यदि \(\mathrm{n}\) संख्या घनत्व है और \(\mathrm{d}\) अणु का व्यास है, तो एक अणु द्वारा दो क्रमागत टक्करों के बीच तय की गई औसत दूरी (अर्थात् माध्य मुक्त पथ) को _______ द्वारा दर्शाया जाता है।

A \(\frac{1}{\sqrt{2 n \pi d^2}}\)
B \(\sqrt{2} \mathrm{n} \pi \mathrm{d}^2\)
C \(\frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}\)
D \(\frac{1}{\sqrt{2} n^2 \pi^2 d^2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{n}=\) प्रति एकांक आयतन में अणुओं की संख्या \(\mathrm{d}=\) अणु का व्यास \(\lambda=\frac{1}{\sqrt{2} \pi \mathrm{d}^2 \mathrm{n}}\) (सिद्धांत के अनुसार)

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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