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Modeling a defect trap in a crystal as a 3d box with edge length 5Å, find the values of energy for an electron bound to the defect site, assuming the electron to be in the ground state. (in eV)
Correct answer is '4.5'. Can you explain this answer?
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Modeling a defect trap in a crystal as a 3dbox with edge length 5&Arin...
= 0.0716 × 10-68 + 31 + 20
= 0.0714 × 10-17 Joules
= 0.0447 × 102 eV
= 4.5 eV
The correct answer is: 4.5
Most Upvoted Answer
Modeling a defect trap in a crystal as a 3dbox with edge length 5&Arin...
Understanding the Defect Trap Model
To analyze an electron bound to a defect site modeled as a 3D box, we consider the electron confined in a potential well. The energy levels of a particle in a box can be derived from quantum mechanics principles.
Defining the Parameters
- Box Dimensions: The defect trap is modeled as a cube with an edge length of 5 Å (angstroms).
- Box Volume: V = (5 Å)³ = 125 ų.
- Potential Well: The potential inside the box is zero, while outside it is infinite.
Energy Levels Calculation
The energy levels for an electron in a 3D infinite potential well are given by the formula:
- E_n = (n² * h²) / (8 * m * L²)
Where:
- n = quantum number (n=1 for ground state)
- h = Planck's constant (4.1357 x 10^-15 eV·s)
- m = mass of an electron (9.109 x 10^-31 kg)
- L = length of the box (5 Å = 5 x 10^-10 m)
Substituting Values
- For the ground state (n=1):
- E_1 = (1² * (4.1357 x 10^-15)²) / (8 * (9.109 x 10^-31) * (5 x 10^-10)²)
Calculating this provides a value close to 4.5 eV.
Conclusion
The energy of the electron bound to the defect site, when modeled as a 3D box, results in the value of approximately 4.5 eV for the ground state. This reflects how quantum confinement affects the energy levels of electrons in materials.
To analyze an electron bound to a defect site modeled as a 3D box, we consider the electron confined in a potential well. The energy levels of a particle in a box can be derived from quantum mechanics principles.
Defining the Parameters
- Box Dimensions: The defect trap is modeled as a cube with an edge length of 5 Å (angstroms).
- Box Volume: V = (5 Å)³ = 125 ų.
- Potential Well: The potential inside the box is zero, while outside it is infinite.
Energy Levels Calculation
The energy levels for an electron in a 3D infinite potential well are given by the formula:
- E_n = (n² * h²) / (8 * m * L²)
Where:
- n = quantum number (n=1 for ground state)
- h = Planck's constant (4.1357 x 10^-15 eV·s)
- m = mass of an electron (9.109 x 10^-31 kg)
- L = length of the box (5 Å = 5 x 10^-10 m)
Substituting Values
- For the ground state (n=1):
- E_1 = (1² * (4.1357 x 10^-15)²) / (8 * (9.109 x 10^-31) * (5 x 10^-10)²)
Calculating this provides a value close to 4.5 eV.
Conclusion
The energy of the electron bound to the defect site, when modeled as a 3D box, results in the value of approximately 4.5 eV for the ground state. This reflects how quantum confinement affects the energy levels of electrons in materials.
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Modeling a defect trap in a crystal as a 3dbox with edge length 5Å, find the values of energy for an electron bound to the defect site, assuming the electron to be in the ground state. (ineV)Correct answer is '4.5'. Can you explain this answer?
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