The magnitude of the energy of an electron in the x^ th excited state of a Be ³⁺ ion is exactly equal to the ionization energy of a hydrogen atom in its ground state. The value of x is :

Step-by-step solution

The ionization energy of a hydrogen atom in its ground state is 13.6 eV . The energy of an electron in the n^ th orbit of a hydrogen-like species is given by E_n = -13.6 Z^2 n^2 eV . For a Be ³⁺ ion, the atomic number is Z = 4 . The magnitude of the energy in the n^ th orbit is |E_n| = 13.6 4^2 n^2 = 13.6 16 n^2 eV . Equating this to the ionization energy of hydrogen: 13.6 16 n^2 = 13.6 n^2 = 16 n = 4 The n = 4 orbit corresponds to the (n-1)^ th excited state. Therefore, it is the 3^ rd excited state, which means x