Question

Which of the following are correct with reference to Maxwells-Boltzmann distribution of velocities? A. The fraction of molecules with very low ($c\rightarrow0$) and very high ($c\rightarrow\infty$) velocities is very small. B. The area under different curve obtained at different temperature is same. C. The maximum of the curve represent average velocity at a particular temperature. D. The area under the curve represents total number of molecules.

• A. A, B, C only
• B. A, B, D only
• C. A, B, C, D
• D. B, C, D only

Hint:

Remember the order of velocities: $v_{mp} < v_{avg} < v_{rms}$. The peak is always the Most Probable ($v_{mp}$).

Answer 1

The Correct Option is B

Step 1: Concept The Maxwell-Boltzmann distribution describes the speeds of molecules in an ideal gas at a given temperature.

Step 2: Meaning The distribution curve shows how many molecules have a certain velocity. The peak of the curve corresponds to the most probable velocity, not the average velocity.

Step 3: Analysis Statement A is true as the curve approaches zero at both ends. Statement B is true because the total probability (the area) is normalized to 1 (or the total number of molecules $N$), which is constant regardless of temperature. Statement D is true as it represents the sum of all molecules. Statement C is false because the peak is the most probable velocity ($v_{mp}$), whereas average velocity ($\bar{v}$) is slightly higher.

Step 4: Conclusion Since A, B, and D are scientifically accurate regarding the distribution, option (B) is the correct choice. Final Answer: (B)