Calculate the bandgap of CdS which has a wavelength of 430 nm. Based on the wavelength, find out the colour of CdS semiconductor materials.

To calculate the bandgap of cadmium sulfide (CdS) based on the given wavelength, we can use the following relationship between the energy of a photon (\(E\)), its wavelength (\(\lambda\)), and Planck's constant (\(h\)):

\[
E = \frac{hc}{\lambda}
\]

Where:
- \(h\) is Planck's constant \((6.626 \times 10^{-34} \, \text{J} \cdot \text{s})\)
- \(c\) is the speed of light in a vacuum \((3.0 \times 10^8 \, \text{m/s})\)
- \(\lambda\) is the wavelength of the photon (in meters)

First, convert the given wavelength from nanometers to meters:

\[
\lambda = 430 \, \text{nm} = 430 \times 10^{-9} \, \text{m}
\]

Now, calculate the energy:

\[
E = \frac{6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \times 3.0 \times 10^8 \, \text{m/s}}{430 \times 10^{-9} \, \text{m}}
\]

\[
E \approx 4.62 \times 10^{-19} \, \text{J}
\]

To express this energy in electron volts (eV), use the conversion factor \(1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J}\):

\[
E = \frac{4.62 \times 10^{-19} \, \text{J}}{1.602 \times 10^{-19} \, \text{J/eV}} \approx 2.88 \, \text{eV}
\]

So, the bandgap of CdS is approximately **2.88 eV**.

### Determining the Color
The wavelength of 430 nm falls within the visible spectrum and corresponds to the blue-violet region of light. Therefore, the CdS semiconductor material would appear **blue-violet** when it absorbs or emits light at this wavelength.

### Additional Questions and Tips
Would you like more details or have any questions? Here are some related questions:

1. What are the practical applications of CdS semiconductors?
2. How does the bandgap of CdS compare to other semiconductors like Si or GaAs?
3. What is the relationship between bandgap energy and the absorption spectrum of a material?
4. How does temperature affect the bandgap of CdS?
5. What role does the bandgap play in determining the efficiency of solar cells?

**Tip:** When calculating the energy of photons, always ensure the wavelength is converted to meters for consistency in units.

Learn how to calculate the bandgap of CdS semiconductor from a given wavelength of 430 nm using the photon energy formula. Discover the color appearance of CdS based on its bandgap energy. Suitable for advanced high school students and beyond.

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