Concept:The fundamental law of radioactive decay states that the rate of decay of a radioactive sample is directly proportional to the number of radioactive nuclei present at that time.
Formula:$$ \frac{\Delta N}{\Delta t} = -\lambda N $$
Solution:- \(\Delta N\) is the change in the number of undecayed nuclei.
- \(N\) is the current number of nuclei, and \(\Delta t\) is the time interval.
- \(\lambda\) is the decay constant.
- The negative sign indicates that the number of parent nuclei \(N\) is decreasing over time. Rearranging yields: \(\Delta N = -\lambda N \Delta t\).
Why other options are incorrect:Option A is missing the decay constant and the negative sign. Option B is a proportionality, not an equation. Option C uses an undefined constant \(K\) and misses the critical negative sign.
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