the wavelengths of the Balmer lines in the hydrogen-atom spectrum as

Experiment#2 – Atomic Structure:Emission SpectroscopyOBJECTIVESIn successfully completing this lab you will:! measure the wavelengths of the Balmer lines in the hydrogen-atom spectrum aswell as the visible flame emission spectra of atomic lithium and sodium;! evaluate the pattern of energy states described by the hydrogen Balmer lineswith respect to the principle quantum number n describing these states todetermine the value of the Rydberg constant; and! investigate electron repulsion in multi-electron atoms as a function of theazimuthal quantum number by determining the effective nuclear charge (Zeff)and radius (reff) for the valence orbitals of atomic lithium and sodium from theirflame emission spectra.€INTRODUCTIONWhen gas-phase atomic samples undergo excitation by an external power source theyemit light with certain specific energies. This observation is evidence of the fact thatelectrons in atoms do not possess a continuous range of energies: only particular energystates are allowed. The pattern of emitted wavelengths is unique to each element and isoften referred to as the spectral fingerprint as shown in Figure 2–1 for atomic samples ofHydrogen Neon and Mercury.Figure 2–1. Discrete emission spectra of various atomic samples of elements.In contrast solid samples containing large groups of connected atoms (known asblackbody radiators) emit light broadly across the continuous spectrum of wavelengthswith intensities that are a function of temperature.Between 1885 and 1888 Johann Balmer and Johannes Rydberg observed that thehydrogen-atom emission wavelengths could be described by a function with a singleinteger variable the principle quantum number (n):#1 1&? = R8 % 2 – 2 ($2 n ‘(1)where n = 3 4 5 or 6 and R8 = 3.2898×1015 Hz. Following the work of Balmer andAuthor: Dr. Jess C. VickeryLast Revised on 1/11/14 by JCV2–1 Experiment#2 – Atomic StructureRydberg Niels Bohr developed a quantitative model of the hydrogen-atom consistingof an electron orbiting like a satellite around a small positively charged nucleus atparticular distances and energies. He used this theory to calculate the wavelengths ofthe spectral lines for hydrogen (and other one-electron systems) with remarkableaccuracy by assuming that energy was absorbed or emitted in integer packets (quanta)when an electron passed between orbits with energies proportional to the ratio of thesquares of the nuclear charge (Z) and the principle quantum number (n):Eelectron = -Z 2 hR8n2(2)Although Bohr’s theory was successful in interpreting the spectrum of the hydrogenatom it did not correctly predict the spectra observed for atoms or ions with more thanone electron. This led Erwin Schrodinger Werner Heisenberg and Paul Dirac toformulate more complete theories which showed that all aspects of atomic andmolecular spectra could be quantitatively explained with extreme precision in terms ofenergy transitions between different allowed quantum states.Properties of Waves. Light is electromagnetic (EM) radiation: it possesses electric andmagnetic properties that vary sinusoidally. Because the electric portion interacts moststrongly with electrons this is often simplified as shown in Figure 2–2.Figure 2–2. Wavelength (? ) and amplitude (A) of the electric-field component of light.The wavelength ? is the distance between consecutive identical points on the wave.For visible light this falls roughly within the range of 400 nm (blue) to 750 nm (red). Acomplementary property of waves is frequency ? which is a measure of how frequentlya given point in space moves between maximum and minimum amplitude (and back tomaximum again) as the wave passes through that location. The unit of frequency isgiven in cycles per seconds (s–1) also called Hertz (Hz).Electromagnetic wavelengths and frequencies are inversely proportional and theirproduct is equal to the speed of light c (approximately 2.9979 × 108 m/s in a vacuum):?·? = c(3)In this experiment a fiber-optic spectrometer will be used to measure the wavelengthsof the spectral lines emitted by gaseous samples of individual atoms from severalelements excited by electric discharge and by a flame. The emitted wavelengths will€then be used to characterize the allowed electronic states.Energy-Levels and Line Spectra of Elements. Electrons in an atom can possess onlydiscrete energy values and are therefore quantized. Lower energy states correspond to2–2 Experiment#2 – Atomic Structureorbits closer to the nucleus while higher energy states correspond to more distant orbits as shown for the hydrogen atom in Figure 2–3. Under the conditions of the hydrogenlamp during electric discharge the vast majority of