15.3 Bohr Model

Okay, our next model we're going to look at is Niels Bohr's model. Bohr ended up being a lab assistant for Rutherford, so he knew quite a bit of reference theories. He also previously worked for Thompson, so he basically took their ideas and fine-tuned them to come up with a somewhat better model. So, we remember we had an issue with Rutherford's model. If the electrons were going to lose energy, they would collapse. Bohr knew that there were problems with the model, but he couldn't trash it because there were some pretty specific things about it that were really good. What he did was he basically said, "Well, the electrons aren't just at some random location. If we have our nucleus of the atom and we have electrons in orbit, they're actually in certain specific levels." He said that these levels are based on how much energy is required to get the electrons there. If they change a level, it's going to give off energy or... [Music] Absorb energy, depending on if it jumps from one orbit to the other. So that's kind of where Niels Bohr's model came from and the reason he figured out that these energies had to be in specific levels, depending on what orbit they're in. He figured this out using spectroscopy, which is basically looking at a spectrum of white light. So, we know we have our ROYGBIV spectrum. What he basically did was he would look at different types of gases going through a diffraction grating and see what kind of spectrum was produced. In this case, he hooked up a gas to a voltage. If we took our three hydrogen, helium, whatever the case may be, he would heat it up. That would cause the electrons to gain energy, which then he thought they would jump from one level to the next. For example, if we had an electron at the first level and it jumped to the second level, he said that when it makes that jump, it's. Gonna give off energy that's gaining energy. It's gonna emit some sort of energy, and we'll see that energy as a certain frequency. So, what he shined in this case, we've got hydrogen. If we shine hydrogen through a diffraction grating, he actually saw that we got a violet band of light, a bluish-green one, and a red. So, it actually gave off three different stripes of light, two had different frequencies. So, he then did Newsted logs because these electrons are jumping. So, if it jumped from one level, that gave off a certain color. If it jumped to the second level, it would give off another color, or if it made one jump from first to third in one motion, then it gave off the third pattern. So, he sort of thought that for hydrogen, we're getting these three possible jumps. So, it's going from 1 to 2, 2 to 3, or 1 to 3 directly. And that's why we're seeing three different energy. Ok, so then what he did was he thought, well, what will happen if... We do it in reverse. So in this case, he shines light through cold gas of hydrogen and all of the white light goes through. When it goes through the diffraction grating, it gives a full spectrum. However, because in this case the electrons are absorbing energy, it absorbs those frequencies out of the spectrum. So, in this case, the violet, blue, and red still show up, but earlier they were taken away from the spectrum. In the emission spectrum, they emit those colors and nothing else. In the absorption spectrum, we see the full rainbow and they absorb those exact same frequencies. So, they kind of work the same, just in one direction. If the electron is going upwards, great! It means it's gaining energy. If it's speeding up, that means it's gaining energy. And if it's slowing down, it's going inwards and it'll give off the same energy that we just calculated. So, those same three lines... The question would be whether the electrons are going in a row, so the question is which ones. Which is this bottom one, the absorption or the mission? And it's the part when the absorption or the emission. So basically, they did some more experiments, and Balmer actually was a Swiss high school teacher. And what he found out was that for hydrogen, we could actually figure out what those wavelengths are gonna be. So he came up with this formula: 1/wavelength formula. And basically, the idea is the "M" stands for the number of orbit. So if we have our electrons at the first energy level and they jump to a second or them to a third, that's our in one, two, three. So you said the wavelength then is just 1/3 squared if the electron was going from one to three. You said it's going 1/3 squared minus 1/1 squared times whatever the constant is. You don't need to know this formula for the Diploma, but the concept is important. Understand that as the electron jumps levels, it's going to emit a wavelength. So, at the bottom here, we theorize that as the electrons fall downwards, let's go back to the previous page. In our bottom diagram, as the electron goes downwards, it means it's going to lose energy. That's where we see the emission line. So, this diagram is actually for the emission lines. And then, what Bohr said is, as the electron speeds up, it's going to need more energy. So, it's going to take it from the white light. That one would be the absorption spectrum. The good news is, you really don't need to remember which is which. You just have to know which level it's jumping