Calculating Photon Energy Needed to Exceed Fused Silica Glass Band Gap

[vachan]

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 800nm- light that are needed to equal or exceed the band gap of fused silica glass?

I tried Energy of photon= hc/$$\lambda$$... but then after that i don't know what to do. ... i know that energy is the J/ photon... so i multiply it by the energy in the band.,... but didnt get it! anyone knows how to do it?!

 

[vachan]

never mind i got it..

 

[sir-pinski]

To calculate the minimum number of photons of 800nm light needed to exceed the band gap of fused silica glass, we can use the formula for energy of a photon: E = hc/λ, where h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of light (800nm = 8.00 x 10^-7 m).

First, we need to determine the energy of a single photon of 800nm light:
E = (6.626 x 10^-34 J*s)(3.00 x 10^8 m/s)/(8.00 x 10^-7 m)
E = 2.48 x 10^-19 J

Next, we need to determine the band gap energy of fused silica glass, which is given as 4eV. We need to convert this to joules:
1eV = 1.602 x 10^-19 J
4eV = (4)(1.602 x 10^-19 J) = 6.41 x 10^-19 J

Now, we can calculate the minimum number of photons needed to exceed the band gap energy:
Number of photons = Band gap energy / Energy of a single photon
Number of photons = (6.41 x 10^-19 J) / (2.48 x 10^-19 J)
Number of photons = 2.58

This means that at least 2.58 photons of 800nm light are needed to exceed the band gap energy of fused silica glass. Since photons cannot be divided, we would need at least 3 photons to exceed the band gap energy.