Line Spectra and Energy Levels A Chem 101A Tutorial
A normal incandescent light bulb contains a hot piece of metal wire, which produces white light. A hydrogen discharge tube contains hot hydrogen gas, which produces lilaccolored light. Let s explore how these differ!
ultraviolet region infrared region 350 400 450 500 550 600 650 700 750 When we pass the white light from the normal light bulb through a prism, we see the entire visible spectrum (the colors of the rainbow ). The colors we see are our brain s way of representing wavelengths. Note that our eyes can only detect wavelengths from roughly 400 nm to 700 nm. Light bulbs also produce infrared and ultraviolet light, but we cannot see these types of radiation.
350 400 450 500 550 600 650 700 750 When we pass the lilac-colored light from the hydrogen discharge tube through a prism, we only observe four specific colors, which appear as colored vertical lines. This pattern is called the line spectrum of hydrogen.
410 nm 434 nm 486 nm 656 nm 350 400 450 500 550 600 650 700 750 Here is the line spectrum of hydrogen superimposed on the entire visible spectrum.
Other elements also produce line spectra when we pass an electrical discharge through them. For example, helium produces bright blue-white light. When we pass this light through a prism, we separate it into the line spectrum of helium. 350 400 450 500 550 600 650 700 750
The line spectrum of every element is unique. For example, both mercury and krypton produce light blue light in a discharge tube, but their line spectra are obviously different. As a result, we can use line spectra to identify the elements in an unknown substance. Line spectrum of mercury 350 400 450 500 550 600 650 700 750 Line spectrum of krypton Appearance of the light produced by either mercury or krypton 350 400 450 500 550 600 650 700 750
Some line spectra are very complex, while others are simple. Neon produces many visible lines, while sodium produces only one. Line spectrum of neon A neon discharge tube 350 400 450 500 550 600 650 700 750 Line spectrum of sodium 350 400 450 500 550 600 650 700 750 A sodium discharge tube
Before we explore line spectra in more detail, we need to change the way we observe them. Instead of looking at wavelengths, we will now focus our attention on the photon energy of the light. Photon energy is inversely proportional to wavelength: E photon = hc λ The photon energy of visible light ranges from 170 kj/mol to 300 kj/mol. Here is the visible spectrum plotted using energy as the scale. Wavelength is shown below the spectrum for comparison. Note that higher energies correspond to shorter wavelengths. 0 50 Energy (kj/mol) 100 150 200 250 300 350 infrared region ultraviolet region 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342
Energy (kj/mol) 0 50 100 150 200 250 300 350???? range of visible spectrum???? 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 Here is the hydrogen line spectrum plotted on our energy scale. Problem: our eyes can only detect radiation whose wavelength is in the range 400 700 nm. Does the hydrogen discharge tube produce other wavelengths that we cannot observe with our eyes?
Energy (kj/mol) 0 50 100 150 200 250 300 350 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 Yes, it does!! If we use film that is sensitive to wavelengths outside the visible range, we observe a vast number of additional lines that we cannot see with our eyes. Some of these lines are widely spaced, while others are bunched tightly together.
0 Energy (kj/mol) 250 500 750 1000 1250 1400 2000 1000 500 Area covered by the previous figure 400 300 200 150 100 85.4 If we look farther into the ultraviolet region, we find still more spectral lines. This diagram shows the complete line spectrum of hydrogen.
0 Energy (kj/mol) 250 500 750 1000 1250 1400 2000 1000 500 400 300 200 150 100 85.4 When we look at the line spectrum of hydrogen, we notice several groups of lines. In each group, the lines start out widely spaced, then get closer and closer until they blur together. Each of these groups of lines is called a series.
0 Energy (kj/mol) 250 500 750 1000 1250 1400 2000 1000 500 400 300 200 150 100 85.4 The first group of lines, lying at the shortest wavelengths and highest energies, is called the Lyman series.
0 Energy (kj/mol) 250 500 750 1000 1250 1400 Lyman series 2000 1000 500 400 300 200 150 100 85.4 The second group, which includes the lines we can see with our eyes, is called the Balmer series.
0 Energy (kj/mol) 250 500 750 1000 1250 1400 Balmer series Lyman series 2000 1000 500 400 300 200 150 100 85.4 The third group, which lies in the infrared region and overlaps the fourth group, is called the Paschen series.
Why does the line spectrum of hydrogen look like this? To understand, we must start with the fact that the electron in a hydrogen atom can only have certain energies. These allowed energies can be calculated from the following formula: E = -1313 kj/mol n 2 The symbol n here stands for a counting number (1, 2, 3 ). Note that all of the possible energies for the hydrogen electron are negative numbers.
