The bandgap energy value of laser diode material is 5.423eV. Find out the max value in nm.

To find the maximum wavelength (in nanometers) corresponding to the bandgap energy of a laser diode material, you can use the following relationship between energy \(E\) (in electron volts, eV) and wavelength \(\lambda\) (in nanometers, nm):

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

Where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) Joule seconds),
- \(c\) is the speed of light (\(3 \times 10^8\) meters per second),
- \(\lambda\) is the wavelength in meters.

To convert the energy from eV to joules, use the conversion factor \(1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J}\).

First, rearrange the formula to solve for \(\lambda\):

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

Now, substituting the given values:

\[
\lambda = \frac{6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \times 3 \times 10^8 \, \text{m/s}}{5.423 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV}}
\]

Let's calculate this.The maximum wavelength corresponding to the bandgap energy of 5.423 eV is approximately **228.81 nm**.

Would you like more details or have any further questions? Here are some related questions:

1. How does the wavelength relate to the color of light in a laser diode?
2. What factors influence the bandgap energy of semiconductor materials?
3. How does temperature affect the bandgap energy of a laser diode material?
4. Can you explain the significance of Planck's constant in determining the wavelength of light?
5. What are some applications of laser diodes with specific bandgap energies?

**Tip:** The energy bandgap of a material directly determines the color (wavelength) of the emitted light in optoelectronic devices, such as LEDs and laser diodes.

Learn how to calculate the maximum wavelength (in nanometers) corresponding to the bandgap energy of a laser diode material. This problem involves using Planck's equation and the energy-wavelength relationship in physics and optics. Suitable for advanced learners and professionals.

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