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Answer the following · Q26

Q.Represent graphically log10 (activity / dps) versus t/s. What is its slope?

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Step 1. The exponential decay law N = N0 e^(-λt), taking log10 of both sides, becomes log10 N = -(λ/2.303) t + log10 N0 -- a straight line in log10 N versus t, with slope -(λ/2.303) and y-intercept log10 N0.

Step 2. Since activity (dN/dt) is directly proportional to N at every instant, the identical straight-line relationship holds when log10(activity) is plotted against t instead of log10 N: log10(activity) = -(λ/2.303) t + log10(activity at t=0).

Step 3. So sketching the graph: a straight line, starting at some positive y-intercept (log10 of the initial activity) and sloping steadily downward as t increases, never actually reaching a y-value of negative infinity within any finite, practical time range, but always trending down. …

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