Question

Carbon (diamond) and silicon have the same covalent crystal structure, yet diamond is transparent while silicon is opaque to visible light, Argue that this should be the case based only on the difference in band gapsroughly \(5 \mathrm{eV}\) for diamond and \(1 \mathrm{eV}\) for silicon.

Short answer

Diamond is transparent and silicon opaque to visible light because of their differing band gaps. Diamond's band gap (5 eV) is larger than the energy range of visible light, hence it does not absorb it and appears transparent. Silicon's band gap (1 eV) falls within the energy range of visible light causing absorption and thus appearing opaque.

Step-by-step solution

Understanding Band Gaps

A band gap in a material is the energy difference between the material's valence band of electrons and the conduction band. It essentially indicates the amount of energy required to excite an electron from the valence band into the conduction band.

Visible Light Energy Levels

Visible light has an energy range which corresponds to a wavelength range. Using the formula \(E = \frac{hc}{\lambda}\) (where \(h\) is Planck's constant, \(c\) is the speed of light and \(\lambda\) is the wavelength), we find that the energy range for visible light is about 1.65 to 3.1 eV.

Comparing Band Gaps to Visible Light Energy

Since diamond has a band gap of about 5 eV, visible light does not have enough energy to excite its electrons to the conduction band, hence it is transmitted through and the material appears transparent. On the other hand, silicon has a band gap of about 1 eV, which is in the energy range of visible light. Therefore, when visible light shines on it, its electrons get excited to the conduction band and energy is absorbed, making it opaque to visible light.

Key concepts

Covalent Crystal Structure

In the realm of materials science, both diamond and silicon share a fascinating attribute: they possess a covalent crystal structure. This means that in both materials, each atom is firmly bound to its neighboring atoms by covalent bonds, which are formed through the sharing of electrons. These strong bonds create a robust and stable lattice structure.

Despite this structural similarity, their electronic properties are notably different, heavily influenced by their distinct band gaps. The band gap is a crucial concept to grasp, as it directly affects how these materials interact with light and electricity.

• The band gap is the energy required to move an electron from the valence band to the conduction band.
• In covalent structures like diamond and silicon, the strength and distribution of these bonds contribute to the size of the band gap.
• Diamond has a larger band gap than silicon, affecting its optical transparency.

Visible Light Energy

Visible light, detectable by the human eye, spans wavelengths from approximately 400 nm (violet) to 700 nm (red). This corresponds to an energy range from about 1.65 eV to 3.1 eV.

Understanding this energy range is key to predicting whether light will be absorbed or transmitted through a material. This depends on if the energy of the light falls within or outside the material's band gap.

• Energy outside this range might be absorbed in the ultraviolet or infrared spectrum.
• If the visible light energy is less than the band gap, the light will pass through, rendering the material transparent.
• Conversely, if energy matches or exceeds the band gap, electron excitation occurs, leading to opacity.

Electronic Excitation

Electronic excitation happens when an electron in a material absorbs enough energy to jump from the valence band to the conduction band. This process is central to the difference in transparency between diamond and silicon.

For diamond, with its 5 eV band gap, visible light at 1.65 to 3.1 eV does not provide enough energy for electronic excitation. As a result, the light passes through, and the material appears transparent.

• Diamond is a non-conductor of electricity at room temperature due to large band gap.
• Silicon, however, has a smaller band gap of about 1 eV.
• Visible light is energetic enough to excite silicon's electrons, allowing it to absorb the light and appear opaque.

In summary, the band gap size dictates whether light will be absorbed or transmitted, influencing a material's transparency or opacity.