એક પ્રથમ ક્રમની પ્રક્રિયાતો અર્ધઆયુષ્ય સમય \(15\) મિનિટ છે. તો એક ક્લાક પછી પદાર્થનો કેટલો જથ્થો બાકી રહેશે ?

A મૂળ જથ્થાનો \(\frac{1}{4}\)
B મૂળ જથ્થાનો \(\frac{1}{8}\)
C મૂળ જથ્થાનો \(\frac{1}{16}\)
D મૂળ જથ્થાનો \(\frac{1}{32}\)

Verified Solution

Answer & Solution

Correct Answer

(C) મૂળ જથ્થાનો \(\frac{1}{16}\)

Step-by-step Solution

Detailed explanation

Given \(t_{1/2}\,=\,15\,minutes\) Total time \((T)\,=\,1\,hr\,=\,60\,min.\) From \(T\,=\,n\times t_{1/2}\) \(n\,=\,\frac {60}{15}\,=\,4\) Now from the formula \(\frac{N}{{{N_0}}}\, = \,{\left( {\frac{1}{2}} \right)^n}\)…

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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