Concept:Activity (\(A\)) is defined as the rate at which nuclei undergo decay. It is mathematically the product of the decay constant and the number of active nuclei.
Formula:$$ A = \lambda N $$
Solution:- Given: \(\lambda = 8.3 \times 10^{-10} \text{ s}^{-1}\) and \(N = 6.7 \times 10^{21}\).
- Multiply the values: $$ A = (8.3 \times 10^{-10}) \times (6.7 \times 10^{21}) $$
- Calculate the scalar part: \( 8.3 \times 6.7 \approx 55.61 \).
- Calculate the exponent part: \( 10^{-10} \times 10^{21} = 10^{11} \).
- Combine them: \( 55.61 \times 10^{11} = 5.561 \times 10^{12} \text{ Bq} \).
- Rounding to two significant figures yields \( 5.6 \times 10^{12} \text{ Bq} \).
Why other options are incorrect:Options A and D represent errors in shifting the decimal place (exponent math). Option C uses the wrong units (Activity is measured in Becquerels, Bq, although it is equivalent to \(s^{-1}\), conventionally Bq is used for activity, and the magnitude \(10^{11}\) is an unshifted decimal error).
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