H2 molecules are separated intoindividual H-atoms. In a certain fraction of these the electron is in the n = 2 n = 3 (orhigher) states due to the energy from the electric discharge. Electrons with extra energyare said to be in an excited state and can lose energy in discrete quantities droppingback down to lower-energy states eventually reaching the lowest possible energy statefor that electron called the ground state.Figure 2–3. Bohr diagram illustrating Balmer transitions observed for H-atoms.The energy lost when an electron transitions from a higher energy state to a lowerenergy state appears as a quantum of light called a photon. A photon possesses energyproportional to frequency with a proportionality constant known as Planck’s constant(h) having a value of 6.6261 × 10–34 J·s. Thus the electron in an excited hydrogen atomcan lose energy by emitting a photon that has an energy corresponding to the transitionfrom the ni to nf energy-levels:hc(4)?E electron = E photon = h? =?The photon energy (Ephoton) can be expressed in joules/photon and is a very tiny amountof energy. This result may be expressed in units of kJ/mol by multiplying the photonenergy by Avogadro’s number and dividing by 1000.€Multi-electron Atoms: Effective Nuclear Charge and Radius. For multi-electron atoms the Bohr model of the atom is incorrect in several important ways. The orbital energy e depends on both the n and quantum numbers so orbitals with different -valueswithin the same quantum shell (e.g. the 2s- vs. 2p-orbitals) have different energies. This€2–3€ Experiment#2 – Atomic Structureenergy difference between orbital sub-shells is described by the effective nuclear charge(Zeff) pulling on electrons in each orbital:2Z eff hR8e n l = -n2## Z eff = n?-e n lhR8(5)To understand how this dependence arises compare the electronic structure of the Hatom to that of the Li-atom. For hydrogen the electron always experiences the samevalue of the nuclear charge: 1. In contrast a ground state Li-atom has an electronconfiguration of 1s22s1 and so the charge experienced by the 2s-electron depends on itsrelative position compared to the two core electrons (1s2) about the nucleus. Electronsclose to the nucleus are said to shield some of the nuclear charge thereby reducing thecharge felt by the electron under consideration. Therefore the Zeff experienced by outerelectrons is simply the difference between the actual charge on the nucleus (Z) and thecumulative shielding (s) as a result of the repulsions of the other electrons:Z eff = Z – s(6)If the core electrons were always closer to the nucleus than the 2s-electron it wouldalways experience a nuclear charge of 1 (the difference between 3 from the protonsand –2 from the core electrons). In this case the electron would be “perfectly shielded”€from the nucleus by the core electrons and would be held by a force similar to that foran H-atom in the n = 2 state. In reality radial probability distributions reveal that the 2selectron is sometimes found close to the nucleus (in the region near 1 ao that is alsooccupied by the 1s-electrons) whereas electrons in the 2p-orbitals do not penetrate closeto the nucleus as shown in Figure 2–4. Thus the 2s-electron is only partially shieldedfrom the full nuclear charge and so (on average) has a Zeff -value greater than 1. This isthe primary reason why the 2s-orbital is lower in energy than the 2p-orbital.Figure 2–4. Li-atom radial distribution functions (RDFs) for the 2s- and 2p-orbitals.2–4 Experiment#2 – Atomic StructureThe 1s-orbital has the lowest energy and is closest to the nucleus because its wavefunction has no nodes. The 2s- and 2p-orbitals have similar energies and radii becausethey both have 1 node. The difference between them arises from the fact that the 2sorbital node is radial (giving rise the small “inner-maximum” observed in Figure 1–4)while the node in the 2p-orbital is angular and cuts right though the nucleus (leading tothe familiar dumb-bell shape) as shown in Figure 2–5. This inner-maximum decreasesthe average shielding leading to a lower energy higher Zeff and smaller reff for 2s vs. 2p.Figure 2–5. Electron density plots for 1s- 2s- and 2p-orbitals.Similar differences in penetration exist for orbitals with different -values in largershells as illustrated for the n = 3 shell of sodium in Figure 2–6. The presence of radialnodes instead of angular nodes gives rise to an analogous pattern of “inner-maxima” inthe radial wave functions like that seen for the 2s orbital in lithium above. This causes€the energies of these orbitals to fall in the well-known sequence: 3s < 3p < 3d.Figure 2–6. Na-atom radial distribution functions (RDFs) for 3s- 3p- and 3d-orbitals.For example the first