Use Balmer's formula to calculate (a) the wavelength, (b) the frequency, and (c) the photon energy for the Hg line of the Balmer series for hydrogen.

Video transcript

Welcome back everyone. We are making observations about a hydrogen atom here. Now, we are told that the hydrogen atom is in an excited state level of N equals four spontaneously admits and returns to the excited state level at N equals two. And we are tasked with finding what its wavelength frequency and energy are in electron volts of this optical transition. So what do we do here? Well, let's start with this. We have that one over our wavelength is equal to our reberg constant times one divided by the level the excited state level that it's returning to. So two squared minus one over the original excited state level of four squared. Now, we have all of our values here. So what does this give us flipping both sides of our equation? What we get is that our wavelength is equal to our reberg constant of one point oh 97 times 10 to the seventh times 16/3, which gives us 486 nanometers. Wonderful. Let me go ahead and change colors here real quick so that we can go ahead and find our frequency where frequency is as simple as this. What we can say is that our frequency is equal to the speed of light divided by our wavelength, we have these values. So let's go ahead and calculate, we have that this is equal to three times 10 to the eighth divided by 486 nanometers or 486 times 10 to the negative ninth meters. And what this gives us is a frequency of 6.17 times 10 to the 14th Hertz. Wonderful changing colors one more time. Now we just have to find the energy of this optical transition. What we have is that our energy is equal to planks, constant times our frequency. So this is gonna be 6.6 to 6 times 10 to the negative 34th times 6.17 times 10 to the 14th giving us four point oh nine times 10 to the negative 19th Jews. However, we needed to find our energy in electron vaults. So let's go ahead and convert. What we're gonna do is we're gonna take four point oh nine times 10 to the negative 19th Jules and multiply it by one electron volt divided by 1.6 times 10 to the negative 19th Jules. What this gives us is a final energy of 2.56 electron volts. So now we have found the wavelength, the frequency and the energy of this optical transition which corresponds to our final answer. Choice of B Thank you all so much for watching. I hope this video helped. We will see you all in the next one.