A photovoltaic cell contains a p–n junction that that converts solar light to electricity. An optimum semiconductor would have its band-gap energy matched to the wavelength of maximum solar intensity at the Earth's surface. (b) Which of the following semiconductors absorb at a wavelength matched with maximum solar intensity? CdTe with a band-gap energy of 145 kJ/mol or ZnSe with a band-gap energy of 248 kJ/mol.

Verified step by step guidance

1. Step 1: Understand that the band-gap energy of a semiconductor is the energy required to excite an electron from the valence band to the conduction band. This energy corresponds to a specific wavelength of light, which can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength.
2. Step 2: Convert the band-gap energies from kJ/mol to J/photon. This can be done by dividing the energy by Avogadro's number (6.022 x 10^23 mol^-1) and then multiplying by 1000 to convert from kJ to J.
3. Step 3: Use the equation E = hc/λ to calculate the wavelength of light that each semiconductor absorbs. Rearrange the equation to solve for λ: λ = hc/E.
4. Step 4: Compare the calculated wavelengths with the wavelength of maximum solar intensity at the Earth's surface, which is about 500 nm. The semiconductor that absorbs light closest to this wavelength will be the one that is best matched to the solar spectrum.
5. Step 5: Remember that the semiconductor with the wavelength closest to the wavelength of maximum solar intensity is the one that will absorb the most solar energy and therefore be the most efficient in a photovoltaic cell.

Key Concepts

Band-Gap Energy

Band-gap energy is the energy difference between the valence band and the conduction band in a semiconductor. It determines the wavelengths of light that a semiconductor can absorb; a smaller band-gap allows for the absorption of lower-energy (longer wavelength) photons, while a larger band-gap absorbs higher-energy (shorter wavelength) photons. For photovoltaic applications, the band-gap should ideally match the solar spectrum to maximize efficiency.

Photovoltaic Effect

The photovoltaic effect is the process by which a semiconductor converts light energy into electrical energy. When photons with energy equal to or greater than the band-gap energy are absorbed, they excite electrons from the valence band to the conduction band, creating electron-hole pairs. This movement of charge carriers generates an electric current when the semiconductor is connected to an external circuit.

Solar Spectrum

The solar spectrum refers to the range of wavelengths of light emitted by the sun, which includes ultraviolet, visible, and infrared light. The maximum solar intensity occurs in the visible range, particularly around wavelengths of 400-700 nm. Understanding the solar spectrum is crucial for selecting semiconductors for photovoltaic cells, as the band-gap energy must align with the wavelengths where solar energy is most abundant to optimize energy conversion.