दो रेडियोधर्मीं तत्व \(A\) तथा \(B\) की अर्द्धआयु क्रमशः \(20 \, min\) तथा \(40\, min\) हैं। प्रारंभ में दोनों के नमूनों में नाभिकों की संख्या बराबर है। \(80 \,min\) के उपरांत \(A\) तथा \(B\) के क्षय हुए नाभिकों की संख्या का अनुपात होंगा:

A \(1 : 4\)
B \(5 : 4\)
C \(1 : 16\)
D \(4 : 1\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(5 : 4\)

Step-by-step Solution

Detailed explanation

For \(A_{t / 2}=20\, min\), \(t=80\,min\), number of half lifes \(n=4\) \(\therefore \) Nuclei remaining \(=\frac{\mathrm{N}_{\mathrm{o}}}{2^{4}} .\) Therefore nuclei decayed \(=\mathrm{N}_{0}-\frac{\mathrm{N}_{0}}{2^{4}}\) For…

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.

Same subject

सूची \(-I\) का सूची \(-II\) से मिलान करें।

सूची \(-I\)	सूची \(-II\)
\((A)\) कोणीय संवेग	\((I)\) \(\left[ ML ^2 T ^{-2}\right]\)
\((B)\) बलाघूर्ण	\((II)\) \(\left[ ML ^{-2} T ^{-2}\right]\)
\((C)\) प्रतिबल	\((III)\) \(\left[ ML ^2 T ^{-1}\right]\)
\((D)\) दाब प्रवणता	\((IV)\) \(\left[ ML ^{-1} T ^{-2}\right]\)

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