So how can we explain these other lines that we see, right? So we have these other lines over here, right? We have this blue green one, this blue one, and this violet one. So if you do the math, you can use the Balmer Rydberg equation or you can do this and you can plug in some more numbers and you can calculate those values.
So those are electrons falling from higher energy levels down to the second energy level. So let's go ahead and draw them on our diagram, here.
So, let's say an electron fell from the fourth energy level down to the second. All right, so that energy difference, if you do the calculation, that turns out to be the blue green line in your line spectrum. So, I'll represent the light emitted like that. And if an electron fell from the fifth energy level down to the second energy level, that corresponds to the blue line that you see on the line spectrum.
And then, finally, the violet line must be the transition from the sixth energy level down to the second, so let's go ahead and draw that in. And so now we have a way of explaining this line spectrum of hydrogen that we can observe. And since we calculated this Balmer Rydberg equation using the Bohr equation, using the Bohr model, I should say, the Bohr model is what allowed us to do this.
So the Bohr model explains these different energy levels that we see. So when you look at the line spectrum of hydrogen, it's kind of like you're seeing energy levels.
At least that's how I like to think about it 'cause you're, it's the only real way you can see the difference of energy.
All right, so energy is quantized. We call this the Balmer series. So this is called the Balmer series for hydrogen. But there are different transitions that you could do.
For example, let's think about an electron going from the second energy level to the first. All right, so let's get some more room here If I drew a line here, again, not drawn to scale. Think about an electron going from the second energy level down to the first. So from n is equal to two to n is equal to one. Let's use our equation and let's calculate that wavelength next. So this would be one over lamda is equal to the Rydberg constant, one point zero nine seven times ten to the seventh, that's one over meters, and then we're going from the second energy level to the first, so this would be one over the lower energy level squared so n is equal to one squared minus one over two squared.
All right, so let's get some more room, get out the calculator here. So, one over one squared is just one, minus one fourth, so that's point seven five and so if we take point seven five of the Rydberg constant, let's go ahead and do that.
So one point zero nine seven times ten to the seventh is our Rydberg constant. Then multiply that by point seven five, right? So three fourths, then we should get that number there. So that's eight two two seven five zero zero. So let's write that down. One over the wavelength is equal to eight two two seven five zero.
So to solve for that wavelength, just take one divided by that number and that gives you one point two one times ten to the negative seven and that'd be in meters. So the wavelength here is equal to one point, let me see what that was again. One point two one five. One point two one five times ten to the negative seventh meters. And so if you move this over two, right, that's nanometers. Carolina is your quality source for a well-equipped lab.
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Feeling the pinch from the current economy? Carolina understands. However, it does contain important features e. Consequently, the Bohr model retains a place in chemistry courses, even though it cannot be applied to other atoms.
In setting up his model, Bohr designated zero energy as the point where the proton and electron are completely separated, level infinity. This energy level represents the highest potential energy state. Moving the electron to any of its lower allowed energy states within the atom results in a decrease in potential energy; a release of energy; and an energy level below zero, i.
Hence the minus sign in the above equation. When an excited-state electron drops back to a lower-energy state, it releases potential energy in the form of light. Some of the possible transitions are shown below. This is shown in the equations below:. The energy difference between levels gets smaller as levels increase.
When the atom absorbs one or more quanta of energy, the electron moves from the ground state orbit to an excited state orbit that is further away. Energy levels are designated with the variable n. The energy that is gained by the atom is equal to the difference in energy between the two energy levels. When the atom relaxes back to a lower energy state, it releases energy that is again equal to the difference in energy of the two orbits see Figure 1.
Recall that the atomic emission spectrum of hydrogen had spectral lines consisting of four different frequencies. This is explained in the Bohr model by the realization that the electron orbits are not equally spaced.
As the energy increases further and further from the nucleus, the spacing between the levels gets smaller and smaller. Based on the wavelengths of the spectral lines, Bohr was able to calculate the energies that the hydrogen electron would have in each of its allowed energy levels. He then mathematically showed which energy level transitions corresponded to the spectral lines in the atomic emission spectrum Figure 2. This is called the Balmer series. The transitions called the Paschen series and the Brackett series both result in spectral lines in the infrared region because the energies are too small.
Unfortunately, when the mathematics of the model was applied to atoms with more than one electron, it was not able to correctly predict the frequencies of the spectral lines. Skip to main content.
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