If a semiconductor material is having the Eg = 6.231eV. Calculate the peak emission 4.

wavelength of the material

To find the peak emission wavelength of a semiconductor material, we can use the relation between the energy gap \(E_g\) (in electron volts, eV) and the corresponding peak emission wavelength \(\lambda\) (in nanometers, nm). The equation that relates the energy and wavelength is derived from the energy of a photon:

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

Where:
- \(E\) is the energy of the photon (in joules, J).
- \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) Js).
- \(c\) is the speed of light (\(3 \times 10^8\) m/s).
- \(\lambda\) is the wavelength (in meters).

To relate the energy gap \(E_g\) in eV directly to the wavelength in nm, we can use the conversion:

\[
E_g (\text{in eV}) = \frac{1240}{\lambda (\text{in nm})}
\]

This conversion factor is obtained from Planck's constant and the speed of light. Now, we can rearrange this equation to solve for \(\lambda\):

\[
\lambda (\text{in nm}) = \frac{1240}{E_g (\text{in eV})}
\]

Given:
- \(E_g = 6.231\) eV

Substituting the given value into the equation:

\[
\lambda = \frac{1240}{6.231}
\]

\[
\lambda \approx 199 \, \text{nm}
\]

Therefore, the peak emission wavelength of the material is approximately 199 nm.

Would you like more details or have any questions?

Here are some related questions that may expand your understanding:

1. How does the energy gap (\(E_g\)) affect the emission wavelength of a semiconductor?
2. What is the significance of a material having a high energy gap (\(E_g\)) in terms of its optical properties?
3. How do temperature changes affect the energy gap and emission wavelength of semiconductor materials?
4. What are some practical applications of semiconductors with high energy gaps, like the one given in this problem?
5. How do different semiconductor materials compare in terms of their energy gaps and emission wavelengths?

**Tip:** The peak emission wavelength is inversely proportional to the energy gap. Materials with larger energy gaps will emit photons with shorter wavelengths, resulting in higher energy light (e.g., ultraviolet).

Learn how to calculate the peak emission wavelength of a semiconductor material with an energy gap (Eg) of 6.231 eV. Understand the relationship between photon energy and wavelength using fundamental quantum mechanics principles. Suitable for advanced high school students and beyond.

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