The exact fine-structure formula for hydrogen (obtained from the dirac equation without ecourse to perturbation theory) is: 21-1/2 enj mc 5+1/2)2 - a2 n - (j1/2) expand to order a4 (noting that a < < 1), and show that you recover: 13.6ev 3 enj 1+ n2 j+1/2 a handy relation, not necessarily needed for the exercises: e1 (6) mc2

We all use gps today, even if we don't drive yet. i bet you have been in the car with a parent and they have asked you to get out your phone to find a specific location. in your car, on the phone, you are using a very sophisticated technology. gps satellites circle the earth twice a day in a very precise orbit and transmit signal information to earth. gps receivers take this information and use trilateration to calculate the user's exact location. essentially, the gps receiver compares the time a signal was transmitted by a satellite with the time it was received. the time difference tells the gps receiver how far away the satellite is. now, with distance measurements from a few more satellites, the receiver can determine the user's position and display it on the unit's electronic map. what type of signal is utilized by the gps satellite?

Copper has free electrons per cubic meter. a 71.0-cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 a of current. (a) how much time does it take for an electron to travel the length of the wire? (b) repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length that carries the same current. (c) generally speaking, how does changing the diameter of a wire that carries a given amount of current affect the drift velocity of the electrons in the wire?

What is the average speed of a car that travels 40 mph for 1 hour and 60 mph in another hour?