The second was defined in 1967 [2] using the hyperfine splitting of the ground state of cesium, which, at HFS = 9 192 631 770 Hz, is in the microwave region of the electro- magnetic spectrum. This was chosen in part for technical reasons, as it was then possible to couple a microwave cavity to an external oscillator to build a clock. However, the fractional instability of an atomic clock is given by the Allan deviation, y() 0 N where 0 is the transition frequency, the width of the transition, N the number of atoms involved, and the interrogation time. It is clear that a more stable clock can be achieved by using a higher transition frequency. While there are still technical challenges to building a very-high precision atomic clock using an optical transition, research is progressing and the second might have to be redefined in the near future. One potential candidate is what is called an optical lattice clock based on strontium atoms. 1. The four excited levels corresponding to the first excited electronic configuration of Sr have the following energy (in units of cm1, with respect to the ground state): 14317.520 14504.351 14898.563 21698.482 (a) Find the term(s) that correspond to the ground electronic configuration and the first excited configuration of Sr and draw an energy diagram with all the levels in the correct order. (b) Discuss the validity of the Russell-Saunders coupling scheme and the Land e interval rule as it applies to Sr. (c) For the first three levels of the first excited electronic configuration, show how each |LSJMJ state is constructed from non-spin-orbit-coupled states |LSMLMS .1 [2 p] 2. The proposed transition for a 87Sr lattice clock was measured as 429 228 004 229 952 Hz, with an uncertainty of 15 Hz. What are the levels involved in this transition? Discuss the transition from the point of view of selection rules. [1 p] 3. By how much does the transition in question 2 change when substituting 88Sr (m = 87.905619 a.m.u.) for 87Sr (m = 86.908884 a.m.u.)? [0.5 p] 4. The Earth's magnetic field is about 5 105 T. What would be the corresponding error on the strontium clock if all allowed MJ transitions were involved? [0.5 p]