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AP EAMCET · PHYSICS · Nuclear Physics

If the half-life of a radioactive element is 12.5 hours, then the time taken to disintegrate 256 g of the substance into 1 g is (in hours)

  1. A 12.5
  2. B 25
  3. C 37.5
  4. D 100
Verified Solution

Answer & Solution

Correct Answer

(D) 100

Step-by-step Solution

Detailed explanation

\(N = N_0 \left(\frac{1}{2}\right)^n\) \(1 = 256 \left(\frac{1}{2}\right)^n \Rightarrow \left(\frac{1}{2}\right)^n = \frac{1}{256} = \left(\frac{1}{2}\right)^8 \Rightarrow n = 8\) \(t = n \times t_{1/2}\) \(t = 8 \times 12.5 = 100 \text{ hours}\)