Rubidium occurs naturally in two isotopes: 85Rb and 87Rb. Rubidium-85, with a relative abundance of 72%, has nuclear spin I = 5/2. The nuclear spin of 87Rb is I = 3/2. The ground state of the single valence electron in rubidium (atomic number 37) is 5s. The first excited state is the 5p. Rather than being single energy levels, the atomic energy levels are split into closely spaced sub-levels of energy EJ, where J = L + S is the total electronic angular momentum of the state. This energy splitting, designated fine structure splitting, originates from the spin-orbit coupling of the electron. The splitting between the ground and first excited state is 780.24 nm. The splitting between the ground state and the second excited state is 794.6 nm. The fine structure splitting is the same for both isotopes of rubidium. In addition to fine structure splitting, the energy levels are further separated into different F sub-levels, where F = I + J and I is the nuclear spin. Allowed F values range from I + J to I - J including the integer values in between. Because the two isotopes differ in their nuclear spin quantum number (I), this splitting, designated hyperfine splitting, is not the same for both isotopes. Hyperfine splitting occurs as a result of the interaction between the electromagnetic multipole moments of the nucleus and the electromagnetic field produced by the electrons. The magnetic dipole moment of the nucleus interacts with the magnetic field of the valence electrons, providing the most significant contribution to the energy shift. A smaller contribution is provided by electrostatic interaction between the electric quadrupole moment of the nucleus and the atomic electrons. Though higher order multipole terms may be non-zero, their contributions are negligible and are generally ignored. Only certain transitions are allowed between ground and excited states. For electric dipole transitions, allowed transitions are those in which AF = 0, ± 1 (F = 0 to F' = 0 excluded). (a) Construct an energy level diagram showing the ground and excited electronic states of both 85 Rb| and 87Rb where you show the allowed fine and hyperfine states. Label the fine states with the appropriate term symbols and the hyperfine states with the appropriate quantum numbers. (b) Use vertical lines to indicate all allowed transitions on your energy level diagram.