There are infinite possible energies for the hydrogen atom, because there are infinite counting numbers. However, the electron cannot have any energy we choose. For instance, the electron cannot have E = -1000 kj/mol. -1000 kj/mol = -1313 kj/mol n 2 n 2 = -1313 kj/mol -1000 kj/mol = 1.313 n = 1.146 (not a counting number)
Here are the first few energies that the electron can have in a hydrogen atom: E 1 = E 2 = E 3 = E 4 = E 5 = E 6 = -1313 kj/mol 1 2 = -1313 kj/mol -1313 kj/mol 2 2 = -328.2 kj/mol -1313 kj/mol 3 2 = -145.9 kj/mol -1313 kj/mol 4 2 = -82.1 kj/mol -1313 kj/mol 5 2 = -52.5 kj/mol -1313 kj/mol 6 2 = -36.5 kj/mol If we let n become infinitely large, E becomes infinitesimally small (it gets closer and closer to zero): lim E n n = 0 kj/mol
0-100 -200 all other levels E 6 = -36.5 kj/mol (n = 6) E 5 = -52.5 kj/mol (n = 5) E 4 = -82.1 kj/mol (n = 4) E 3 = -145.9 kj/mol (n = 3) (n = 7 to infinity) Electron Energy (kj/mol) -300-400 -500-600 -700 E 2 = -328.2 kj/mol (n = 2) We can represent these allowed energies by plotting them on a vertical graph. This graph is called the energy level diagram for the hydrogen atom. -800-900 -1000-1100 Remember that every allowed energy for a hydrogen atom fits the formula E = -1313 kj/mol n 2-1200 -1300 E 1 = -1313 kj/mol (n = 1)
0-100 -200 all other levels E 6 = -36.5 kj/mol E 5 = -52.5 kj/mol E 4 = -82.1 kj/mol E 3 = -145.9 kj/mol -300 E 2 = -328.2 kj/mol Electron Energy (kj/mol) -400-500 -600-700 -800-900 -1000-1100 If we have a collection of cold hydrogen atoms, each atom s electron will have the lowest possible energy (-1313 kj/mol), because that is the most stable state for the electron. This lowest energy level is called the ground state. -1200-1300 e e e e e e e e E 1 = -1313 kj/mol (ground state)
Electron Energy (kj/mol) 0-100 -200-300 -400-500 -600-700 -800-900 e e e e e e e e e e all other levels E 6 = -36.5 kj/mol E 5 = -52.5 kj/mol E 4 = -82.1 kj/mol E 3 = -145.9 kj/mol E 2 = -328.2 kj/mol excited states If we add a lot of energy, though, many of the hydrogen atoms will absorb this energy and their electrons will rise to higher energy levels, called excited states. We will end up with electrons in a variety of levels. -1000-1100 -1200-1300 E 1 = -1313 kj/mol
Electron Energy (kj/mol) 0-100 -200-300 -400-500 -600-700 -800-900 e E 6 = -36.5 kj/mol E 5 = -52.5 kj/mol E 4 = -82.1 kj/mol E 3 = -145.9 kj/mol E 2 = -328.2 kj/mol Any electron that is above the ground state will eventually drop back to the ground state. It can do so in one step or in several. For instance, an electron that is in level 5 might drop to level 4, then to level 2, and finally to level 1. -1000-1100 -1200-1300 E 1 = -1313 kj/mol
0-100 e Low energy photon (small energy change) Electron Energy (kj/mol) -200-300 -400-500 -600-700 Medium energy photon (moderate energy change) As the electron drops from one level to another, it loses energy. This energy comes out in the form of a photon of electromagnetic radiation (light). -800-900 -1000-1100 High energy photon (large energy change) The energy of the photon exactly equals the size of the energy change for the electron. -1200-1300
0-100 -52.5-82.1 e ΔE = -82.1-52.5 = -29.6 kj/mol -200-145.9 ΔE = -328.2-82.1 = -246.1 kj/mol -300-328.2 Electron Energy (kj/mol) -400-500 -600-700 -800-900 ΔE = -1313-328.2 = -985 kj/mol We can calculate the energy of each photon by calculating the difference between the starting and final energy levels for each jump. -1000-1100 -1200-1300 -1313
0-100 e ΔE = -29.6 kj/mol E photon = 29.6 kj/mol -200 ΔE = -246.1 kj/mol E photon = 246.1 kj/mol Electron Energy (kj/mol) -300-400 -500-600 The photon energy equals the energy change for the electron, but it is a positive number. -700-800 ΔE = -985 kj/mol E photon = 985 kj/mol -900-1000 -1100-1200 -1300
0 Energy (kj/mol) 250 500 750 1000 1250 1400 E = 29.6 kj/mol (4040 nm) E = 246.1 kj/mol (486 nm) E = 985 kj/mol (121 nm) 2000 1000 500 400 300 200 150 100 85.4 Here is what we will observe. We will see three specific wavelengths of light being emitted from the atom, corresponding to the three photon energies we calculated.
