Question

The gas molecules randomly move in all directions and collide with each other and with the wall of the container. It is difficult to determine the speed of an individual molecule but it has become possible to work out the distribution of molecules among different molecular speeds. This is known as Maxwell Boltzmann distribution.
Consider the following graph about Maxwell's distribution of speeds at two different temperatures $T_1$ and $T_2$.

The curve has which of the following characteristics?
(i) It has symmetrical distribution of molecules against molecular velocity.
(ii) The area under the curve gives the total number of molecules.
(iii) The maxima of the curve shifts towards right as the temperature is raised.
(iv) The area under the curve is independent of temperature.
Select the correct statements from the codes given below.

• A. (i), (ii)
• B. (i), (ii) and (iii)
• C. (ii), (iii) and (iv)
• D. All are correct

Answer 1

The correct option is D All are correct

The curve has all of the following characteristics.
(i) It has symmetrical distribution of molecules against molecular velocity.
(ii) The area under the curve gives the total number of molecules.
(iii) The maxima of the curve shifts towards right as the temperature is raised. The fraction of molecules with most probable speed decreases with increase in temperature.
Most probable speed increases with increase in temperature.
(iv) The area under the curve is independent of temperature. Total area under the curve at $T_1$ is equal to that under curve at $T_2$.

Note:
$\alpha =\sqrt{\frac{2RT}{M}}$