Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 7, n = 4 to n = 8, n = 2 to n = 5, and n = 1 to n = 3.

Video transcript

Welcome back everyone to another video, arrange the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed N equals three to N equals six, N equals five to N equals seven, N equals two to N equals four and N equals one to N equals two. And very given four answer choices ABC and D which essentially give us different ranking. So let's solve this problem. We can actually solve this problem two ways qualitatively and quantitatively essentially, we're going to calculate the energy values for this problem for the transitions or the energy change. Because as far as we know energy of a photon is equal to the planks constant multiplied by frequency. So the greater the energy change, the greater the frequency we can use the formula delta E, the change in energy is equal to negative 2.18 multiplied by sensitive power of negative 18 juuls multiplied by one divided by an NF which is our final energy level squared minus one divided by an I which is our initial energy level squared. So now we can use this formula and let's apply it to each scenario. First of all, we have N equals three to N equals six. So we are going to state that delta E is equal to negative 2.18 multiplied by 10 of the power of negative 18 joules. And now we're substituting our final energy level. So that would be N equals six, one divided by six squared minus one, divided by three squared since we as our initial and then we can calculate the result here. So we get 1.82 multiplied by 10 to the power of negative 19 choose. And from here, we are going to repeat this calculation several times, right. So we essentially need to calculate this result for the second one. And we are also going to do or basically perform the same calculation for the final two transitions. So let's just add our work and let's just modify our number slightly. Now, for the second one, we're going from N equals five to N equals seven, that means we're going to change our initial and final energy levels. Let's actually erase all the numbers that we had previously. And now from here, let's perform the calculations. So for the second case, we're going to use our final S seven. So we're taking one divided by seven squared, our initial S five. For the third case, the final one is four, the initial is two. And for the fourth case, the final one is to the initial one is warm. And now let's calculate the resultant energies. So for the second case, we have 4.1 C seven multiplied by 10 to the power of negative 20th. That would be the value for the second transition. For the third one, we end up with 4.09 multiplied by 10 to the power of negative 19th. And for the final one week at 1.64 multiplied by its sense of the power of the negative 18th. Now, from here, we can actually rank them. We can clearly see that the largest one is N equals one to N equals four, which makes total sense. The energy gap between the first level and the second level is the largest because those gaps decrease whenever we go higher. So it makes perfect sense. We're going to state that the final one would be number four in our ranking. Now thinking about the rest, we have the lowest one, which is the second one. So that's number one. And now between the first one and the third one, we can clearly see that the first one is lower and the third one is higher. So now what can we tell? Well, essentially the first one is the transition from N equals five to N equals seven, which immediately tells to us that the correct answer is B right. So we're going to label it as our final answer and then we are just going to check the rest. So first of all, N equals five to N equals seven is the smallest energy change, which corresponds to the smallest frequency followed by N equals three to N equals six, which is our second one. Then we have N equals two to N equals four, which makes total sense. And finally, N equals one to N equals two corresponds to the highest frequency that would be it for today. And thank you for watching.