Develop an equation for the calculation of the effectiveness factor from Eq$.1,$ obtained from the mass balance in a spherical particle in a steady state where An irreversible first$-$order reaction occurs using the specified boundary conditions

$\frac{d^{2}C}{d{r}^2}+\frac{2}{r}\frac{dC}{dr}=\frac{{}_p{k}_{1}C}{De}Ec.1$

$c.f\mathrm{.}1$: $r=0$; $\frac{dC}{dr}=0$

$c.f\mathrm{.}2$: $r=R$; kmam$(C_b-C_s)=4R^{2}De(-\frac{dC}{dr}{)}_r=R$