The triply ionized beryllium ( Be ⁺⁺⁺ ) has the same electron orbital radius as that of the ground state of hydrogen. Hence, the energy state of triply ionized beryllium is (Given Z = 4 for beryllium)

Step-by-step solution

The radius of the n -th Bohr orbit for a hydrogen-like atom is given by r = r₀ n^2 Z , where r₀ is the Bohr radius. For the ground state of hydrogen, n = 1 and Z = 1 . r_H = r₀ 1^2 1 = r₀ For triply ionized beryllium ( Be ⁺⁺⁺ ), Z = 4 . Let its principal quantum number be n . r_ Be = r₀ n^2 4 Given that the orbital radii are equal, r_ Be = r_H . r₀ n^2 4 = r₀ n^2 = 4 n = 2 Answer: n = 2