S18 HW3Modern Physicsdue 5pm M 3/5/2018
Problem 1
Suppose a photon with energy 200 [MeV] is traveling along the x-axis. Another photon has the energy 300 [MeV] and is traveling along the y-axis.
a) What is the total energy of this system of two photons?
b) What is the total momentum?
c) If a single particle had this same total energy and momentum, what would be its mass?
d) In what direction would it be traveling and at what speed?
Problem 2Relativity
Discuss the difference between Special Relativity and General Relativity.
Problem 3Millikan Oil-Drop Experiment
The following data were obtained in a Millikan oil-drop experiment:
Tter, g / 15.2 / 15.0 / 15.1 / 15.0 / 14.9 / 15.1 / 15.1 / 15.0 / 15.2 / 15.2Tter,b / 6.4 / 6.3 / 6.1 / 24.4 / 24.2 / 3.7 / 3.6 / 1.8 / 2.0 / 1.9
Where Tter,g and Tter,b stand for the times measured in a Millikan experiment for free fall (sub_g) and in an electric field (sub_b).
Additional information: distance travelled by drops 8.3 10-4 m, oil 839 kg/m3, viscosity of air = 1.6 10-5 Ns/m2, electric field E = 1.21 105 N/C.
a)Calculate 1/Tter,g + 1/Tter,b and show that within error this quantity is always an integer multiple of a fixed number, and, therefore, that the charge is always a multiple of one fixed fundamental charge.
b)Find the radius of the droplet.
c)Find the different charges, which have been sitting on the droplet in the experiments. What is the best estimate of e within error based on this experiment?
Hint: Calculate standard deviations from the data and use error propagation to determine the error in calculated properties where necessary.
Problem 4Thomson e/m
In a Thomson e/m experiment the Helmholtz coils had N=100 windings and the coil diameter was 50[cm]. A current of 1[A] was fed into the coils. The radius of the electron path was measured by a student. She found r = 20 [cm].
a) How fast were the electrons?
b) If you were to repeat the experiment with protons what would you modify in the experimental setup and to what values would you modify it to get a reasonable apparatus?
c) If you were to repeat the experiment with hypothetical particles that carry a million times the charge of the electron but which have the same mass as the proton, what would you modify in the experimental setup and to what values would you modify it to get a reasonable apparatus?
d) Can you think of any sources of experimental error that are based in the very construction of the apparatus of part a) that would limit your knowledge of v?