
. Calculate the wavelength of TiO2 which has a band gap of 2.8 eV? Based on the wavelength, find out the colour of semiconductor material.

To calculate the wavelength corresponding to the band gap of TiO₂ (Titanium Dioxide), we can use the relationship between energy, wavelength, and the speed of light:

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

Where:
- \( E \) is the energy of the band gap (in electron volts, eV)
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \))
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \))
- \( \lambda \) is the wavelength (in meters)

First, let's convert the band gap energy from electron volts to joules:

\[ 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \]

So, the energy in joules:

\[ E = 2.8 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV} \]
\[ E = 4.486 \times 10^{-19} \, \text{J} \]

Now, rearrange the energy equation to solve for wavelength \( \lambda \):

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

Substituting the values:

\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s})(3 \times 10^8 \, \text{m/s})}{4.486 \times 10^{-19} \, \text{J}} \]

Let's calculate this value:

\[ \lambda = \frac{1.9878 \times 10^{-25} \, \text{J} \cdot \text{m}}{4.486 \times 10^{-19} \, \text{J}} \]

\[ \lambda \approx 4.43 \times 10^{-7} \, \text{m} \]

Converting meters to nanometers:

\[ \lambda \approx 443 \, \text{nm} \]

### Determining the Color:
A wavelength of approximately 443 nm falls within the visible spectrum, specifically in the violet to blue region.

**Conclusion:**
- The wavelength of light corresponding to a band gap of 2.8 eV for TiO₂ is approximately 443 nm.
- Based on this wavelength, TiO₂ would exhibit a **blue** color.

Would you like further details or have any other questions?

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Here are 5 related questions you might find interesting:
1. How does the band gap of a semiconductor affect its electrical properties?
2. What are some other common materials with similar band gaps, and how do their colors compare?
3. How is the band gap of a material experimentally determined?
4. Can the band gap of a material be engineered or modified, and if so, how?
5. How does the wavelength of light absorbed by a semiconductor affect its applications in devices like solar cells?

**Tip:** When working with semiconductor materials, it's essential to understand how the band gap energy relates not only to color but also to the material's ability to absorb or emit light at specific wavelengths.

Learn how to calculate the wavelength of Titanium Dioxide (TiO2) with a 2.8 eV band gap using the energy-wavelength relationship. Understand the color of semiconductor materials based on their wavelength. Suitable for undergraduate students and researchers.

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