Goal: Calculate the fission rate of the bomb grade [math]U^{235}[/math] that has a mass of [math].91*10^{-3}[/math] Procedure:
Givens- [math] T_{1/2} = 7.038 \cdot 10^{8} year \times 3.1536 \cdot 10^{7} sec = 2.2195 \cdot10^{16} sec[/math]
[math] m = .91 \cdot 10^{-3} g[/math]
Calculations- [math]\lambda = \frac{\ln{2}}{T_{1/2}} = \frac{\ln{2}}{2.2195 \cdot 10^{16} sec} = 3.12 \cdot 10^{-17} sec^{-1}[/math]
[math]N = \frac{N_a}{A} m = \frac{6.022 \cdot 10^{23} \frac{nuclei}{mol}}{235 \frac{g}{mol}} .91 \cdot 10^{-3} g = 2.33 \cdot 10^{18} nuclei[/math]
[math]R = \lambda N = 3.12 \cdot 10^{-17} sec^{-1} \times 2.33 \cdot 10^{18} nuclei = \textbf{72.70 fissions/sec}[/math]