from in order to figure it out. So, in this case, we could use this formula and it just says, "What would it be if it jumps from the base level to the 3rd?" So, we go from 1, 2, 3, plug it into the formula, and we're good. We're not going to do many of these calculations because I'm going to show you in a few minutes. The type of question you're expected to do, because this only works for hydrogen, and we need to know some numbers and stuff that's no longer in the curriculum. So, other guys besides these, they actually figured out different patterns. So, Lyman found for hydrogen that you could go from 5 down to 1, 4, 2, 1, 3, 2, 1, 2, 2, 1. And that basically emitted ultraviolet light. If it left from level 5 down, it gave off ultraviolet light. So, they named it after him. Balmer found out that if we only go from 5 down to 2 or less, it gave off visible light. So, that's why we see the three colors that we do. And Paschen was one that found out if we only go from five down to three, it's very little energy. So, that ends up being infrared. So, we don't see those. So, in this case, if we're to actually look at the Balmer series, we would only see three. Different colors. The rest of them would be outside of our visible range. So the key then, he says, they did some more calculations and they could actually figure out what the radius of the orbits are and what the energies of the orbits are. But once again, this only applies to hydrogen. So we're not going to use these formulas. And like I said, we just have to basically remember that as an electron jumps orbits (so that goes from 1 to 2), it's gonna give off or absorb energies. But you'd see whatever that wavelength is going to be for that transition. And if we went downwards, it'd be the same wavelength, just one's positive and one's negative. One's gaining energy, one's giving off energy. Ok, that's the key thing you want to remember with that. Because these formulas only work for hydrogen, we're not going to basically use them. What we are going to do is you're going to get questions where they'll give you the energy levels, kind of like this diagram. So in this case, it's saying we can jump. From 1 to 4, they give us all the energies for that transition. Ok, so this first one says to determine the total number of possibilities as the electrons fall from 4 to 1. So, we could go from 4 to 3, we could go 3 to 2, 2 to 1 - that would be 3 transitions. Or, we could go forward to 2, and then 2 to 1, so that would be the same. Or, we could go forward to 3 (which we already have), and then we could go 3 to 1. So, we won't bother redoing these ones. That would be another option. Or, we could go from 4 to 1 directly. So, we actually end up getting 6 different possible energy transitions to go from 4 down to 1. That means, if these were all visible, we would see 6 different bands of light for this situation. Part B now says, what's the wavelength if we go from 3 to 1? So, if we go from 3 to 1, we can see we have... Negative 1.5 down to negative 13.6. All we have to do is subtract those, and you don't need to worry about the negative. The negative just means one is absorbing energy, and the other is giving off energy, so that doesn't matter. Just subtract the two. In this case, we would get 12.1. That means we have 12.1 electron volts of energy being emitted. Now, to calculate the wavelength, we just need to use the equation E = hc/λ. So, if we go hc divided by E, that should work. For h, we can use the electron volts formula: 4.14 × 10^-15 times c (speed of light) raised to the power of 8. Divided by 12.1. If we do that calculation, we get an answer of 1.02 × 10^-7. Meters, which would be about a hundred nanometers. 102 nanometers, which would be the one violet of violets. 350. So in this case, we would say it's likely ultraviolet radiation that would go from three to one. And lastly, here's a diploma-type question. So it looks exactly the same, just the numbers a little bit different. So in this case, they're showing you zero electron volts as being the base level. And as we go to different levels, it's going to gain more and more. So it'll be sort of like one, two, three, four, kind of like that. So this question says, if the electron is in the SiC one point six, so it's saying if it has one point six electron volts, we want to know how much it's gonna take to ionize it. So ionizing it would be, it's gonna go right out of the atoms, we're gonna lose it completely. So we'd have to get to that ten point. Four, so ten point four minus one point six. We do that calculation, we get eight point eight electron volts. So now we just need to figure out the frequencies. Energy equals hf, so our frequency would be energy divided by H. So we take that eight point eight and divide it by four point one four to the negative fifteen, and that gives us two point one to the positive fifteen Hertz. So that should be our answer, letter B. So what they're doing now in diplomas quite often, they'll tell you where the ionized level is. And ionizing just basically means we're removing the electron altogether. So the zero would be the base level. In this case, our electron to be in the first orbit, we want to get rid of it completely. Something that's got to get past that negative 10.4 level, and that's all.