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The figure shows a typical radioactive decay (amount of undecayed nucleus (N) vs. time (t)) from a heavy nucleus. Such a decay may be best expressed by an equation like : ON-N₁ (At) ON No / Xt -At ON = N₂e ON= N₂ e-1/At

The figure shows a typical radioactive decay (amount of undecayed nucleus (N) vs. time (t)) from a heavy nucleus. Such a decay may be best expressed by an equation like : ON-N₁ (At) ON No / Xt -At ON = N₂e ON= N₂ e-1/At

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**Radioactive Decay of a Heavy Nucleus** The figure illustrates a typical radioactive decay process, depicting the amount of undecayed nucleus (N) versus time (t). The graph and accompanying table provide insights into how a heavy nucleus decays over time. **Graph & Table Analysis** The graph is a plot with: - The x-axis: Time in multiples of the half-life (\(t_{1/2}\)). - The y-axis: Number of nuclides (N) × 10³. The red curve represents the decay pattern, showing a decrease in the amount of undecayed nucleus over time. The table highlights specific time points measured in multiples of the half-life (\(t_{1/2}\)) and the corresponding number of nuclei (N): | Time (in multiples of \(t_{1/2}\)) | N | |--------------------------------------|-----------| | 0 | 1,000,000 | | \(t_{1/2}\) | 500,000 | | 2\(t_{1/2}\) | 250,000 | | 3\(t_{1/2}\) | 125,000 | | 4\(t_{1/2}\) | 62,500 | | 5\(t_{1/2}\) | 31,250 | | 6\(t_{1/2}\) | 15,625 | | 7\(t_{1/2}\) | 7,813 | | 8\(t_{1/2}\) | 3,906 | | 9\(t_{1/2}\) | 1,953 | | 10\(t_{1/2}\) | 977 | **Mathematical Representation** The decay of the nucleus can be best expressed using an exponential decay equation. Choose the correct equation from the options below: - \( \circ \, N = N_0 (\lambda t)^{\frac{1}{2}} \) - \( \circ \, N = N_0 / \lambda t \) - \( \circ \, N = N_0 e^{-\lambda t} \) - \( \circ \, N = N_0 e^{-1/ \lambda t} \) To understand this better, remember that the
Transcribed Image Text:**Radioactive Decay of a Heavy Nucleus** The figure illustrates a typical radioactive decay process, depicting the amount of undecayed nucleus (N) versus time (t). The graph and accompanying table provide insights into how a heavy nucleus decays over time. **Graph & Table Analysis** The graph is a plot with: - The x-axis: Time in multiples of the half-life (\(t_{1/2}\)). - The y-axis: Number of nuclides (N) × 10³. The red curve represents the decay pattern, showing a decrease in the amount of undecayed nucleus over time. The table highlights specific time points measured in multiples of the half-life (\(t_{1/2}\)) and the corresponding number of nuclei (N): | Time (in multiples of \(t_{1/2}\)) | N | |--------------------------------------|-----------| | 0 | 1,000,000 | | \(t_{1/2}\) | 500,000 | | 2\(t_{1/2}\) | 250,000 | | 3\(t_{1/2}\) | 125,000 | | 4\(t_{1/2}\) | 62,500 | | 5\(t_{1/2}\) | 31,250 | | 6\(t_{1/2}\) | 15,625 | | 7\(t_{1/2}\) | 7,813 | | 8\(t_{1/2}\) | 3,906 | | 9\(t_{1/2}\) | 1,953 | | 10\(t_{1/2}\) | 977 | **Mathematical Representation** The decay of the nucleus can be best expressed using an exponential decay equation. Choose the correct equation from the options below: - \( \circ \, N = N_0 (\lambda t)^{\frac{1}{2}} \) - \( \circ \, N = N_0 / \lambda t \) - \( \circ \, N = N_0 e^{-\lambda t} \) - \( \circ \, N = N_0 e^{-1/ \lambda t} \) To understand this better, remember that the
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