Consider a universe in which the $\pi$ -meson orbits around the nucleus instead of electron.  Assuming a Bohr model for a $\pi$ -meson of mass  $m_{\pi }$ and of the same charge as the electron  is in a circular orbit of radius r about the nucleus with an orbital angular momentum $\frac{h}{2\pi }$. If  the radius of a nucleus of atomic number Z is given by $R=1.6\times {10}^{-15}{Z}^{1/3}m$ ,the total  number of elements in this universe that can exist is given as ‘N’. Fill $\left[\frac{N-1}{12}\right]$  in OMR  sheet.
 [Given $\frac{{\epsilon }_0{h}^2}{\pi m_e{e}^2}=0.53\stackrel{\text{o}}{\text{A}}$ ; $\frac{m_{\pi }}{m_e}=265$; neglect any shielding effect for the heavier atoms  and assume non relativistic physics to be applicable and take $5^{1/4}\approx 1.5$ ]