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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c939cff-bc46-4066-b22a-d4e55e2c89ab%2Fec44f59c-d9d3-4ffd-94a6-7b240aef1aeb%2F5cgzjpk_processed.png&w=3840&q=75)
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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