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A nuclide has a half-life of 10 ms - AQA - A-Level Physics - Question 28 - 2022 - Paper 2

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A nuclide has a half-life of 10 ms. The decay constant for this nuclide lies between A. 1 s$^{-1}$ and 10 s$^{-1}$. B. 10 s$^{-1}$ and 10$^{2}$ s$^{-1}$. C. 10$^... show full transcript

Worked Solution & Example Answer:A nuclide has a half-life of 10 ms - AQA - A-Level Physics - Question 28 - 2022 - Paper 2

Step 1

Determine the decay constant using the half-life

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Answer

The relationship between the half-life ( h) and the decay constant ( λ) is given by the formula:

ext{λ} = rac{ ext{ln} 2}{t_{1/2}}

Substituting the half-life provided:

ext{λ} = rac{0.693}{10 imes 10^{-3} ext{ s}} = 69.3 ext{ s}^{-1}

Step 2

Analyze the options

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Answer

Given that the decay constant calculated is approximately 69.3 s−1^{-1}, we analyze the options:

  • A. 1 s−1^{-1} and 10 s−1^{-1}: Incorrect, as 69.3 s−1^{-1} is not within this range.
  • B. 10 s−1^{-1} and 102^{2} s−1^{-1}: This includes 69.3 s−1^{-1}, hence it is a valid option.
  • C. 102^{2} s−1^{-1} and 103^{3} s−1^{-1}: Incorrect, as 69.3 s−1^{-1} is below 100 s−1^{-1}.
  • D. 103^{3} s−1^{-1} and 106^{6} s−1^{-1}: Incorrect, as 69.3 s−1^{-1} is far less than 1000 s−1^{-1}.

Thus, the correct choice is B.

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