Spontaneous fission rate for sample of U-235 (1mg/cm^2)

Goal: Calculate the fission rate of the bomb grade [math]\displaystyle{ U^{235} }[/math] that has a mass of [math]\displaystyle{ .91*10^{-3} }[/math] Procedure:

 Givens- [math]\displaystyle{  T_{1/2} = 7.038*10^{8} year \times 3.1536*10^{7} sec = 2.2195*10^{16} sec }[/math]

         [math]\displaystyle{  m = .91 \times 10^{-3} g }[/math]

 Calculations- [math]\displaystyle{ \lambda = \frac{\ln{2}}{T_{1/2}} = \frac{\ln{2}}{2.2195*10^{16} sec} = 3.12*10^{-17} sec^{-1} }[/math]

               [math]\displaystyle{ N = \frac{N_a}{A} m = \frac{6.022*10^{23} \frac{nuclei}{mol}}{235 \frac{g}{mol}} .91 * 10^{-3} g = 2.33*10^{18} nuclei }[/math]

               [math]\displaystyle{ R = \lambda N = 3.12*10^{-17} sec^{-1} \times 2.33*10^{18} nuclei = \textbf{72.70  nuclei} }[/math]