Question

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.

Answer 1

n = 6

Step-by-step explanation:

The processes of multifontic absorption various photons are absorbed simultaneously

`E_(g)` = 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 =
`E_(g)` / Eo

n = 9.3 / 1.55

n = 6

Six photons need to be absorbed at the same time