Use the Balmer equation to calculate the wavelength in nano-meters of the spectral line for hydrogen when n = 6 and m = 2. What is the energy in kilojoules per mole of the radiation corresponding to this line?

Video transcript

Hey everyone. We're asked, what is the wavelength in nanometers of the spectral line? For hydrogen. When an electron transitions from end, final equals five to end initial equals to using the bomber equation, What is the energy of the radiation corresponding to this line in killing jewels? Permal first. Let's go ahead and write out our bomber equation. And this is going to be one over wavelength equals our Rydberg constant times one over and final squared minus one over N initial squared. And as we've learned, our Rydberg constant is going to be 1.97 times 10 to the negative two nanometers to the negative first. So let's go ahead and plug in our values. We have one over wavelength equals our Rydberg constant, which is 1.97 times 10 to the negative two nanometers to the negative first. Times one over NF squared which is going to be five squared minus one over an initial squared, which is going to be two squared. And when we calculate this out, we end up with a one over wavelength of 2.303, 7 times 10 to the negative third nanometers to the negative first. To calculate for our wavelength, we end up with 434.08 nm. Now let's go ahead and calculate for our energy to calculate for energy, we're going to use equation energy equals our plank's constant times the speed of light over our wavelength. So, plugging in the values we get 6.626 times 10 to the negative 30 for jewels time seconds. And this is going to be multiplied by our speed of light, which is 2.998 times 10 to the eight m/s. And we will divide this by our wavelength, which we calculated to be 434 point oh eight nanometers. But since we want to convert this into meters, we can use dimensional analysis and we know that we have 10 to the nine nanometers per one m. Now, since we want our energy to be in killing joules per mole, we can go ahead and convert our jewels into jewels using dimensional analysis. So we know that per one kill a jewel. We have 10 to the third jewels. And lastly we know that we have 6.022 times 10 to the 23rd jewels per one mole. So when we calculate this out and cancel out all of our units, We end up with an energy of 275.5813 kg joules per mole. So we can simply round this up to kg jewels Permal. And this is going to be our final answers. Now, I hope that made sense. And let us know if you have any questions