To determine the color of the CdS (Cadmium Sulfide) semiconductor material, and to calculate the wavelength of absorption for GaAs (Gallium Arsenide) with a band gap of 1.35 eV, let's follow these steps:

1. Color of CdS Semiconductor

CdS is a direct bandgap semiconductor with a band gap of approximately 2.42 eV at room temperature. The wavelength corresponding to this band gap can be found using the relation:

$\lambda = \frac{hc}{E_g}$

where:

• $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{J} \cdot \text{s}$),
• $c$ is the speed of light in vacuum ($3.0 \times 10^8 \, \text{m/s}$),
• $E_g$ is the band gap energy (in joules),
• $\lambda$ is the wavelength of the photon absorbed or emitted.

First, convert the band gap energy from eV to joules:

$E_g = 2.42 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV} = 3.87484 \times 10^{-19} \, \text{J}$

Now calculate the wavelength:

$\lambda = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{3.87484 \times 10^{-19}} \, \text{m}$

$\lambda \approx 512 \, \text{nm}$

This wavelength corresponds to green light, meaning that CdS would appear greenish-yellow.

2. Wavelength of Absorption for GaAs (Band Gap: 1.35 eV)

We can use the same formula to calculate the wavelength for GaAs with a band gap of 1.35 eV.

First, convert the band gap energy from eV to joules:

$E_g = 1.35 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV} = 2.1627 \times 10^{-19} \, \text{J}$

Now calculate the wavelength:

$\lambda = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{2.1627 \times 10^{-19}} \, \text{m}$

$\lambda \approx 574 \, \text{nm}$

This wavelength is in the yellow-orange part of the spectrum.

Summary

• CdS: Appears greenish-yellow (wavelength ~512 nm).
• GaAs (Band Gap 1.35 eV): Wavelength of absorption is ~574 nm (yellow-orange).

Would you like more details on these calculations, or do you have any questions?

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Here are 5 related questions you might explore next:

1. How does the band gap energy of a semiconductor change with temperature?
2. What are the applications of CdS in optoelectronic devices?
3. How does doping affect the band gap of semiconductor materials?
4. Can the band gap of GaAs be altered by changing its composition?
5. What is the significance of the direct vs. indirect band gap in semiconductors?

Tip: The color of a semiconductor material often corresponds to the visible light wavelength that is absorbed, which is directly related to the material's band gap.