In an interstellar gas cloud at 42.6 k, the pressure is 1.06 x 10-8 pa. assuming that the molecular diameters of the gases in the cloud are all 19.2 nm, what is their mean free path?

Answer : The mean free path is, 33.88 m

Explanation :

First we have to calculate the volume of for mole of gas by using ideal gas equation.

where,

P = pressure of gas =

V = volume of gas = ?

T = temperature of gas = 42.6 K

n = number of moles of gas = 1 mole

R = gas constant =

Now put all the given values in the ideal gas equation, we get:

Now we have to calculate the number of molecules per unit volume.

Now we have to calculate the mean free path.

Formula used :

where,

d = diameter pf molecule =

conversion used :

= number of molecules per unit volume

Now put all the given values in this formula, we get:

Therefore, the mean free path is, 33.88 m

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