Final answer:
The semiconductor with a band gap of 1.75 eV will not absorb wavelengths longer than 708 nm. Therefore, among the provided options, 720 nm is the only wavelength the semiconductor will not absorb. The correct answer is option b.
Step-by-step explanation:
To determine which wavelengths a semiconductor with a band gap of 1.75 eV will not absorb, we can make use of the relationship between the energy of a photon (E) and its wavelength (λ). This relationship can be expressed through the equation E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J s) and c is the speed of light (3 x 10^8 m/s). For ease of calculation within the scope of electron-volt (eV) and nanometer (nm), we can use the constant hc = 1240 eV nm.
Thus, E (in eV) = 1240 / λ (in nm). A semiconductor will not absorb photons with energies less than its band gap (i.e., E < 1.75 eV). To find the corresponding wavelength cutoff, λ_cutoff = 1240 / 1.75 eV, which is approximately 708 nm. Therefore, any wavelength longer than 708 nm (smaller energy) will not be absorbed by the semiconductor.
Comparing the given options with the calculated cutoff wavelength:
- 475 nm - shorter than cutoff, absorbed
- 720 nm - longer than cutoff, not absorbed
- 545 nm - shorter than cutoff, absorbed
- 695 nm - shorter than cutoff, absorbed
- 615 nm - shorter than cutoff, absorbed
The only wavelength from the options that the semiconductor with a band gap of 1.75 eV will not absorb is 720 nm.