મોડર્ન વેક્યૂમ પમ્પ રૂમ તાપમાને\((300\, K)\) પાત્રનું દબાણ \(4.0 \times {10^{ - 15}}\, atm\) જેટલું ઘટાડે છે. જો \(R = 8.0\, JK^{-1}\, mole^{-1}\) , \(1\, atm = 10^5\, Pa\) અને \(N_ {Avogadro} = 6 \times 10^{23}\, mole^{-1}\) હોય તો વાયુના બે અણું વચ્ચેનું સરેરાશ મુક્તપથ કેટલાના ક્રમનો મળે?

A \(0.2\,\mu m\)
B \(0.2\,mm\)
C \(0.2\,cm\)
D \(0.2\,nm\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(0.2\,mm\)

Step-by-step Solution

Detailed explanation

Formula for mean free path- \(Y=\frac{K T}{\sqrt{2} \pi \sigma^{2} p}\) -wherein \(\sigma=\) Diameter of the molecule \(p=\) pressure of the gas \(T=\) temperature \(K=\) Boltzmann's Constant Let intermolecular distance be \(D\) then in a volume \(\frac{4 \pi}{3} D^{3}\) there…

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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