Show that the probability P(E) that an energy level having energy E is not occupied is where .
The probability P(E) that an energy level having energy E is not occupied is.
The probability of an electron occupying a certain energy state is called the occupancy probability of that state. The total probability, of an electron, occupying or not occupying a state is 1. Thus the probability of not occupying a state is equal to the difference between 1 and the probability of occupying a state.
The probability that a state is occupied by an electron is P and the probability that the state is unoccupied by an electron is P' . Thus, we can write-
Hence, the probability of an unoccupied state is, where .
When a photon enters the depletion zone of a p-n junction, the photon can scatter from the valence electrons there, transferring part of its energy to each electron, which then jumps to the conduction band. Thus, the photon creates electron–hole pairs. For this reason, the junctions are often used as light detectors, especially in the x-ray and gamma-ray regions of the electromagnetic spectrum. Suppose a single 662keV gamma-ray photon transfers its energy to electrons in multiple scattering events inside a semiconductor with an energy gap of 1.1eV, until all the energy is transferred. Assuming that each electron jumps the gap from the top of the valence band to the bottom of the conduction band, find the number of electron – hole pairs created by the process.
Figure 41-1a shows 14 atoms that represent the unit cell of copper. However, because each of these atoms is shared with one or more adjoining unit cells, only a fraction of each atom belongs to the unit cell shown. What is the number of atoms per unit cell for copper? (To answer, count up the fractional atoms belonging to a single unit cell.)
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