Calculate the wavelength of absorption of GaAs which has a band gap 1.35eV.

To calculate the wavelength of absorption for GaAs (Gallium Arsenide) with a band gap of 1.35 eV, we can use the following formula:

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

where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \)),
- \( c \) is the speed of light in vacuum (\( 3.0 \times 10^8 \, \text{m/s} \)),
- \( E_g \) is the band gap energy in joules,
- \( \lambda \) is the wavelength in meters.

### Step 1: Convert the Band Gap from eV to Joules

\[
E_g = 1.35 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV} = 2.1627 \times 10^{-19} \, \text{J}
\]

### Step 2: Calculate the Wavelength

\[
\lambda = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{2.1627 \times 10^{-19}} \, \text{m}
\]

\[
\lambda = \frac{1.9878 \times 10^{-25}}{2.1627 \times 10^{-19}} \, \text{m}
\]

\[
\lambda \approx 918 \, \text{nm}
\]

### Result
The wavelength of absorption for GaAs with a band gap of 1.35 eV is approximately **918 nm**, which falls in the **infrared** region of the electromagnetic spectrum.

Would you like any further explanation on this calculation, or do you have any additional questions?

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Here are 5 related questions you might explore next:
1. What are the applications of GaAs in infrared technology?
2. How does the wavelength of absorption affect the efficiency of solar cells made from GaAs?
3. How does GaAs compare to other semiconductor materials like Silicon in terms of band gap and applications?
4. What is the significance of GaAs's band gap in optoelectronic devices?
5. How does temperature influence the band gap of GaAs?

**Tip:** Understanding the band gap and corresponding absorption wavelength is crucial in designing materials for specific optoelectronic applications, such as detectors and lasers.

Learn how to calculate the absorption wavelength of Gallium Arsenide (GaAs) with a band gap of 1.35 eV using quantum mechanics and semiconductor physics principles. Understand the application of Planck's equation and the energy-band gap relation in determining optical properties of semiconductors.

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