excited-state of the Na-atom has the electron configuration:1s22s22p63p1 and the Zeff experienced by the valence 3p-electron will be different fromthat for a 3s-electron. As shown in Figures 2–6 and 2–7 there is a greater probability offinding a 3s-electron very close to the nucleus than there is for a 3p- or 3d-electron and so2–5 Experiment#2 – Atomic Structureit should experience less shielding from the 10 core electrons.Figure 2–7. Electron density plots for 3s- 3p- and 3d-orbitals.The 3s-orbital penetrates closer to the nucleus more often compared to the 3p-orbitals which likewise penetrate closer than 3d-orbitals. As a result the 3s-electron experiencesless shielding from core electrons and thus a greater effective nuclear charge than 3p- or3d-electrons: Zeff (3s) > Zeff (3p) > Zeff (3d). Thus the 3s-electron is bound more tightly to thenucleus yielding a lower (more negative) energy than 3p- or 3d-electrons.The average distance of an electron from the nucleus called the effective radius (reff) can be calculated in Bohr units (ao) using orbital n- and -values and the Zeff value:3n 2 – ( 1)ao(7)2Z eff€Together the Zeff and reff values for orbitals can be determined from the orbital energyand used to rationalize physical properties such as ionization energy electron affinity and electronegativity.€To determine the absolute energies of the valence orbitals one additional piece ofinformation is required: the ground state ionization energy. Ionization energy is theminimum energy required to remove an electron from an atoms. For lithium theionization energy describes the transition energy from the 2s-orbital to the n = 8 level and is experimentally found to be 520.3 kJ/mol. For sodium the ionization energydescribes the transition energy from the 3s-orbital to the n = 8 level and isexperimentally found to be 495.8 kJ/mol. Therefore the absolute energy of the 2s-orbitalin lithium is –520.3 kJ/mol while that for the 3s-orbital in sodium is –495.8 kJ/mol. Thiscan be combined with the emission peaks to determine absolute energies for the orbitalsshown in Figure 2–8 on the following page.reff =2–6 Experiment#2 – Atomic StructureFigure 2–8. Relative orbital energy diagram for multi-electron atoms.In the first part of this experiment you will measure the emission spectra of H-atomsfrom a discharge tube. In the second part you will make similar measurements for Liand Na-atoms and use the emission wavelength to establish the characteristics of thevalence orbitals for these atoms. The energies of the photons should be calculated inunits of kJ/mol and represent the energy difference between the 2s- and 2p-orbitals forlithium and the 3s- 3p- and 3d-orbitals for sodium.Equipment and Supplies: Ocean Optics spectrometer with fiber optic probe; hydrogengas discharge tube with power supply; Nichrome wire inserted in cork; butane cookingtorch or high-intensity Bunsen burner; usb transfer drive and/or computer configuredwith Microsoft Excel and a printer.Chemicals: solid lithium and sodium chloride in labeled vials; 6 M hydrochloric acid indropper bottles with accompanying small test tubes (for cleaning the Nichrome wires).2–7 Experiment#2 – Atomic StructureSAFETY PRECAUTIONS! High voltage sources: power supplies used for the spectrum tubes are sourcesof high voltage that represent a danger to the unwary user.! Metal salts and acids: wear gloves and rinse any affected surface with water. Inorder to prevent the breathing of any toxic metal vapors place the gas burnersused to heat metal salts in a fume hood. Use the 6 M hydrochloric acid to cleanthe Nichrome wires only in the fume hood.EXPERIMENTAL PROCEDUREPart 1: Indexing the H-atom Spectrum. Measure the visible emission spectrum ofhydrogen by placing the fiber-optic probe of an Ocean Optics spectrometer near theoutput of the discharge tube. Vary the distance and angle of the fiber-optic probe untilthe most intense transition (near 650 nm) has an intensity of just below 65 000 counts.Save the spectrum to your flash drive for processing in Microsoft Excel. Note: four linesfall within the visible portion of the EM-spectrum (roughly between 400 – 700 nm);make sure you are able to determine the wavelengths for all four. This may requirerecording a second spectrum after adjusting the probe to increase the amount of lightentering the fiber optic. If so some of the more intense peaks may go off-scale as shownin Figure 2–9. Record and print all spectra for inclusion in your report.Hydrogen Emission Spectrum45004000Intensity (counts)3500300025002000150010005000350400450500550600650700Wavelength (nm)Figure 2–9. Emission spectrum of atomic hydrogen with detector saturation.2–8750 Experiment#2 – Atomic StructurePart 2: Metal-Ion