If a semiconductor material is having the Eg = 6.231eV. Calculate the peak emission wavelength of the material

To calculate the peak emission wavelength of a semiconductor material given its energy band gap (\(E_g\)), we can use the relationship between the energy of a photon and its wavelength. The energy of a photon is given by:

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

Where:
- \(E\) is the energy of the photon (in electron volts, eV)
- \(h\) is Planck's constant (\(4.1357 \times 10^{-15} \, \text{eV} \cdot \text{s}\))
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\))
- \(\lambda\) is the wavelength of the photon (in meters)

Given:
- \(E_g = 6.231 \, \text{eV}\)

We rearrange the equation to solve for the wavelength \(\lambda\):

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

Substituting the values:

\[
\lambda = \frac{(4.1357 \times 10^{-15} \, \text{eV} \cdot \text{s}) \times (3 \times 10^8 \, \text{m/s})}{6.231 \, \text{eV}}
\]

Let's calculate the value.The peak emission wavelength of the semiconductor material with a band gap energy of \(6.231 \, \text{eV}\) is approximately \(199.12 \, \text{nm}\).

Would you like more details or have any questions?

Here are 5 related questions that might interest you:
1. How does the band gap energy affect the color of light emitted by a semiconductor?
2. What are the applications of materials with such a high band gap energy?
3. How is the band gap energy measured in semiconductors?
4. Can the peak emission wavelength shift under different conditions, such as temperature changes?
5. What is the relationship between a semiconductor’s band gap and its electrical conductivity?

**Tip:** The peak emission wavelength determines the color of the light emitted, which is crucial for designing optoelectronic devices like LEDs and laser diodes.

Learn how to calculate the peak emission wavelength of a semiconductor material with a band gap energy of 6.231 eV. Understand the relationship between photon energy, wavelength, Planck's constant, and the speed of light. Ideal for advanced high school students and college-level learners.

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