KCET · Physics · Nuclear Physics

A radioactive substance contains 10000 nuclei and its half-life period is 20 days. The number of nuclei present at the end of 10 days is

A 7070
B 9000
C 8000
D 7500

Verified Solution

Answer & Solution

Correct Answer

(A) 7070

Step-by-step Solution

Detailed explanation

We know, \(\frac{N}{N_{0}}=\left(\frac{1}{2}\right)^{t / T}\)
\(\Rightarrow \quad \frac{N}{10000}=\left(\frac{1}{2}\right)^{10 / 20}\)
\(\Rightarrow \quad N=\frac{10000}{\sqrt{2}}=\frac{10000}{1.414}=7070\)

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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