CUET · PHYSICS · PYQ PAPER 2023
A radioactive isotope has a half life of T years. How long (in years)will it take the activity to reduce to 3.125% of it's original value?
- A 4T
- B 5T
- C 3T
- D 6T
Answer & Solution
Correct Answer
(B) 5T
Step-by-step Solution
Detailed explanation
\(A = A_0 \left(\frac{1}{2}\right)^n\) \(0.03125 A_0 = A_0 \left(\frac{1}{2}\right)^n\) \(0.03125 = \left(\frac{1}{2}\right)^n\) \(\frac{1}{32} = \left(\frac{1}{2}\right)^n\) \(\left(\frac{1}{2}\right)^5 = \left(\frac{1}{2}\right)^n\) \(n = 5\) \(t = nT\) \(t = 5T\)
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