Forbidden energy gap of a silicon semiconductor is 1.12 eV. In order to generate electron-hole pairs in it, the maximum wavelength of the incident photons will be -

Options

A. 11080 Å
B. 11250Å
C. 12370 Å
D. 14400Å

Answer

To find the maximum wavelength of the incident photons that can generate electron-hole pairs in silicon, we can follow these steps:

### Step 1: Understand the Energy-Wavelength Relationship
The energy of a photon (E) is related to its wavelength (λ) by the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) = energy of the photon (in joules)
- \( h \) = Planck's constant (\( 6.63 \times 10^{-34} \, \text{Js} \))
- \( c \) = speed of light (\( 3.00 \times 10^8 \, \text{m/s} \))
- \( \lambda \) = wavelength (in meters)

### Step 2: Convert the Energy from eV to Joules
The forbidden energy gap of silicon is given as 1.12 eV. To convert this energy into joules, we use the conversion factor:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Thus, the energy in joules is:
\[ E = 1.12 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} \]
\[ E = 1.792 \times 10^{-19} \, \text{J} \]

### Step 3: Rearrange the Energy-Wavelength Equation
To find the maximum wavelength, we rearrange the energy-wavelength equation:
\[ \lambda = \frac{hc}{E} \]

### Step 4: Substitute the Values into the Equation
Substituting the known values into the equation:
\[ \lambda = \frac{(6.63 \times 10^{-34} \, \text{Js}) \times (3.00 \times 10^8 \, \text{m/s})}{1.792 \times 10^{-19} \, \text{J}} \]

### Step 5: Calculate the Wavelength
Calculating the above expression:
\[ \lambda = \frac{1.989 \times 10^{-25}}{1.792 \times 10^{-19}} \]
\[ \lambda \approx 1.107 \times 10^{-6} \, \text{m} \]

### Step 6: Convert Meters to Angstroms
To convert the wavelength from meters to angstroms (1 angstrom = \( 10^{-10} \) m):
\[ \lambda \approx 1.107 \times 10^{-6} \, \text{m} \times 10^{10} \, \text{angstrom/m} \]
\[ \lambda \approx 11070 \, \text{angstrom} \]

### Final Answer
Thus, the maximum wavelength of the incident photons that can generate electron-hole pairs in silicon is approximately **11070 angstroms**.

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