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Homework #6: Do not turn these in since there is a test next week. I will post my solutions so you can check your work.
That's all for homework #6. Be sure that you can construct the Lorentz Force vector as well as calculating its magnitude (e.g. using the dot product).
- Consider a conductor made of 82Pb (lead). Assume 82Pb has a band gap energy 0.83eV. Calculate the following:
(a) The number density of electrons in the ground state in this conductor. Note that 82Pb has 4 valence electrons. And recall that http://webelements.com/ is a useful site.
(b) The number density of electrons in the conducting band of 82Pb at 1,500K, 1,200K, 525K, 350K, and 273K.
- Boron is used to dope silicon to make semiconductors. This doping will change the band gap energy is an Si-B semiconductor to 0.045eV. Assume that one atom in 5x106 in a silicon matrix is replaced by a boron atom. Determine:
(a) The number density of boron electrons/holes (you have to choose which) in the ground state at T=300K.
(b) The number density of those electrons/holes in the conduction band.
(c) Comment on how this number conpares to the number density of conduction electrons in both pure silicon and pure aluminum conductors (Al contributes 1 electron/atom to the conduction band).
- What electric field is required to accelerate an electron from rest to 0.32c within a distance of 18cm? Assume the electric field is uniform. And recall from physics-2 that E=V/d for uniform E fields.
- You are in a location where the electric field has a magnitude of 450N/C and points in the positive x-direction. A magnetic field of strength 37,000nT points in the negative x-direction. A proton is fired into this region at 0.15c. Find (a) the Lorentz Force vector on this proton, and (b) the magnitude of the Lorentz Force.
- An electron has been accelerated to a speed of 0.27c (27% the speed of light). The electron is traveling due north in a region where Earth's magnetic field has a strength of 52,000nT, and points at an angle of 55° below the horizontal. As in class, the horizontal component of the field points due north.
(a) What potential (i.e., voltage) was required to accelerate the electron to this speed? Yes, this is physics-2 electric work-energy.
(b) Find the final equation (numbers, units, unit vectors) for the Lorentz Force (vector) on the electron. You must use x for east, y for north and z for straight up from Earth's surface.
(c) By how much does this electron deflect from due north after it has traveled a distance of 20cm northward?