TS EAMCET · Physics · Nuclear Physics
A radioactive material of half-life 2.5 hours emits radiation that is 32 times the safe maximum level. The time (in hours) after which the material can be handled safely is
- A \(10\)
- B \(25\)
- C \(5\)
- D \(12.5\)
Answer & Solution
Correct Answer
(D) \(12.5\)
Step-by-step Solution
Detailed explanation
\(\frac{N}{N_0} = \left(\frac{1}{2}\right)^{t/T_{1/2}}\) \(\frac{1}{32} = \left(\frac{1}{2}\right)^{t/2.5}\) \(\left(\frac{1}{2}\right)^5 = \left(\frac{1}{2}\right)^{t/2.5}\) \(5 = \frac{t}{2.5}\) \(t = 5 \times 2.5\) \(t = 12.5\)
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