-meson of charge ' e ', mass 208 me moves in a circular orbit around a heavy nucleus having charge +3 e . The quantum state ' n ' for which the radius of the orbit is same as that of the first Bohr orbit for hydrogen atom ts [approximately]

Step-by-step solution

For hydrogen atom, r_n= n^2 h^2 4 ^2 m k e^2 r₁= h^2 4 ^2 m k e^2 ....(i) For -meson, m 208 ~m , Z =3 r_n= n^2 h^2 4 ^2(208 m) k(3) e^2 ....(ii) From eq(i) and (ii), we get h^2 4 ^2 mke ^2 = n ^2 ~h ^2 208 3 4 ^2 mke ^2 n = 208 3 25