Energy (kj/mol) 0 250 500 750 1000 1250 1400 0 2000 1000 500 400 300 200 150 100 250 500 750 1000 1250 85.4 1400 This line was produced when the electron jumped from level 5 to level 4 This line was produced when the electron jumped from level 4 to level 2 This line was produced when the electron jumped from level 2 to level 1 2000 1000 500 400 300 200 150 100 85.4 If we compare these wavelengths with the actual line spectrum of hydrogen, we find an exact match!
0 Energy (kj/mol) 250 500 750 1000 1250 1400 2000 1000 500 400 300 200 150 100 85.4 In fact, every line in the hydrogen line spectrum corresponds to an electron jump. The energy of the photon equals the amount of energy the electron loses (the change in the electron energy). E photon = ΔE electron
0 Energy (kj/mol) 250 500 750 1000 1250 1400 2000 1000 500 400 300 200 150 100 85.4 Let s see how the lines in the spectrum match up with electron transitions (jumps between energy levels). We ll begin with the Lyman series.
950 Energy (kj/mol) 1000 1050 1100 1150 1200 1250 1300 1350 125.9 121.5 nm 984.7 kj/mol 120 115 110 105 102.5 nm 1167 kj/mol 100 97.18 nm 1231 kj/mol 95 94.90 nm 1260 kj/mol 90 88.61 series limit 91.11 nm 1313 kj/mol Here is an expanded view of the Lyman series, with the wavelengths and energies of some lines. We can match each of these lines with an electron transition. 93.71 nm 1277 kj/mol 93.01 nm 1286 kj/mol
0 kj/mol E photon = 984.8 kj/mol 2-328.2 kj/mol Line 1 ΔE electron = -984.8 kj/mol 121.5 nm 1-1313 kj/mol The first line in the Lyman series is produced by electrons moving from level 2 to level 1.
3 0 kj/mol -145.9 kj/mol E photon = 1167 kj/mol Line 2 ΔE electron = -1167 kj/mol 102.5 nm 1-1313 kj/mol The second line in the Lyman series is produced by electrons moving from level 3 to level 1.
4 0 kj/mol -82.1 kj/mol E photon = 1231 kj/mol Line 3 ΔE electron = -1231 kj/mol 97.18 nm 1-1313 kj/mol The third line in the Lyman series is produced by electrons moving from level 4 to level 1.
5 0 kj/mol -52.5 kj/mol E photon = 1260 kj/mol Line 4 ΔE electron = -1260 kj/mol 94.90 nm 1-1313 kj/mol The fourth line in the Lyman series is produced by electrons moving from level 5 to level 1.
0 kj/mol E photon = 1313 kj/mol series limit ΔE electron = -1313 kj/mol 91.11 nm 1-1313 kj/mol The series limit for the Lyman series is produced by electrons moving from the infinitieth energy level to level 1.
950 Energy (kj/mol) 1000 1050 1100 1150 1200 1250 1300 1350 level 2 level 1 level 3 level 1 level 4 level 1 5 1 6 1 7 1 1 125.9 120 115 110 105 100 95 90 88.61 wavelength (nm) Any line in the line spectrum corresponds to an electron transition (a jump from one level to another). For the Lyman series, the electron always ends up in level 1. This diagram shows the electron transitions that correspond to the first six lines of the Lyman series, plus the series limit.
0 Energy (kj/mol) 250 500 750 1000 1250 1400 2000 1000 500 400 300 200 150 100 85.4 All other series (Balmer, Paschen, etc.) Now that we ve explored the Lyman series, let s apply the same ideas to the other series we observe in the line spectrum of hydrogen. Lyman series If will help us see the individual series if we expand that section of the line spectrum.
Energy (kj/mol) 0 50 100 150 200 250 300 350 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 Here is the region of the spectrum from 0 to 350 kj/mol. The four lines we can observe with our eyes are shown in their actual colors.
