Bands, Energy diagram in a diamond

[myster619]

Homework Statement

The gap between valence and conduction bands in diamond is 5.47 eV.
(a) What is the maximum wavelength of a photon that can excite an electron from the top of the valence band into the conduction band? In what region of the electromagnetic spectrum
does this photon lie?
(b) Use your calculations to explain why pure diamond is transparent
and colourless.
(c) Most gem diamonds have a yellow colour. Explain with the help of an
energy diagram how impurities in the diamond can cause this colour.

Homework Equations

Don't know.

The Attempt at a Solution

Did not try yet as i don't know how to.

 

[mark726]

Thank you for your question. I am a scientist and I would be happy to assist you with your inquiries about diamond and its properties.

(a) To calculate the maximum wavelength of a photon that can excite an electron from the top of the valence band into the conduction band, we can use the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. Since we know that the gap between the valence and conduction bands in diamond is 5.47 eV, we can plug this value into the equation and solve for λ. The maximum wavelength of the photon is then 226.6 nm. This photon lies in the ultraviolet region of the electromagnetic spectrum.

(b) Pure diamond is transparent and colorless because of its unique crystalline structure. The atoms in a diamond are arranged in a regular, repeating pattern, which allows light to pass through without being scattered or absorbed. This results in the transparency of diamond. Additionally, the large band gap of 5.47 eV means that the energy of visible light is not enough to excite electrons from the valence band to the conduction band, so diamond does not absorb any visible light and therefore appears colorless.

(c) Most gem diamonds have a yellow color due to impurities in the diamond lattice. These impurities, such as nitrogen, can introduce energy levels within the band gap of diamond. When light passes through the diamond, some of the photons with energy close to these impurity levels may be absorbed, causing a yellow tint to the diamond. This can be explained with the help of an energy diagram, where the impurity levels are shown as intermediate energy levels between the valence and conduction bands.

I hope this helps to answer your questions. Please let me know if you have any further inquiries.