A positive ion with exactly one electron ejects this electron when it absorbs a photon of wavelength 228 Å or shorter. Determine the ion.

Step-by-step solution

The ionization of a hydrogen-like ion corresponds to the transition of an electron from n = 1 to n = . Using the Rydberg formula: 1 = R Z^2 ( 1 1^2 - 1 ^2 ) 1 = R Z^2 Substituting = 228 = 228 10⁻¹⁰ m and the Rydberg constant R 1.097 10^7 m ⁻¹ : Z^2 = 1 R = 1 228 10⁻¹⁰ 1.097 10^7 Z^2 = 1000 250.116 4 Z = 2 The ion with atomic number Z = 2 and exactly one electron is He ^+ .