A student is modelling the decay of a radioactive isotope using the numerical iteration:
ΔNΔt=−0.15N \frac{\Delta N}{\Delta t} = -0.15 N ΔtΔN=−0.15NThe student chooses a time step of Δt=0.50 s\Delta t = 0.50\text{ s}Δt=0.50 s. The initial number of radioactive nuclei is N=8000N = 8000N=8000 at t=0t = 0t=0.
Part of the modelling spreadsheet is shown below:
| t/st / \text{s}t/s | Number N N\,N of radioactive nuclei remaining at time ttt | Number of nuclei decaying in the next 0.50 s |
|---|---|---|
| 0 | 8000 | 600 |
| 0.50 | 7400 | |
| 1.00 | ||
| 1.50 |
What is the model's prediction for the number of nuclei remaining, NNN, at t=1.50 st = 1.50\text{ s}t=1.50 s?
638863886388
684568456845
633263326332
491349134913
