Question 31.WE.8: A sample initially contains 1000 undecayed nuclei of an isot...
A sample initially contains 1000 undecayed nuclei of an isotope whose decay constant λ = 0.10 min^{−1}. Draw a graph to show how the sample will decay over a period of 10 minutes.
Step 1 We have N_{0} = 1000 and λ = 0.10 min^{−1}. Hence, we can write the equation for this decay:
N = 1000 e^{(−0.10 × t)}
Step 2 Calculate values of the number N of undecayed nuclei at intervals of 1.0min (60s); this gives Table 31.4 and the graph shown in Figure 31.12.
| t / min | 0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 |
| N | 1000 | 905 | 819 | 741 | 670 | 607 |
| t / min | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 | |
| N | 549 | 497 | 449 | 407 | 368 |
Table 31.4 For Worked example 8.
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