Question

it is observed that, the energy liberated in the recombination of a hole-electron pair is converted into electromagnetic radiation. if the maximum wavelength emitted is 820 nm, what is the band gap ?

Answer 1

The band gap for a material that emits a maximum wavelength of 820 nm due to the recombination of an electron-hole pair is 1.51 eV, calculated using the formula E = hc / λ with hc equal to 1240 eV nm.

Step-by-step explanation:

The question pertains to the relationship between the energy of a photon and its wavelength when it causes an electron to move from the valence band to the conduction band in a semiconductor material. This transition releases energy in the form of electromagnetic radiation and the band gap of the material can be calculated from the maximum wavelength of this radiation using the formula:

E (eV) = hc / λ

where:

• E is the energy gap in electron volts (eV)
• h is Planck's constant (6.626 x 10-34 Joule seconds)
• c is the speed of light (approximately 3 x 108 meters per second)
• λ is the wavelength in meters (820 nm in the question, which is 820 x 10-9 meters)

Since h and c are constants, they can be combined into a single constant in terms of eV nm: hc = 1240 eV nm. Substituting these values into the equation and converting 820 nm to meters gives us:

E = 1240 eV nm / 820 nm = 1.51 eV

Therefore, the band gap for a material that emits the maximum wavelength of 820 nm when an electron-hole pair recombines is 1.51 eV.