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1. Discuss briefly the origin of the differing electronic properties of metals, semiconductors and insulators. Under what circumstances will the nearly-free electron model be useful for describing the band structure of a solid?
A weak periodic potential
W(z) = W_0 cos (2*pi*z)/a
with W_0 > 0, is imposed on a one-dimensional free-electron gas lying along the z direction. Discuss the form of the resulting wavefunctions at the first Brillouin zone boundary. Explain why a gap arises.
A simple model of a two-dimensional band structure can be obtained by summing together two one-dimentional band structures. Consider the energy band
E(k_x, k_y) = U cos (k_x * a) - U cos (k_y * a)
with U > 0, corresponding to a particular two-dimensional crystal with square lattice and period a. Give the wavevectors and energies of the highest and lowest energy states in teh band. Draw labelled constant energy contours in the first Brillouin zone near these particular states. Comment on the form of the constant-energy contours near the centre fo teh first Brillouin zone.
A 180 W light bulb is plugged into a standard 110 Voutlet. How much does it cost per month (31 days) to leavethe light turned on, evaluate What is the current of the bulb
A solenoid with 1200 turns per meter has a diameter of 8 centimeter. A current I = 2.60 Amp flows in the counterclockwise direction in the solenoid. Obtain the magnitude of the magnetic flux through the loop
Describe in 100 words or less how electromagnetic theory has influenced or affected today's world society
Two initially uncharged capacitors, of capacitance C and2C, are connected in series across a battery. The voltage across each capacitor is the same. The energy stored by each capacitor is the same.
The author's cat enjoys chasing chipmunks in the front yard.
The plates of a 2.5 E-9 F parallel plate capacitor are separated by 1.2 mm. What is the area of each plate
A sailor strikes the side of his ship just below the surface of the sea. He hears echo of the wave reflected from the ocean floor directly below 9 s later. How deep is the ocean at this point.
The image behind a convex mirror (radius of curvature = 62 centimeter) is placed 22 centimeter from the mirror. Estimate where is the object located
a piano note is compared to a tuning fork vibrating at 440 Hz. Four beats per second are discerned by the piano tuner. What was the initial frequency of the piano wire
An unknown substance has a mass of 0.125 kg and an initial temperature of 112.3°C. The substance is then dropped into a calorimeter made of aluminum containing 0.285 kg of water initially at 27.8°C.
A 5.40 kg mass attached to a spring oscillates with a period of 0.445 s and an amplitude of 17.0 cm. Find the total mechanical energy of the system
Assume that positive -axis is directed toward the direction of motion of cart 2.
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