question_answer

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?. Find the value of\[\left[ \frac{N-1}{12} \right]\]. [Given \[\frac{{{\varepsilon }_{0}}{{h}^{2}}}{\pi {{m}_{e}}{{e}^{2}}}=0.53\overset{\text{o}}{\mathop{\text{A}}}\,;\frac{{{m}_{\pi }}}{{{m}_{c}}}=265;\] neglect any shielding effect for the heavier atoms and assume non relativistic physics to be applicable and take \[{{5}^{1/4}}=1.5\]]

Answer:

3.00