Show that the radial wave function $R_{21}(r)=Ar{e}^{-\frac{r}{2a_0}}$ satisfies the following equation

$\frac{1}{r^2}\frac{d}{dr}(r^2\frac{dR}{dr})+\frac{2}{{}^2}[E-V-\frac{{}^2}{2}\frac{l(l+1)}{r^2}]R=0$

for $l=1r,A,a_0,$ and $.r^2\frac{d{R}_{21}}{dr}.$

Second, calculate $\frac{d(r^2\frac{d{R}_{21}}{dr})}{dr}.$

Third, calculate $\frac{2}{{}^2}[V(r)+\frac{{}^{2}l(l+1)}{2r^2}]R_{21}-\frac{1}{r^2}\frac{d(r^2\frac{d{R}_{21}}{dr})}{dr}.$

Fourth, calculate $\frac{1}{R_{21}}\{\frac{2}{{}^2}[V(r)+\frac{{}^{2}l(l+1)}{2r^2}]R_{21}-\frac{1}{r^2}\frac{d(r^2\frac{d{R}_{21}}{dr})}{dr}\}.$

Finally, calculate $E-=\frac{1}{R_{21}}\{[V(r)+\frac{{}^{2}l(l+1)}{2r^2}]R_{21}-\frac{{}^2}{2r^2}\frac{d(r^2\frac{d{R}_{21}}{dr})}{dr}\}.$

$E-=$

$Is$ this consistent with the Bohr model?

Yes

$No$