Energy (kj/mol) 0 50 100 150 200 250 300 350 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 Balmer series 400 342 Let s start with the Balmer series. This series contains the second most energetic photons (after the Lyman series).
Energy (kj/mol) 0 50 100 150 200 250 300 350 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 656 nm 182.3 kj/mol Here is the Balmer series with the wavelengths and energies of a few of its lines. Let s match these photon energies with the ΔE values for the electron. 500 486 nm 246.2 kj/mol 434 nm 275.7 kj/mol 400 410 nm 291.8 kj/mol 397 nm 301.5 kj/mol 342 series limit 364 nm 328.2 kj/mol
0 kj/mol E photon = 182.3 kj/mol 3 2-145.9 kj/mol ΔE electron = -182.3 kj/mol -328.2 kj/mol Line 1 656 nm The first line in the Balmer series is produced by electrons moving from level 3 to level 2.
4 0 kj/mol -82.1 kj/mol E photon = 246.1 kj/mol 2 ΔE electron = -246.1 kj/mol -328.2 kj/mol Line 2 486 nm The second line in the Balmer series is produced by electrons moving from level 4 to level 2.
5 0 kj/mol -52.5 kj/mol E photon = 275.7 kj/mol 2 ΔE electron = -275.7 kj/mol -328.2 kj/mol Line 3 434 nm The third line in the Balmer series is produced by electrons moving from level 5 to level 2.
Energy (kj/mol) 0 50 100 150 200 250 300 350 level 3 level 2 level 4 level 2 5 2 6 2 7 2 2 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 The Balmer series corresponds to a new set of electron transitions. For the Balmer series, the electron always ends up in level 2. This diagram shows the electron transitions that correspond to the first five lines of the Balmer series, plus the series limit.
0 Energy (kj/mol) 250 500 750 1000 1250 1400 3 2 4 2 5 2 2 1 3 1 4 1 5 1 2000 1000 500 400 300 200 150 100 85.4 Balmer series Lyman series We now know how the Lyman and Balmer series lines are formed. The Lyman series is produced by electrons dropping from higher levels into level 1. The Balmer series is produced by electrons dropping from higher levels into level 2.
0 Energy (kj/mol) 250 500 750 1000 1250 Balmer series 182 328 kj/mol Lyman series 985 1313 kj/mol 2 Small ΔE values The Lyman series falls in a much higher energy range than the Balmer series, because electrons lose a very large amount of energy when they drop into level 1. All of the possible drops into level 2 release far less energy. Very large ΔE values 1
0 Energy (kj/mol) 250 500 750 1000 1250 1400 2000 1000 All other series (Paschen, Brackett, Pfund, etc.) 500 400 300 Balmer series (All transitions that end up in the 2 nd level.) 200 150 We can analyze the remaining series in the same fashion. However, all of the remaining series overlap with one another to some extent, so it becomes difficult to tell which lines belong to which series. 100 Lyman series (All transitions that end up in the 1 st level.) 85.4 Let s expand the remaining series to make them a little easier to see.
Brackett series Energy (kj/mol) 0 50 100 150 10000 5000 3000 2000 1500 1200 1000 900 Paschen series This diagram highlights the Paschen series (series #3) and the Brackett series (series #4). Notice that these two series overlap one another, and the Brackett series overlaps with some of the lowerenergy series.
Energy (kj/mol) 0 50 100 150 10000 5000 3000 2000 1500 1200 1000 900 Here is the Paschen series with all of the other series removed.
Energy (kj/mol) 0 50 100 150 level 4 level 3 level 5 level 3 level 6 level 3 7 3 8 3 10000 5000 3000 2000 1500 1200 1000 900 800 The Paschen series contains all of the photons produced when the electron drops into level 3. For example, the first line in this series (at 63.8 kj/mol = 1874 nm) is produced when the electron drops from level 4 to level 3. 4-82.1 kj/mol ΔE = -63.8 kj/mol 3-145.9 kj/mol
0 50 Energy (kj/mol) 100 150 10000 5000 3000 2000 1500 1200 1000 900 Here is the Brackett series with all other series removed.
0 50 Energy (kj/mol) 100 150 level 5 level 4 level 6 level 4 7 4 8 4 9 4 10000 5000 3000 2000 1500 1200 1000 900 The Brackett series contains all of the photons produced when the electron drops into level 4. For example, the second line in this series (at 45.6 kj/mol = 2624 nm) is produced when the electron drops from level 6 to level 4. 6-36.5 kj/mol 5 ΔE = -45.6 kj/mol 4-82.1 kj/mol
Balmer? 2 Paschen? 3 Brackett? 4 Pfund? 5 Lyman? 1 Each series in the line spectrum of hydrogen correlates with the final energy level for an electron transition. Lyman series: transitions that end up in level 1 Balmer series: transitions that end up in level 2 Paschen series: transitions that end up in level 3 Brackett series: transitions that end up in level 4 Pfund series: transitions that end up in level 5
Let s practice! Can we answer these questions Where is the fifth line of the Paschen series? What is the corresponding electron transition? What is the energy of this line?
