TS EAMCET · Physics · Nuclear Physics
Two radioactive substances A and B have same number of initial nuclei. If the halflives of A and B are 1.5 days and 4.5 days respectively, then the ratio of the number of nuclei remaining in A and B after 9 days is
- A \(1: 16\)
- B \(1: 1\)
- C \(1: 4\)
- D \(1: 8\)
Answer & Solution
Correct Answer
(A) \(1: 16\)
Step-by-step Solution
Detailed explanation
\(n_A = \frac{t}{T_{1/2, A}} = \frac{9}{1.5} = 6\) \(n_B = \frac{t}{T_{1/2, B}} = \frac{9}{4.5} = 2\) \(\frac{N_A}{N_B} = \frac{N_0 (1/2)^{n_A}}{N_0 (1/2)^{n_B}} = \frac{(1/2)^6}{(1/2)^2} = \frac{1/64}{1/4} = \frac{4}{64} = \frac{1}{16}\)
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