Band gaps

the energy gaps between the valence and conduction bands are called band gaps. for silicon, the band gap is 1.1ev; for fused silica glass, it is 9.3ev.

part c

glass is transparent to visibile light under normal conditions; however, at extremely high intensities, glass will absorb most of the light incident upon it. this works through a process known as multiphoton absorption. in this process, several photons are absorbed at the same time. if very intense light whose photons carry 2ev of energy is shined onto a material with a band gap of 4ev, that light can be absorbed through two-photon absorption, because two photons have the right amount of energy to bridge the band gap. what is the minimum number of photons of 800-nm light that are needed to equal or exceed the band gap of fused silica glass?

express your answer as an integer.

n = 6

Explanation:

The processes of multifontic absorption various photons are absorbed simultaneously

          = n E₀

Where Eg is the energy gap, E₀ is the energy of each photon and n is an integer.

In our case, let's calculate the photon's energy using Planck's relationship

          E = h f

The speed of light is related to wavelength and frequency

         c = λ f

         f = c / λ

We replace

        E = h c /λ

Let's calculate

       E₀ = 6.63 10⁻³⁴ 3 10⁸/800 10⁻⁹

       E₀ = 2,486 10⁻¹⁹ J

We reduce to eV, they are easier to use

       E₀ = 2,486 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

       E₀ = 1.55 eV

We clear from the first equation

        n =    / Eo

        n = 9.3 / 1.55

        n = 6

Six photons need to be absorbed at the same time

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