Determine the radius and energy of a He ^+ ion in the state n = 10 .

Step-by-step solution

The radius of a hydrogen-like ion in the n^ th state is given by: r_n = 0.529 n^2 Z For He ^+ , the atomic number Z = 2 . For the state n = 10 : r₁₀ = 0.529 10^2 2 = 0.529 50 = 26.45 26.5 The energy of a hydrogen-like ion in the n^ th state is given by: E_n = -13.6 Z^2 n^2 eV For He ^+ in the state n = 10 : E₁₀ = -13.6 2^2 10^2 = -13.6 4 100 = -0.544 eV