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The maximum wavelength of electromagneti...

The maximum wavelength of electromagnetic radiation, which can create a hole-electron pair in germanium. (Given that forbidden energy gap in germanium is 0.72 eV)

A

`1.7xx10^(-6)` m

B

`1.5xx10^(-5)` m

C

`1.3xx10^(-4)` m

D

`1.9xx10^(-5)` m

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The correct Answer is:
To find the maximum wavelength of electromagnetic radiation that can create a hole-electron pair in germanium, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Energy Gap**: The energy required to create a hole-electron pair in germanium is given as the forbidden energy gap \( E_G = 0.72 \, \text{eV} \). 2. **Convert Energy from eV to Joules**: Since we will be using the formula that involves Planck's constant and the speed of light, we need to convert the energy from electron volts to joules. \[ E_G = 0.72 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 1.152 \times 10^{-19} \, \text{J} \] 3. **Use the Energy-Wavelength Relationship**: The relationship between energy, wavelength, and the constants is given by the formula: \[ E = \frac{hc}{\lambda} \] Where: - \( E \) is the energy in joules, - \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)), - \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)), - \( \lambda \) is the wavelength in meters. 4. **Rearrange the Formula to Solve for Wavelength**: Rearranging the formula to find the wavelength gives: \[ \lambda = \frac{hc}{E} \] 5. **Substitute the Values**: Now, substitute the values of \( h \), \( c \), and \( E_G \) into the equation: \[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{1.152 \times 10^{-19} \, \text{J}} \] 6. **Calculate the Wavelength**: Performing the calculation: \[ \lambda = \frac{1.9878 \times 10^{-25}}{1.152 \times 10^{-19}} \approx 1.725 \times 10^{-6} \, \text{m} \] This can be rounded to: \[ \lambda \approx 1.7 \times 10^{-6} \, \text{m} \text{ or } 1700 \, \text{nm} \] ### Final Answer: The maximum wavelength of electromagnetic radiation that can create a hole-electron pair in germanium is approximately \( 1.7 \times 10^{-6} \, \text{m} \).

To find the maximum wavelength of electromagnetic radiation that can create a hole-electron pair in germanium, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Energy Gap**: The energy required to create a hole-electron pair in germanium is given as the forbidden energy gap \( E_G = 0.72 \, \text{eV} \). 2. **Convert Energy from eV to Joules**: ...
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