Suppose the ionization energy of a hydrogen-like ion A is greater than that of another hydrogen-like ion B . Let r , u , E , and L denote the orbit radius, electron speed, atom energy, and electron orbital angular momentum, respectively. For the ground state,

Step-by-step solution

The ionization energy of a hydrogen-like ion in the ground state is given by I = 13.6 Z^2 eV. Given I_A > I_B , we have Z_A > Z_B . For the ground state, the principal quantum number is n = 1 . The electron speed is u Z , which implies u_A > u_B . The orbital angular momentum is L = nh 2 , which implies L_A = L_B . The total energy is E = -13.6 Z^2 eV, which implies E_A The orbit radius is r 1 Z , which implies r_A < r_B .