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7/06 Atomic Spectra ATOMIC SPECTRA About this lab After the discoveries that matter was atomic, that atoms contained charged constituents, and that there was a massive, charged nucleus (Rutherford), there was a major mystery. A classical planetary model of light, negatively charged electrons orbiting a heavy, positively charged nucleus under the influence of an attractive 1/ r 2 force law (just the form of point gravitational attraction) was easy to construct. But this suffered from major stability conflict with observation: the electron should orbit into the nucleus in a death spiral, emitting a continuous spectrum as it did so. In fact, atoms are stable, and the light they emit is not continuous, but involves very characteristic wavelengths and corresponding frequencies. Bohr provided an ad hoc particle solution by postulating unmotivated rules which explained the observed spectrum of hydrogen, de Broglie gave a rationale involving wave character of the orbiting electron, and Schrodinger extended the wave picture into three dimensions, with probabilistic interpretation of the meaning of the wave amplitude. Apparatus: spectrometer, spectral tubes, power supply, incandescent lamp. Introduction Figure 1 Bohr's schematic planetary model of a multi-electron atom. The number of negative electrons equals the positive charge on the nucleus, so the atom in neutral. 7/06 Atomic Spectra Figure 2 Bohr's planetary model of neutral hydrogen atom, with orbit allowed by successful, but ad hoc, rules. 1 2 Coulomb force law, it was known that a negative electron would orbit a r positive, heavy nucleus in planetary ellipses, just as do satellites under the influence of the 1 gravitational force. But, classically, any orbit should be possible, and the 2 r accelerating, charged electron should emit a continuum of light wavelengths, very quickly losing its energy and spiraling in to the nucleus. So the stability of the atom posed a conundrum for classical physics. From the 7/06 Atomic Spectra Figure 3 Energy levels of the hydrogen atom, with allowed electron “transitions” between more energetic (“higher, nupper ”) states and less energetic (“lower, nlower “) states. The state energies are given (in electron volts) by 13.6 En= - 2 , where the integer n is the orbit quantum number. A single photon is n emitted, with frequency given by energy conservation: hc E photon = ( Eupper - E lower ) = hf = (h = Planck's constant). Note that the total electron energies shown are negative (the electron is “bound” to the proton (nucleus)) and ( E upper - E lower ) is positive ( E lower is more negative than E upper (more tightly bound)). http://www.physics.northwestern.edu/vpl/atomic/hydrogen.html The theory of the discrete spectral lines and structure of the atom was first developed by Niels Bohr (1913). He postulated that the negative electron moves with discrete integer 7/06 Atomic Spectra multiples of angular momentum. In consequence, the electron also has quantized orbital level energies and radii, and this explained the discrete spectral lines. It was later realized from the work of de Broglie (1924) that the electron moves in an orbit around the positive nucleus as a wave, with wavelength inverse to linear momentum p: de Broglie = h . p The electron wave can “fit” around the nucleus only as a whole multiple of a wavelength the electron wave must constructively interfere with itself over the orbital path, and only certain wavelengths qualify. Any other wavelengths result in destructive interference. This constructive interference means that the angular momentum, and correspondingly the energy and radius of the orbiting electron, are quantized, just as Bohr postulated. These discoveries were foundation stones of quantum mechanics. (There is a different, fixed, wavelength associated with any material particle, the Compton h wavelength Compton = m where m 0 is the rest mass. The Compton wavelength relates 0c to the Heisenberg uncertainty in position arising due to the finite rest mass.) Figure 4 A stable electron orbit de Broglie wave that reinforces itself http://mutuslab.cs.uwindsor.ca/schurko/molspec/animations/bird_concordia/HydrogenSpect rum_2.htm 7/06 Atomic Spectra Using a grating spectroscope to separate the colors of light emitted from hot, glowing hydrogen gas, you see bright emission lines and not a continuous spectrum (rainbow) of colors. Observed (inverse) wavelengths of the lines are given by: 1 1 1 = 0.01097{ 2 - 2 } nanometers-1 n l nu Equation 1 n I 4 3 2 1 Figure 5 The Balmer series, containing photon energies in the visible range for the human eye. Balmer transitions end on nl = 2. The numerical constant, 0.01097 , is called the Rydberg constant and