Does a photon of red light with a frequency of 4.29 * 1014 Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?

Video transcript

hey everyone in this example, we're told that the band gap in Germany um is 0.67 electro volts. What a photon of orange light with a frequency of 4.84 times 10 to the 14 hertz possess sufficient energy to promote an electron from the valence band to the conduction band. So our first step is to recall our formula for energy of a photon, which we can find from taking plank's constant. And multiplying this by our value for frequency. So from the prompt, we can say that our energy of a photon is equal to planck's constant, which we should recall is 6.626 times 10 to the negative 34th power jewels times seconds. Which we will multiply by the frequency from the prompt as 4.84 times 10 to the 14th power hertz. And we should recall that we can also interpret frequency in units of hertz or inverse seconds, which are equivalent to one another. So we can go ahead and actually plug this in as inverse seconds, which would allow us to cancel our units of seconds. Leaving us with jewels as our unit for energy. And so this gives us a value of energy equal to 3.207 times 10 to the negative 19th power jewels, which we can convert to electro volts by recalling our conversion factor that we have 1.602 times 10 to the negative 19th power Jewels for one electron volt. And so now we can cancel out jewels leaving us with electro volts as our final unit for the energy of a photon, which is going to equal a value of two point oh electro volts. So we can therefore determine that two point oh electro volts is much greater than 0.67 electro volts as given in the prompt for the band gap for germanium. And so we would say therefore the energy of a photon is greater than the energy of Germany umS band gap. Thus a photon of orange light will have sufficient energy to promote an electron from the valence band two, the conduction band, and just so everything is visible. Let's move this explanation over. So for our final answer, we would say that the photon of orange light will have sufficient energy. And again, that is due to the fact that we calculated that the photon of orange light will have An energy of 2.0 Electro volts. And so it will be able to promote the electron from the valence band to the conduction band. So I hope that everything I explained was clear. If you have any questions, please leave them down below. And I will see everyone in the next practice video