GaAs and GaP make solid solutions that have the same crystal structure as the parent materials, with As and P randomly distributed throughout the crystal. GaPxAs1 - x exists for any value of x. If we assume that the band gap varies linearly with composition between x = 0 and x = 1, estimate the band gap for GaP0.5As0.5. (GaAs and GaP band gaps are 1.43 eV and 2.26 eV, respectively.) What wavelength of light does this correspond to?

Verified step by step guidance

1. Identify the given band gaps for GaAs and GaP: GaAs has a band gap of 1.43 eV and GaP has a band gap of 2.26 eV.
2. Recognize that the problem states the band gap varies linearly with composition. This means we can use a linear interpolation formula to find the band gap for GaP_{0.5}As_{0.5}.
3. Apply the linear interpolation formula: E_{gap}(GaP_{0.5}As_{0.5}) = (1-x) * E_{gap}(GaAs) + x * E_{gap}(GaP), where x = 0.5.
4. Substitute the known values into the formula: E_{gap}(GaP_{0.5}As_{0.5}) = (1-0.5) * 1.43 eV + 0.5 * 2.26 eV.
5. To find the corresponding wavelength of light, use the equation \( \lambda = \frac{hc}{E} \), where \( h \) is Planck's constant, \( c \) is the speed of light, and \( E \) is the energy in electron volts.