If the energy of a photon of sodium light ( `lambda`=589 nm) equals the band gap of semiconductor, the minimum energy required to create hole electron pair

Options

A. 1.1 eV
B. 2.1 eV
C. 3.2 eV
D. 1.5 eV

Explanation

To solve the problem of determining the minimum energy required to create a hole-electron pair in a semiconductor when the energy of a photon of sodium light (with a wavelength of 589 nm) equals the band gap of the semiconductor, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula for Energy of a Photon**:
The energy \( E \) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is the Planck constant (\( 6.63 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3.00 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the light (in meters).

2. **Convert Wavelength to Meters**:
The given wavelength of sodium light is \( 589 \, \text{nm} \). To convert this to meters:
\[ \lambda = 589 \, \text{nm} = 589 \times 10^{-9} \, \text{m} \]

3. **Substitute Values into the Formula**:
Now, substitute the values of \( h \), \( c \), and \( \lambda \) into the energy formula:
\[ E = \frac{(6.63 \times 10^{-34} \, \text{Js}) \times (3.00 \times 10^8 \, \text{m/s})}{589 \times 10^{-9} \, \text{m}} \]

4. **Calculate the Energy**:
Performing the calculation:
\[ E = \frac{(6.63 \times 10^{-34}) \times (3.00 \times 10^8)}{589 \times 10^{-9}} \approx 3.37 \times 10^{-19} \, \text{J} \]

5. **Convert Energy from Joules to Electron Volts**:
To convert the energy from joules to electron volts, use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E \text{ (in eV)} = \frac{3.37 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 2.10 \, \text{eV} \]

6. **Conclusion**:
The minimum energy required to create a hole-electron pair in the semiconductor, which is equal to the energy of the photon of sodium light, is approximately \( 2.1 \, \text{eV} \).