the n's are “principal” quantum numbers. nl (lower level) is smaller than nu (upper level); both n’s are integers equal to 1,2, 3... By trying various values for nu and nl , we find that the only transitions we see with our eyes have nl = 2 and nu = 3,4,5,---. This set of visible transitions with nl = 2 is known as the Balmer series. These are shown in the figure above. Each transition down to a lower energy level (orbit) emits a photon of energy equal to the difference between those of the upper and lower levels. Note that some Balmer lines lie in the near-ultraviolet beyond the eye's sensitivity limit at 380 nm. (Equation 1 is given by energy conservation, with Planck's expression for the quantization of photon energy in terms of frequency f: E photon = hf | E final |= | E initial | + hf = | E initial |+ hc (E's are negative) so 7/06 Atomic Spectra −19 1 1 13.6 x 1.6 x 10 = ( E f - Ei ) = hc hc and E f are negative.) ( 1 1 - 2 ) meters-1 in mks units. (Recall that 2 n l nu Ei (The series of spectral lines involving electron transitions ending on nl = 1 are called the Lyman series. These are too far in the ultraviolet for our sight, but are prominent instrumentally and are seen strongly in stellar spectra.) Procedure Using a diffraction grating spectrometer, measure some of the wavelengths of the visible members of the hydrogen spectrum Balmer series nl = 2) and compare the results with the predictions of the Bohr model of the hydrogen atom. The diffraction grating equation gives the wavelength in terms of the measured deviation angle and the spacing d 1 between adjacent grating lines: d = , in meters (mks unit). # of grating lines per meter Figure 6 grating. Interference maxima of various “orders” produced by a diffraction Diffracting grating maxima are given by the grating equation m = dsin( ) where m is integral. Equation 2 This implies that you may see more than one angle for a given wavelength or color (multiple orders of m), as long as sin(θ ) < 1. (In this experiment, m is used in the grating equation to avoid confusion with the orbital momentum integer, n). 7/06 Atomic Spectra Figure 7 Hydrogen discharge light source with grating spectrometer 7/06 Atomic Spectra Figure 8 A grating spectrometer. A lens at the entrance makes parallel the rays diverging from a source slit. After diffraction by the grating , another lens refocuses parallel rays diffracted at various angles onto corresponding portions of a focal plane. The eyepiece is for adapting to the individual eye. Since the light entering from the source is limited by a vertical slit, the image is linear: a “line” spectrum, with various colors at different parts of the focal plane. You will see the lines in first order (m = 1), and some, maybe, in second order (m = 2). Second order of a given wavelength has the same color as first order. The grating equation, with knowledge of the number of grating lines per meter and assumption as to order number, permits conversion of the observed angle to the corresponding wavelength. The essential elements of the spectrometer are: * The slit entrance, aimed at the spectral lamp. The slit can be turned vertical (parallel to the grating lines), and its width is adjustable, in general, (but leave yours alone!). This shapes and limits the light beam entering the collimating lens. 7/06 Atomic Spectra * A fixed diffraction grating. Most diffraction gratings for this experiment have 6000 lines per centimeter ==> 6 x 105 per meter. This implies that the slit separation 1 −6 meter = 1.667 x 10 meter = 1667 nanometers distance is d = 5 6 x 10 * A telescope tube with an eyepiece fitted with a cross hair for pointing. This assembly rotates about the grating center. The angle with respect to the slit barrel can be read to 0.1o with a vernier scale. (The Sargent-Welch spectrometers are calibrated in wavelength-but for a different grating spacing than usually used. Therefore, the spectrometer wavelength scale is not valid. You must use the measured angle (see below) and the integer order number m to calculate wavelength λ from the grating equation (Eq.2)). 