Greetings, let's continue our examination of models of the atom, and work through a few more examples of the Bohr model of the hydrogen atom. Remember, one of the early models that we talked about was the Rutherford model of the atom. Now this was a big improvement on earlier models such as the Plum Pudding model because the Rutherford model put most of the mass of the atom in that tiny dense center of the nucleus. And then there were the electrons that were orbiting in the space around the nucleus. This model has stuck and people tend to use it for all kinds of drawings of the atom. For example, here's a bunch of seals used by Atomic Energy Agencies. You can see that all of them have Rutherford like atoms drawn, as the model that they're using for the atom. The Bohr model was a refinement of the Rutherford model. And so it's sometimes called the Rutherford-Bohr model. Remember that what Bohr did, was, he was able to use the quantum mechanics model. And show that the atom is quantized, and that those levels that are allowed for the electron give rise to the visible spectrum of the electron, and also give rise to the ultra-violet and infra-red emission lines of the hydrogen atom. Let's continue with the Bohr model by doing an example. Remember that the Bohr model had these shells which were designated by different values of n. So n = 1 is closest to the nucleus and then as we move out, the value for n goes up. In this review example, let's pretend that we have an electronic transition, where the electron is going to start at n = 2 and move to n = 3. For this electronic transition would you predict that, that's going to be an energy absorption or do you think that's an energy emission? [BLANK_AUDIO] Thank you for submitting your answer. In that case the electron is starting at a lower energy level and moving to a higher energy level, so for this process to happen the atom needs to absorb energy. So, that's an energy absorption. Is this process spontaneous or not spontaneous? Well, the energy had to come from outside of the atom. So that can't be something that happened spontaneously. This was not a spontaneous process. And finally, we are witnessing a change in the energy of the atom. Is the sign of that change of energy for this particular transition, a positive number or a negative number? And remember whenever we have change of a variable in chemistry, it is the final state of that variable minus the initial state, so think about which value is larger. Is the final energy larger, or the initial energy? And then determine if the change in energy will be a positive or a negative number. Thank you for your submission. Here, the final energy is a higher value. So, we have a larger number minus a smaller number and that gives us a positive value for the change in the energy. Now the model that I've drawn here isn't very accurate because it shows equal distances between each of the allowed energy levels. The real situation is quite a bit different from that. So this model is not to scale at all. For one thing, there's a lot larger distance between the nucleus and where the electrons are allowed to be than is shown there. But also there's not the same distance between n = 2 and n = 3 as there is between n = 1 and n = 2. We can calculate the energy of the nth orbital for each of those orbitals. And remember, that equal minus z squared, hr, divided by n squared. Z, here, is the nuclear charge, which is 1. H is Planck's constant, R is reverse constant, and n is that integer. Let's pretend for the sake of argument that the numerator of this expression, the Z squared times h times R equaled 1. Now, Z squared does equal 1, because Z is 1 for a hydrogen atom. That's the nuclear charge. But Planck's constant times Rydberg's constant does not equal 1. But for the sake of argument, let's pretend that it does equal 1, so let's make the numerator 1 and then we're going to divide by n squared. So the expression then becomes the energy of the nth orbital is proportional to minus 1 over n squared. Let's plot that for different values of n. Remember, n is a natural number. Natural numbers start with 1 and go up, 1, 2, 3, 4, 5. In order to do this, as I have been doing throughout the course, I'm going to plot energy On the y axis. In this case, the energy's a little bit more complicated because I've taken out that factor of Planck's constant and Rydberg's constant. And the next thing I'm going to do is plot minus 1 over n squared for a bunch of different values. Notice that 0 is up at the top of this graph. So all the numbers I'm going to be plotting are negative numbers. The first number I'm going to plot is minus 1 over 1 squared. And that gives me a value of minus 1. If n = 2, then I would have minus 1 over 2 squared, or minus 1 quarter. That's about where that would plot. If n = 3, then I would have minus 1 over 3 squared, or minus 1 ninth. If n = 4, I have minus 1 over 16, and if n = 5, I have minus 1 over 25. What you see happening here is that as N gets larger, I start to approach zero but the distance between each increment of N gets smaller and smaller, doesn't it? So even this picture isn't quite accurate but it's more accurate than the picture on the previous slide. As the electron gets further away from the nucleus, the shells where it's allowed to be, which are now thought of as clouds, not shells. But the, the volume of space where it's allowed to occupy gets closer and closer together. Keeping this in mind, let's think about another question. Which of these transitions emits a photon of greater energy the n = 2 to n = 1 transition or the n = 6 to n = 2 transition? Which of those two situations is going to emit a greater energy photon? Thank you for your submission. It might be useful when solving this problem to think about the model we've been using all along. And in this model, there's a larger difference between n = 2 and n = 1 than there is between n = 2 and n = 3. But what about going all the way from n = 6 to n = 2? Can you see that even though I'm going from n = 6 to n = 2, that is a smaller distance in energy than the difference in energy between n = 2 and n =1? So in fact if we wanted to measure the energy that the photon emits, we could just measure the distance between the allowed energy levels, and here we have a larger distance for n = 2 to n = 1. Then we see up here for n = 6 going to n = 2. The larger energy means that the photon emitted is going to have higher energy. The transition that's shown on this particular slide is going from an excited state of n = 2 to the ground state back at n = 1. And remember, that transition gives off a photon that's in the ultraviolet range. So if we look at the electromagnetic spectrum here, we go from having relatively low energy waves, such as radio waves, through microwaves and infrared, finally to the visible, and at higher energies in the visible, we see the ultraviolet X-ray and gamma ray. It turns out that in that hydrogen atom. Going from n = 2 to n = 1 gives us an ultraviolet transition. Remember it was the transitions going from higher energy levels down to two so stopping at an intermediate step that gave us the visible light. Here's a question to consider, here are the four lines in a hydrogen atom spectrum, red, green, blue, and violet. Each of those corresponds with one of these transitions shown on the left with the pink arrows, a, b, c, or d. Which of these transitions a, b, c or d corresponds to the violet photon? So one of them's red, one of them's kind of a greenish blue, one of them's blue and one of them's violet. Which one is the violet one? [BLANK_AUDIO] Thank you for considering that question. Let's compare red light to violet light in terms of wavelength and frequency and then think about of how that relates to energy. The red light remember is going to have all those visible colors that I've listed the red light will have the longest wavelength. And the smallest frequency, or the lowest frequency. In contrast then, the violet light is going to have the shortest wave length and the highest frequency. Well, if we think back to our equations, right, we need to know that c = lambda nu and e = h nu. So if we have a higher frequency that is directly proportional to having a higher energy. Well, the largest energy here, remember, energy's on the y-axis, the largest energy is for a. So a must be the one that is the violet photon. This concludes the second part of the introduction to some of the early models of atomic structure. Remember the boar model gave scientists some of their first insights into the quantized nature of the atom. It is now considered to be a fairly primitive model, but it does explain the particular energies that we see in the UV IR invisible emission spectrum of hydrogen. So what remains an important model for understanding the basic structure of the atom, and for understanding the quantised nature of the atom. Please tune in to the additional lectures to hear more about quantum mechanics and the structure of the atom. [BLANK_AUDIO]