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

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 = 72.70  fissions/sec[/math]

 Probability of fission per decay = [math]2.0 \cdot 10^{-7} % =\gt  2.0 \cdot 10^{-9} \times 72.70 fissions/sec[/math]

                [math]= 1.454 \cdot 10^{-5}%[/math] chance there will be a fission each second [math]=\gt  \textbf{not probable}[/math]