1. (20 points) The transition dipole matrix element (2p|r|1s) between the 2p and the 1s state of hydrogen is given by (256/243) ao/2, where ao is the Bohr radius. Evaluate the Einstein A coefficient, A = a (2p|F|1s) 4 w c and calculate the natural lifetime of the 2p state*. Compare your result to the experimentally measured value (the Lyman alpha transition); see e.g. the mea- surements reported in the Physical Review paper by William Bickel and Allan Goodman, Mean lives of the 2p and 3p levels in atomic hydrogen