The gap between valence and conduction bands in silicon is 1.12 eV. A nickel nucleus in an excit

step 1 Okay, so we're talking about diamond in this problem, and we're told that the gap between the va

The gap between valence and conduction bands in silicon is...

The gap between valence and conduction bands in silicon is $1.12 \mathrm{eV}$. A nickel nucleus in an excited state emits a gamma-ray photon with wavelength $9.31 \times 10^{-4} \mathrm{nm} .$ 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?

Key Concepts

Impurity-Induced Coloration

Impurities in a crystalline structure like diamond can introduce additional energy levels within the band gap. These intermediate levels can allow the absorption of visible light, specifically that which might impart color. When certain wavelengths are absorbed more than others, the gem appears colored (such as yellow), because the transmitted or reflected light is missing the absorbed wavelengths.

Band Gap Energy

The band gap is the energy difference between the valence band and the conduction band in a material. It determines the minimum photon energy required to excite an electron into a conduction state. For materials like diamond, a large band gap means that only high-energy (short wavelength) photons can be absorbed to cause this electronic transition.

Photon Energy and Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, as given by the equation E = hc/?. This relationship is used to calculate the maximum wavelength of light that can induce a transition across the band gap, meaning only photons with energy equal to or greater than the band gap energy can be absorbed.

Electromagnetic Spectrum

The electromagnetic spectrum ranges from low-energy radio waves to high-energy gamma rays. In the context of diamond, determining the maximum wavelength needed to bridge the band gap shows that the photon lies in the ultraviolet region, which is outside the visible part of the spectrum.

Optical Transparency

Materials are transparent if they do not absorb visible light. In pure diamond, the photon energies in the visible range are insufficient to overcome the large band gap, hence they are transmitted rather than absorbed. This lack of absorption in the visible range results in the material appearing colorless.

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