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Q

1

Show that the number of collisions a molecule makes per second , called the collision frequency , $$ f $$ , is given by $$ f = \bar{v}/l_{m} $$ , and thus $$ f = 4\sqrt{2} \pi r^{2} \bar{v} N / V $$

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Q

2

The mean free path , of a molecule is the average distance that a molecule travels before colliding with another molecule. It is given by

$$l=\dfrac{1}{\sqrt{2}\pi d^2N_v}$$

where d is the diameter of the molecule and $$N_V$$ is the number of molecules per unit volume. The number of collisions that a molecule makes with other molecules per unit time, or collision frequency f, is given by

$$f=\dfrac{^u_{avg}}{l}$$

(a) If the diameter of an oxygen molecule is $$2.00 \times 10^{-10} m$$, find the mean free path of the molecules in a scuba tank that has a volume of 12.0 L and is filled with oxygen at a gauge pressure of 100 atm at a temperature of $$25.0^0C$$. (b) What is the average time interval between molecular collisions for a molecule of this gas?

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Q

3

At some instant , suppose we have $$ N_{0} $$ identical molecules . Show that the number $$ N $$ of molecules that travel a distance $$ x $$ or more before the next collision is given by $$ N = N_{0} e^{-x / l_{M}} $$ where $$ l_{M} $$ is the mean free path . This is called the survival equation .

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Q

4

For the case of nitrogen under standard conditions find:

(a) the mean number of collisions experienced by each molecule per second;

(b) the total number of collisions occurring between the molecules within $$1 \ cm^3$$ of nitrogen per second.

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Q

5

If X is the total number of collisions which a gas molecule registers with other molecules per unit time under particular conditions, then the collision frequency of the gas containing N molecules per unit volume is:

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