Photovoltaic materials convert sunlight directly to electric power. Some of the photons that are incident upon the material displace electrons that are in turn collected to create an electric current. The overall efficiency of a photovoltaic panel, \(\eta\), is the ratio of electrical energy produced to the energy content of the incident radiation. The efficiency depends primarily on two properties of the photovoltaic material, (i) the band gap, which identifies the energy states of photons having the potential to be converted to electric current, and (ii) the interband gap conversion efficiency, \(\eta_{\mathrm{bg}}\), which is the fraction of the total energy of photons within the band gap that is converted to electricity. Therefore, \(\eta=\eta_{\mathrm{bg}} F_{\mathrm{bg}}\) where \(F_{\mathrm{bg}}\) is the fraction of the photon energy incident on the surface within the band gap. Photons that are either outside the material's band gap or within the band gap but not converted to electrical energy are either reflected from the panel or absorbed and converted to thermal energy.

Consider a photovoltaic material with a band gap of \(1.1 \leq B \leq 1.8 \mathrm{eV}\), where \(B\) is the energy state of a photon. The wavelength is related to the energy state of a photon by the relationship \(\lambda=1240 \mathrm{eV} \cdot \mathrm{nm} / B\). The incident solar irradiation approximates that of a blackbody at \(5800 \mathrm{~K}\) and \(G_{S}=1000 \mathrm{~W} / \mathrm{m}^{2}\).

(a) Determine the wavelength range of solar irradiation corresponding to the band gap.

(b) Determine the overall efficiency of the photovoltaic material if the interband gap efficiency is \(\eta_{\mathrm{bg}}=0.50\).

(c) If half of the incident photons that are not converted to electricity are absorbed and converted to thermal energy, determine the rate of heat absorption per unit surface area of the panel.