (at NTP) = 2.7 xx 10^(25) m^(-3) . Compare it with interatomic distance for water = 40 Å .

Two gaseous molecules A and B are traveling towards each other. Let the mean free path of the molecule be sigma and Z be the collision number with other molecules at pressure 1 atm . Answer the following questions The free path of gas molecule is the distance

A flask contains argon and chlorine in the ratio 2:1 by mass. The temperature of the mixture is 27^(@)C . Obtain the ratio of (i) average kinetic energy per molecule, and (ii) root mean square speed of the molecules of two gases. Atomic mass of argon = 39.9 u, Molecular mass of chlorine = 70.9 u.

Statement-1: The total translational kinetic energy of fall the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume because. Statement-2: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.