Suppose a piece of very pure germanium is to be used as a light detector by observing, through the absorption of photons, the increase in conductivity resulting from generation of electron–hole pairs. If each pair requires $0.67$ eV of energy, what is the maximum wavelength that can be detected? In what portion of the spectrum does it lie?

A forward-bias voltage of $15.0$ mV produces a positive current of $9.25$ mA through a $p-n$ junction at $300$ K. What does the positive current become if the forward-bias voltage is reduced to $10.0$ mV?

The maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (b) Explain why pure silicon is opaque.

At a temperature of $290$ K, a certain $p-n$ junction has a saturation current $I_S=0.500$ mA. Find the current at this temperature when the voltage is (i) $1.00$ mV, (ii) $-1.00$ mV, (iii) $100$ mV, and (iv) $-100$ mV.

Silver has a Fermi energy of $5.48$ eV. Calculate the electron contribution to the molar heat capacity at constant volume of silver, $C_V$, at $300$ K. Express your result as a multiple of $R$.

At the Fermi temperature $T_F$, $E_F=k{T}_F$ (see Exercise $42.22$). When $T=T_F$, what is the probability that a state with energy $E=2E_F$ is occupied?

Pure germanium has a band gap of $0.67$ eV. The Fermi energy is in the middle of the gap. For temperatures of $250$ K, $300$ K, and $350$ K, calculate the probability $f\left(E\right)$ that a state at the bottom of the conduction band is occupied.