Paschen series (in red) Balmer series Lyman series First, we need to find the Paschen series. It is the third series, counting from the right (i.e. it has the lines with the third-highest energies). You should learn the sequence: Lyman, Balmer, Paschen (from highest energy to lowest).
1 2 3 4 5 (in yellow) Next, we need to find the fifth line in the series. The lines in each series are numbered from left to right (from lowest energy to highest energy). Now we need to identify the electron transition that produces this line.
The light we observe is the result of the electron moving between two levels. The Paschen series is the third series, which means that for all lines in the Paschen series, the electron ends up in level 3. But where does it start??? 3-145.9 kj/mol
We can work this out systematically. For the first line, the electron makes the smallest possible jump: level 4 to level 3 For the second line, the electron jumps from level 5 to level 3 Third line: level 6 to level 3 Fourth line: level 7 to level 3 Fifth line: level 8 to level 3 8 7 6 5 4 1 2 3 4 5 3
To get the energy of this light, we subtract the energies of the two levels. ΔE electron = (-145.9 kj/mol) (-20.5 kj/mol) = -125.4 kj/mol The photon energy is positive: E photon = 125.4 kj/mol 8-20.5 kj/mol ΔE electron = -125.4 kj/mol 3-145.9 kj/mol
??????? All other elements have line spectra, as do all ions that contain at least one electron. What can we tell from their line spectra?
Ions that have only one electron show line spectra that are similar to that of hydrogen. Examples are He +, Li 2+, and Be 3+. However, the energies are much larger. The energies of all lines are increased by a factor of Z 2, where Z is the atomic number of the element.
Energy (kj/mol) 0 1000 2000 3000 4000 5000 H 200 100 75 50 40 30 25 0 1000 2000 3000 4000 5000 He + 500 200 100 75 50 40 30 25 Here is a comparison of the line spectra of H and He + For He, the atomic number (Z) is 2. Therefore, the energies of all helium lines are 4 times as large as they are for hydrogen (2 2 = 4)
Energy (kj/mol) 0 1000 2000 3000 4000 5000 H 0 200 100 75 50 40 30 x 2 2 1000 2000 3000 4000 5000 25 He + 500 200 100 75 50 40 30 25 For example, the energies of the Lyman series for H range from 984.8 kj/mol to 1313 kj/mol. The energies of the corresponding series in the He + spectrum range from 3939 kj/mol to 5252 kj/mol. 984.8 kj/mol x 2 2 = 3939 kj/mol 1313 kj/mol x 2 2 = 5252 kj/mol
Energy (kj/mol) 0 50 100 150 200 250 300 350 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 However, line spectra for uncharged elements other than hydrogen do not resemble the line spectrum for hydrogen, and they do not fit any simple pattern. Here is the line spectrum of uncharged helium as it appears to our eyes. Remember that we can only see wavelengths from 400 nm to 700 nm.
Energy (kj/mol) 0 50 100 150 200 250 300 350 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 The line spectrum of sodium (shown here) is unusually simple. There are many other lines, but they are so faint and the prominent yellow line at 590 nm is so bright that the other lines are usually not visible. What can we tell from this spectrum?
Energy (kj/mol) 0 50 100 150 200 250 300 350 E photon = 203 kj/mol 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 The photon energy of 590 nm light is 203 kj/mol. This tells us that sodium atoms can lose 203 kj/mol of energy. Somewhere among the allowed energy levels of Na, there must be two levels that are 203 kj/mol apart. But we cannot determine the energies of these two levels, or whether there are other levels between them. E initial =???? ΔE electron = -203 kj/mol E final =????
Energy (kj/mol) 0 50 100 150 200 250 300 350 10000 5000 3000 2000 1500 1200 1000 900 800 700 600 500 400 342 However, other measurements have shown that the lower energy level for this electron transition is -495 kj/mol. Therefore, we can calculate that the upper energy level must be -292 kj/mol. Line spectra tell us how far apart energy levels are, but they do not give us the actual energies of the levels. E initial = -292 kj/mol ΔE = -203 kj/mol E final = -495 kj/mol