Chapter 42: Problem 19
The gap between valence and conduction bands in silicon is 1.12 eV. A nickel nucleus in an excited state emits a gammaray photon with wavelength 9.31 \(\times\) 10\(^-$$^4\) nm. How many electrons can be excited from the top of the valence band to the bottom of the conduction band by the absorption of this gamma ray?
Short Answer
Step by step solution
Convert Wavelength to Energy
Convert Energy from Joules to Electronvolts
Calculate Number of Electrons Excited
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Band Gap
To make the semiconductor conduct electricity, electrons need to gain energy equivalent to the band gap to jump from the valence band to the conduction band.
- The size of the band gap determines the electrical properties of the material.
- A larger band gap means the material is less conductive at room temperature.
- To conduct current, electrons need external energy to transition from the valence to the conduction band.
Valence Band
When an electron absorbs energy, it can jump from the valence to the conduction band, leading to electrical conductivity.
- The valence band is filled with valence electrons.
- Valence electrons are involved in chemical bonding with neighboring atoms.
- Electrons must reach the energy level of the conduction band to participate in conduction.
Conduction Band
- This free movement of electrons allows them to carry electric current.
- Transitioning requires external energy to push valence electrons to the conduction band.
- In metals, conduction bands overlap with the valence bands, allowing for free electron flow without added energy.
Gamma Ray
- Wavelengths are incredibly short, below 0.01 nm, contributing to their high energy.
- They are often emitted by radioactive substances during nuclear reactions.
- Contact with gamma rays can lead to significant electron excitations due to their high energy.
Electron Transition
- External energy must match or exceed the band gap for transition.
- Upon absorbing energy, an electron transitions from the valence band to the conduction band, resulting in electrical conductivity.
- The reverse process involves emitting energy as the electron drops back to the lower energy level.