In addition to the spin-orbit and kinematic corrections, there is a third relativistic correction term to the hamiltonian of the hydrogen atom due to the relativistic correction of the potential energy, "darwin term", defined as e2 5(7) 2m2c24tte tuh2 h' calculate the first-order energy shift due to this term, and explain in words your method of calculation (hint: you only have to consider the /= 0 case, and the darwin term commutes with l2, l7, and s2,

Astone is dropped from the upper observation deck of a tower, 250 m above the ground. (assume g = 9.8 m/s2.) (a) find the distance (in meters) of the stone above ground level at time t. h(t) = (b) how long does it take the stone to reach the ground? (round your answer to two decimal places.) s (c) with what velocity does it strike the ground? (round your answer to one decimal place.) m/s (d) if the stone is thrown downward with a speed of 2 m/s, how long does it take to reach the ground? (round your answer to two decimal places.) s