Question

If only one gas molecule is taken in a container, the correct relation between average speed ‘c’,root mean square speed ‘u’ and most probable speed ‘a’ becomes [ ]a) a < c < u b) a = c = u c) c < u < a d) u < c < a​

Answer 1

Answer:

If only one gas molecule is taken in a container, the correct relation between average speed ‘c’,root mean square speed ‘u’ and most probable speed ‘a’ becomes [ ]a) a < c < u b) a = c = u c) c < u < a d) u < c < a.

B) is correct answer.

Answer 2

Option B is the correct answer.

• The Root means square(RMS), average speed, and most probable speed are the different velocities possible by different molecules present in the gas container.
• The RMS velocity is given by the formula of a gas molecule with weight M, Temperature T, and universal gas constant R is given by,

=>$U_{rms} = \sqrt{3RT}/\sqrt{M}$,

• The most probable speed is given by the formula,

=>$U_{mp} = \sqrt{2RT}/\sqrt{M}$,

• The average speed is given by the formula,

=>$U_{avg} = \sqrt{8RT}/\sqrt{\pi M}$,

• The ratio of the speeds of RMS, average speed, and most probable speed is 1.224:1.128:1.
• As the container contains only a single type of gas molecule all they have the same type of speed uniformly.
• Hence, the ratio of all the speeds is equal. a = c = u is the correct answer.

Hence, Option B is the correct answer.