7/06 Atomic Spectra Figure 9 Spectrometer table graduated in angle and wavelength. wavelengths are valid only for a particular grating line spacing. The 1. Hydrogen spectrum a. First, pull out the telescope from the viewing end. Look through and adjust the eyepiece to focus on the cross-hairs. The eyepiece slides in and out of its draw tube. Put the telescope assembly back into the spectrometer. Be sure the eyepiece is focused on the cross hairs. (If cross hairs are missing, you can later focus on a line image.) b. Turn on the power supply that applies a high voltage to the tube containing hydrogen gas. 5000 VOLTS: BE CAREFUL ABOUT ELECTRIC SHOCKS. c. Align the entire spectrometer in a straight line. Look through the eyepiece and put the slit in the center of the field. Set θ = 0o on the base plate. This is the m = 0 maximum which occurs at θ = 0° for all wavelengths; thus, you see a mix of all original colors. You may need to rotate the entrance slit to get it upright and parallel with the grating lines. d. Increase θ by swinging the telescope part to the left, and locate the angular position of the first (m = 1) three or four lines (red, green-blue, and two (?) violet) in the visible 7/06 Atomic Spectra spectrum of hydrogen. Ignore the fainter lines, which are from contamination (water and air). e. If the cross-hairs cannot be observed, center the slit image in the telescope eyepiece and average a few readings. Record the wavelengths of any other observed lines. f. Compute the wavelength of each of the three (four?) lines from the grating equation and give the differences from the wavelengths predicted from quantum theory (Eq.1) for n l = 2 and nu = 3,4, --- . If there is sufficient intensity, measure the second order angle (m = 2) to double check your measured λ's. 2. Atomic spectra of other elements The spectrum of atomic hydrogen, an atom with just one electron, is simple and the energy levels are given by the simple relation of Eq. 1. Other elements with many orbiting electrons have more complicated atomic spectra; their electrons interact with each other ,as well as with the dominant nuclear charge. Nevertheless, the spectral line pattern is unique for each element. You will be given spectral tubes of "unknown" elements, helium (He), neon (Ne), or mercury (Hg), which you must identify. Measure the wavelengths of the lines in the emission spectrum of each. Identify each element by referring to the list of wavelengths of prominent spectral lines in the table below. Use your wavelength measurements, not chart colors. Note that some lines will be brighter than others. Observe also, qualitatively, the sodium (Na) yellow “doublet” line, in first and second order. Be careful when changing spectral tubes: they become hot. It is best to hold them at the larger ends, which are cooler. 3. Absorption spectrum An emission spectrum is caused by electrons “dropping” to lower atomic energy states; electromagnetic energy in the form of photons of light is given off in each transition “downwards”. The electrons got into the higher energy states by collisional excitation, namely atomic collisions with other energetic free electrons. Now, we are going to investigate the opposite effect. Imagine an electron in a low orbital energy state, and along comes a photon of energy that the electron absorbs. The energy is the correct amount to boost the electron into a higher energy state. The excited atom will give up this energy very quickly in any number of ways: re-emit the same energy photon but in a direction different than the original photon; emit two or more lower energy photons as the electron "cascades" down through two or more energy levels or, before the atom can emit a photon, interact with another electron or atom with de-excitation of the atom back to 7/06 Atomic Spectra its original state. The net result is that photons of a particular energy are removed from a beam of light. If we are observing a continuous spectrum (think of a rainbow) with a spectroscope, we will see a zone of relative darkness, an absorption line, superposed on the continuous bright wavelength spectrum. Remember that energy is not destroyed, just converted to other wavelengths or even thermal energy. The procedure is first to observe a continuous spectrum emitted by a tungsten filament lamp. Then attach to the front end of the spectroscope a didymium filter that produces the absorption spectrum. Determine the central wavelength of a few of the dark absorption "lines" by measuring the angles corresponding to the left and right fringes of the dark absorption band and averaging to estimate the center of the band. 7/06 Atomic Spectra SPECTRAL LINE WAVELENGTHS Wavelengths are in nanometers. The colors are approximate; they should not be used to identify the elements. Neon 489, 496 (blue-green), 534 (green), 622, 633, 638, 640, (orange-red) 585 (yellow) 651, 660, 693 (red) Helium 447 (blue) 471 (turquoise) 492 (blue-green) 501 (green) 587 (yellow) 667(red) Mercury 404 (violet) 435 (blue) 491 (green) 546 (green) 576 (yellow) 579 (yellow) Sodium 568, 569 (green), 589, 590 (yellow), 615, 616 (red) Figure 10 Emission spectra of some multi-electron elements 7/06 Atomic Spectra Appendix 1 The Bohr Model The total energy of an negative electron (charge -e) held in circular orbit by the electrostatic attraction of the oppositely charged heavy nucleus with charge +Ze is E = KE + PE = E =− kZe 2r 2 1 2 kZe . mv r 2 2 F = ma or 2 2 kZe mv kZe 1 = KE = =− PE and 2 r 2r 2 r 2 (negative because the negative PE is twice as big as the positive KE). So, for classical physics, any total energy E and any r is possible. Bohr's orbital angular momentum rule limited the coupled r and E: h L = mvr = n ℏ where n is integral and ℏ = is Planck's blackbody constant h over 2 2π. Substituting this restriction leads to 2 rn = ( 2 ℏ n ) and 2 mke Z 2 4 2 1 mk e Z En= - ( ) 2 n = 1, 2, 3, 4, --- . Substituting numerically, 2 ℏ2 n 2 E n =−13.606 ( Z ) eV where 1electron volt = 1.6 x 10−19 Joules . n2 Energy is conserved in transition between upper (less bound) and lower (more tightly bound) states by emission of a single photon of energy hf (note h , not ℏ : E final = E initial + hf = E initial + hc so 1 1 13.6 x 1.6 x 10 = ( E f - Ei )= hc hc E i and E f are negative.) −19 Z 2 ( 1 1 - 2 ) meters-1 in mks units. (Recall that 2 nl nu 7/06 Atomic Spectra How to Read a Vernier Scale A vernier scale, shown below in the dashed box, is used to interpolate an extra digit of accuracy. The position of the zero is used to read the scale to the accuracy of the drawn or "ruled" lines. The extra vernier's digit will line up with the scale's ruled lines to indicate the next digit of accuracy. Below, the vernier zero lies between 23 and 24. Notice that the vernier's "6" lines up with a ruled line on the scale. This means the answer is 23.6. Figure 11 Venier scale Split Personalities: Wave and Particle Bohr's quantization of atomic electron orbits, and de Broglie's more profound matter wave description established wave/particle duality for matter, just as Planck and Einstein had done earlier for the photon messenger particles of the electromagnetic interaction. This completion established Planck's tiny quantum h as the organizing principle of our universe. Bohr lived and worked in his native Copenhagen, which became a center for research and for discussion of the interpretation of the quantum mechanical wave function. During World War II, Bohr and his family fled occupied Denmark to Sweden in a fishing boat. He later made his way to America, where he was very influential in the development of the first nuclear bomb. A recent play, Copenhagen, examines the political and moral issues involved in nuclear weapons development, in terms of an historical wartime meeting between Niels Bohr and Werner Heisenberg. 7/06 Atomic Spectra In 1913 de Broglie was awarded his Licence ès Sciences from the Sorbonne, but before his career had progressed much further World War I broke out. During the War de Broglie served in the army. He was attached to the wireless telegraphy section for the whole of the war and served in the station at the Eiffel Tower. During these war years all his spare time was spent thinking about technical problems. Niels Henrik David Bohr Born: 7 Oct 1885 in Copenhagen, Denmark Died: 18 Nov 1962 in Copenhagen, Denmark 1922 Nobel Laureate in Physics for his services in the investigation of the structure of atoms and of the radiation emanating from them. 7/06 Atomic Spectra Louis Victor Pierre Raymond duc de Broglie Born: 15 Aug 1892 in Dieppe, France Died: 19 March 1987 in Paris, France PRINCE LOUIS-VICTOR DE BROGLIE 1929 Nobel Laureate in Physics for his discovery of the wave nature of electrons. 7/06 Atomic Spectra The Nobel Prize in Physics 1929 Presentation Speech by Professor C.W. Oseen, Chairman of the Nobel Committee for Physics of the Royal Swedish Academy of Sciences Your Majesty, Your Royal Highnesses, Ladies and Gentlemen. The question as to the nature of light rays is one of the oldest problems in physics. In the works of the ancient philosophers are to be found an indication and a rough outline of two radically different concepts of this phenomenon. However, in a clear and definite form they appear at the time when the foundations of physics were laid, a time that bears the stamp of Newton's genius. One of these theories asserts that a light ray is composed of small particles, which we may term corpuscles, which are projected into space by light-emitting substances. The other states that light is a wave motion of one type or another. The fact that these two theories, at this elementary stage, are equally possible, is attributable to their explaining equally well the simplest law governing a light ray, viz. conditions being undisturbed it propagates in a straight line. The 19th century sealed the victory of the wave theory. Those of us whose studies coincide with that period have certainly all learned that light is a wave motion. This conviction was based on the study of a series of phenomena which are readily accounted for by the wave theory but which, on the other hand, cannot be explained by