The ratio of angular momentum in 3rd orbit and orbital angular momentum of 3d-orbital is:

angular momentum in 3rd orbit=$\frac{\mathrm{nh}}{2\mathrm{\pi }}=\frac{3\mathrm{h}}{2\mathrm{\pi }}$

Orbital angular momentum of 3d-orbital(l=2)=$\frac{\mathrm{h}}{2\mathrm{\pi }}\sqrt{\mathrm{l}(\mathrm{l}+1)}=\frac{\mathrm{h}}{2\mathrm{\pi }}\sqrt{2(2+1)}=\sqrt{\frac{3}{2}}\frac{\mathrm{h}}{\mathrm{\pi }}$

The ratio of angular momentum in 3rd orbit and orbital angular momentum of 3d-orbital =$\frac{3\mathrm{h}}{2\mathrm{\pi }}\times \sqrt{\frac{2}{3}}\frac{\mathrm{\pi }}{\mathrm{h}}=\sqrt{\frac{3}{2}}$