Determine the radius and energy of a He ^+ ion in the state n = 1 .

Step-by-step solution

The radius of the n^ th Bohr orbit for a hydrogen-like species is given by r_n = 0.529 n^2 Z For He ^+ , the atomic number Z = 2 . For the state n = 1 , r₁ = 0.529 1^2 2 = 0.2645 0.265 The energy of the n^ th state for a hydrogen-like species is given by E_n = -13.6 Z^2 n^2 eV For He ^+ in the state n = 1 , E₁ = -13.6 2^2 1^2 = -13.6 4 = -54.4 eV