TS EAMCET · Physics · Kinetic Theory of Gases

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 m s^{- 1}$ , then the rms speed of Helium molecules at the same temperature is

A $100 \sqrt{7} m s^{- 1}$
B $350 m s^{- 1}$
C $50 \sqrt{14} m s^{- 1}$
D $100 m s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(A) $100 \sqrt{7} m s^{- 1}$

Step-by-step Solution

Detailed explanation

Nitrogen is a diatomic molecule and its molecular mass is MN2=28 g mol-1. Helium is a monatomic molecule and its molecular mass is MHe=4 g mol-1. The rms speed of gas molecules at a temperature T is given by,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If the root mean square (rms) speed of nitrogen molecules at room temperature is 100 m s-1, then the rms speed of Helium molecules at the same temperature is

Step-by-step Solution

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 m s^{- 1}$ , then the rms speed of Helium molecules at the same temperature is