the corpuscular theory. One of these phenomena is the diffraction undergone by a light beam when it passes through a small hole in an opaque screen. Alongside the diffracted ray there are alternate light and dark bands. This phenomenon has long been considered a decisive proof of the wave theory. Furthermore, in the course of the 19th century a very large number of other, more complex, light phenomena had been learnt of which all, without exception, were completely explainable by the wave theory, while it appeared to be impossible to account for them on the basis of the corpuscular theory. The correctness of the wave theory seemed definitely established. The 19th century was also the period when atomic concepts have taken root into physics. One of the greatest discoveries of the final decades of that century was the discovery of the electron, the smallest negative charge of electricity occurring in the free state. Under the influence of these two currents of ideas the concept which 19th century physics had of the universe was the following. The universe was divided into two smaller worlds. One was the world of light, of waves; the other was the world of matter, of atoms and electrons. The perceptible appearance of the universe was conditioned by the interaction of these two worlds. Our century taught us that besides the innumerable light phenomena which testify to the truth of the wave theory, there are others which testify no less decisively to the correctness of the corpuscular theory. A light ray has the property of liberating a stream of electrons from a substance. The number of electrons liberated depends on 7/06 Atomic Spectra the intensity of the ray. But the velocity with which the electrons leave the substance is the same whether the light ray originates from the most powerful light source that can be made, or whether it originates from the most distant fixed stars which are invisible to the naked eye. In this case everything occurs as if the light ray were composed of corpuscles which traversed the spaces of the universe unmodified. It thus seems that light is at once a wave motion and a stream of corpuscles. Some of its properties are explained by the former supposition, others by the second. Both must be true. Louis de Broglie had the boldness to maintain that not all the properties of matter can be explained by the theory that it consists of corpuscles. Apart from the numberless phenomena which can be accounted for by this theory, there are others, according to him, which can be explained only by assuming that matter is, by its nature, a wave motion. At a time when no single known fact supported this theory, Louis de Broglie asserted that a stream of electrons which passed through a very small hole in an opaque screen must exhibit the same phenomena as a light ray under the same conditions. It was not quite in this way that Louis de Broglie's experimental investigation concerning his theory took place. Instead, the phenomena arising when beams of electrons are reflected by crystalline surfaces, or when they penetrate thin sheets, etc. were turned to account. The experimental results obtained by these various methods have fully substantiated Louis de Broglie's theory. It is thus a fact that matter has properties which can be interpreted only by assuming that matter is of a wave nature. An aspect of the nature of matter which is completely new and previously quite unsuspected has thus been revealed to us. Hence there are not two worlds, one of light and waves, one of matter and corpuscles. There is only a single universe. Some of its properties can be accounted for by the wave theory, others by the corpuscular theory. In conclusion I would like to point out that what applies to matter applies also to ourselves since, from a certain point of view, we are part of matter. A well-known Swedish poem has as its opening words "My life is a wave". The poet could also have expressed his thought by the words: "I am a wave". Had he done so, his words would have contained a premonition of man's present deepest understanding of the nature of matter. Monsieur Louis de Broglie. When quite young you threw yourself into the controversy raging round the most profound problem in physics. You had the boldness to assert, without the support of any known fact, that matter had not only a corpuscular nature, but also a wave nature. Experiment came later and established the correctness of your view. You have covered in fresh glory a name already crowned for centuries with honour. The Royal Academy of Sciences has sought to reward your 7/06 Atomic Spectra discovery with the highest recompense of which it is capable. I would ask you to receive from the hands of our King the Nobel Physics Prize for 1929.