આરંભમાં જયારે વાયુનું દબાણ \(500 \,torr\) હોય ત્યારે વાયુમય સંયોજન \(A\) નો વિધટન માટે અર્ધઆયુષ્ય \(240\, s\) છે. જ્યારે દબાણ \(250 \,torr\) હોય ત્યારે અર્ધ આયુષ્ય \(4.0 \,min\) મળે છે. તો પ્રક્રિયાક્રમ \(........\) છે. (નજીકના પૂર્ણાંકમાં)

A \(4\)
B \(3\)
C \(2\)
D \(1\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(1\)

Step-by-step Solution

Detailed explanation

\(\left( t _{1 / 2}\right)_{500 \text { torr }}=240\,sec =4\,min\). \(\left( t _{1 / 2}\right)_{250 \text { torr }}=4\,min\) \(t _{1 / 2} \propto a ^{1- n }\) As \(t _{1 / 2}\) is independent of initial pressure. Hence, order is \(1^{st}\) order.

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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