Sketch a qualitative (no numbers) graph of the resistance as...

Sketch a qualitative (no numbers) graph of the resistance as a function of temperature between $100 \mathrm{~K}$ and $0 \mathrm{~K}$ for (a) an ordinary conductor, such as $\mathrm{Cu} ;$ (b) a superconductor with a transition temperature of $30 \mathrm{~K}$.

Key Concepts

Energy Quantization and Conservation in Electron Excitation

This principle highlights that energy is absorbed or emitted in discrete amounts (quanta). When a gamma-ray photon interacts with a semiconductor, the energy of the photon must be exactly sufficient to excite an electron from the valence band to the conduction band without being partially used; any excess energy is not subdivided to excite additional electrons. This underscores the rules of energy conservation in quantum systems, meaning that if a photon’s energy far exceeds the band gap of the material, the excess energy is not used for further electron excitations.

Photon Energy Calculation

Photon energy is determined by its wavelength through the formula E = hc/?, where h is Planck’s constant and c is the speed of light. This calculation is essential for comparing the energy provided by an incident photon with the energy required to overcome the semiconductor band gap. Understanding how to compute photon energy allows one to ascertain whether the photon has sufficient energy to induce electronic transitions.

Semiconductor Band Gap

This concept refers to the energy difference between the valence band and the conduction band in a semiconductor. The band gap is a critical property that determines how much energy is required to excite an electron from a bound state (in the valence band) to a free state (in the conduction band), where it can contribute to electrical conductivity. In silicon, for example, a gap of 1.12 eV means each electron needs at least that much energy to be promoted to the conduction band.

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