1)The wavelengths of CdS are 388nm, 406nm, 458 nm and are shown/different colours when it is exposed to light. Justify it with respect to the band gap. Find the band gap and draw a band gap diagram according to the results.

### Explanation of Color Observation and Band Gap in CdS

Cadmium Sulfide (CdS) is a semiconductor material with a specific band gap energy. When it is exposed to light, the wavelengths corresponding to 388 nm, 406 nm, and 458 nm are associated with different colors. These wavelengths are due to electronic transitions between the valence band and the conduction band in CdS.

#### 1. **Band Gap and Photon Absorption**
- **Band Gap Energy (Eg):** The band gap energy is the energy difference between the top of the valence band and the bottom of the conduction band. When light is absorbed by CdS, if the energy of the photons is equal to or greater than the band gap, electrons can be excited from the valence band to the conduction band.
- **Color Observation:** The color observed corresponds to the energy of the photons absorbed. For example, the wavelength of 388 nm corresponds to violet light, 406 nm corresponds to violet-blue, and 458 nm corresponds to blue light.

#### 2. **Calculation of Band Gap Energy**
The energy \( E \) of a photon can be calculated using the equation:

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

Where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) J·s),
- \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength in meters.

Let's calculate the band gap energy corresponding to each wavelength:

1. **For \( \lambda = 388 \) nm (Violet Light):**

\[
E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{388 \times 10^{-9}} = 5.12 \times 10^{-19} \, \text{J} = 3.2 \, \text{eV}
\]

2. **For \( \lambda = 406 \) nm (Violet-Blue Light):**

\[
E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{406 \times 10^{-9}} = 4.89 \times 10^{-19} \, \text{J} = 3.05 \, \text{eV}
\]

3. **For \( \lambda = 458 \) nm (Blue Light):**

\[
E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{458 \times 10^{-9}} = 4.34 \times 10^{-19} \, \text{J} = 2.71 \, \text{eV}
\]

#### 3. **Band Gap Value**
The smallest band gap energy will be the threshold energy, corresponding to the longest wavelength that can still cause an electronic transition from the valence band to the conduction band. Therefore, the band gap energy \( E_g \) for CdS can be approximated as \( 2.71 \, \text{eV} \), which corresponds to the 458 nm wavelength.

### Band Gap Diagram for CdS

The band gap diagram can be drawn as follows:

1. **Valence Band (VB):** Lower energy band, filled with electrons.
2. **Conduction Band (CB):** Higher energy band, empty at 0 K, where electrons can be excited.
3. **Band Gap (Eg):** Energy gap of 2.71 eV between the VB and CB.

The diagram should show the electron excitation from the valence band to the conduction band when light of wavelength 458 nm (or shorter) is incident on CdS.

### Diagram

Here's how the band gap diagram looks:

- **Labeling:** Energy axis vertically. Valence band (bottom), conduction band (top).
- **Band Gap:** 2.71 eV gap between valence and conduction bands.
- **Transitions:** Indicate photon-induced transitions (wavelengths labeled).

---

Would you like me to generate the band gap diagram or any additional details on this topic?

---

### Related Questions

1. How does the band gap of CdS compare with other semiconductor materials?
2. What factors can affect the band gap of a material like CdS?
3. Why do we observe different colors for different wavelengths in semiconductor materials?
4. How does temperature influence the band gap of CdS?
5. What are some applications of CdS based on its band gap properties?

### Tip
Understanding the relationship between band gap energy and photon wavelength is crucial for designing optoelectronic devices like LEDs and solar cells.

Explore the relationship between CdS band gap energy and photon absorption. Learn how wavelengths of 388nm, 406nm, and 458nm correspond to different colors observed in CdS. Calculation of band gap energy and detailed band gap diagram included.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation