જો \(\mathrm{n}\) એ સંખ્યા ઘનતા હોય અને \(\mathrm{d}\) એ અણુનો વ્યાસ હોય, તો બે ક્રમિક અથડામણો વચ્ચે અણુ દ્વારા આવરી લેવાયેલ સરેરાશ અંતર (એટલે કે સરેરાશ મુક્ત પથ) ને _______ દ્વારા દર્શાવવામાં આવે છે.

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

\(\mathrm{n}=\) પ્રતિ એકમ કદ દીઠ અણુઓની સંખ્યા \(\mathrm{d}=\) અણુનો વ્યાસ \(\lambda=\frac{1}{\sqrt{2} \pi \mathrm{d}^2 \mathrm{n}}\) (સિદ્ધાંત મુજબ)

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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