બે રેડિયો એકિટવ તત્વો \(A\) અને \(B\) ના અર્ધ- આયુષ્ય ક્રમશ : \(20\) મિનિટ તથા \(40\) મિનિટ છે.પ્રારંભમાં બંને નમુનાઓમાં નાભિકોની સંખ્યા સમાન છે. \(80\) મિનિટ પછી \(A\) અને \(B\) ના ક્ષય થયેલ નાભિકોનો ગુણોત્તર હશે :

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.

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