The diameter of an oxygen molecule is approximately 3 Å . Calcula… - Vidyadip

Question

The diameter of an oxygen molecule is approximately $3 \text Å $. Calculate the mean free path of oxygen molecules and the mean time taken between collisions at normal temperature and pressure. At normal temperature and pressure the number of molecules per cubic is $3 \times 10^{19}$.

✓

Answer

$ \begin{array}{l} d =3 \textÅ =3 \times 10^{-8} cm \\ n _0 =3 \times 10^{19}\end{array}$
Mean free path
$\begin{aligned}\lambda & =\frac{1}{\sqrt{2} n_0 \pi d^2} \\& =\frac{1}{1.414 \times 3 \times 10^{19} \times 3.14 \times\left(3 \times 10^{-8}\right)^2} \\& =\frac{1}{1.414 \times 3 \times 3.14 \times 9 \times10^{19} \times 10^{-16}} \\& =\frac{1}{119.88 \times 10^3}=8.33 \times 10^{-6} cm\end{aligned}$
Mean time taken in collisions
$\begin{aligned} t & =\frac{\lambda}{\overline{ C }}=\lambda\left[\frac{ M }{3 RT }\right]^{\frac{1}{2}} \\ & =8.33 \times 10^{-6} \times\left[\frac{32}{3 \times 8.3 \times 10^7 \times 273}\right]^{\frac{1}{2}} \\ & =1.75 \times 10^{-10} sec .\end{aligned}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from PART - 2 CH - 12 Kinetic Theory→PART - 2 CH - 12 Kinetic Theory — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

When two waves of almost equal frequencies $n_1$ and $n_2$ reach at a point simultaneously, what is the time interval between successive maxima?

A block of mass m moving at a speed v compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring.

If earth contracts to half its radius, what would be the duration of the day? Ans. According to the law of conservation of angular momentum,

Show that the slope of p-V diagram is greater for an adiabatic process as compared to an isothermal process.

If angular momentum is conserved in a system whose moment of inertia is decreased, will its rotational kinetic energy be also conserved? Explain.

Two conducting spheres of radii $R_1$ and $R_2$ are kept widely separated from each other. What are their individual capacitances? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series-parallel connections.

When a glass rod is heated at high temperature, why does its ends becomes rounded?

Two large glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to 1mm. Find the rise of water in the space between the plates. Surface tension of water = 0.075N/m.

Two point sources of sound are kept at a separation of $10\ cm$. They vibrate in phase to produce waves of wavelength $5.0\ cm.$ What would be the phase difference between the two waves arriving at a point $20\ cm$ from one source$-$

On the line joining the sources.
On the perpendicular bisector of the line joining the sources?

What is the difference between static friction, kinetic friction and rolling friction?