Flame Tests. Clean each Nichrome wire with successive immersion ofthe tip into a small test tube containing 6 M HCl followed by heating in the hot-portionof a Bunsen burner flame until the typical yellow color of sodium contamination is nolonger observed. Then obtain pea-sized quantities of each salt on the tip of the labeledwire and immerse it in the hot portion of the flame. (Note: it may be helpful to wet the endof the wire with 6 M HCl to help the salt grains adhere.) Record the flame emission spectrumfor each salt starting with the fiber optic ~14 cm away from the flame. Move it closeruntil you obtain a sufficiently intense spectrum. Make sure you DO NOT expose thefiber optic tip to the intense heat of a flame OR crimp the fiber optic (which can snapthe glass fiber within). For sodium the sample must be in the hottest part of the flamein order to observe the second emission peak (located a little beyond 800 nm).Figure 2–10. Schematic and metal chloride flame test emissions for Li Na & K.Schematic adapted from Blitz et. al. J. Chem. Educ. 2006 83 277.2–9 Experiment#2 – Atomic StructureSave the (x y) data for each spectrum and make plots of the emission intensity versuswavelength for H Li and Na (similar to that shown in Figure 2–9) using a spreadsheetprogram such as Microsoft Excel®. Present each spectrum as a scatter plot withsmoothed lines and no data markers displayed and include the precise wavelengthvalues for each of the emission peaks labeled on the plot.Clean up. Clean your Nichrome wire as directed by your TA and neutralize any HClspills with NaHCO3 (sodium bicarbonate). While still wearing gloves use a wet papertowel to wipe any salt residue deposited on the fume hood surface. Have your TAcheck your work and initial your lab notebook. Turn in your carbonless-copy datasheets prior to leaving the lab.CALCULATIONSCalculate the photon energy (in kJ/mol) for the single Li emission and the two Naemission wavelengths. To accomplish this first calculate the energy in units of J/photonfrom Equation (4) and then multiply the result by Avogadro’s number to express theenergy in J/mol of photons. Lastly convert the result to units of kJ/mol.Next use the photon energies to determine the valence orbital energies for both Li andNa. For lithium the transition is from the 2p- to the 2s-orbital and the 2s-orbital energyis –520.3 kJ/mol. Use this to find the energy of the 2p-orbitals in Li. For sodium thehigher-energy photon is emitted when the electron drops from one of the 3p-orbitals tothe 3s-orbital while the lower energy photon is emitted when the electron drops fromone of the 3d-orbitals to one of the 3p-orbitals. Use these facts along with the knownenergy of the 3s-orbital (–495.8 kJ/mol) to find the energies of the 3p- and 3d-orbitals.Make an orbital energy diagram similar to that shown in Figure 1–8 including theenergies for the valence orbitals of Li and Na.Using the orbital energies discussed above find the Zeff values for the 2s- and 2p-orbitalsin Li and the 3s- 3p- and 3d-orbitals in Na using Equation (5). Next use these Zeff valuesto calculate the values of the shielding parameter (s) for each orbital using Equation (6)and the effective radius (reff) of each orbital from Equation (7).RESULTS/DISCUSSIONInclude the following in the summary portion of your report:1. Include figures of each of the emission spectra you recorded in your report. Forthe four H-atom emission peaks convert the observed emission wavelengths tothe corresponding frequencies (?) in Hz and use a program such as MicrosoftExcel® to make a scatter plot of ? (y-axis) versus [1/22 – 1/n2] (x-axis) and add abest-fit line through the data to determine the value of the Rydberg constant asdescribed in Equation (1). Format the equation of the best-fit line to yield fivesignificant figures and include the R2-value. Report your percent error from theliterature value of 3.2898×1015 Hz for R8 using:%Error =experimental – literature×100%literature2 – 10 Experiment#2 – Atomic Structure2. Report the photon energy (in kJ/mol) for the single Li emission and the two Naemission wavelengths. Create two orbital energy diagrams similar to that shownin Figure 2–8 and label the energies of the valence orbitals for Li and Na.3. Report the Zeff and reff values for the 2s- and 2p-orbitals in Li and the 3s- 3p- and3d-orbitals in Na. Also summarize the values of the shielding parameter (s) foreach orbital.4. Rationalize your Zeff and reff results. Comment on the relative values of theeffective nuclear charges and radii for 3s- 3p- and 3d-orbitals in Na with respectto the number of radial vs. angular nodes in these wave functions (along with theimpact this has upon the shielding produced by the other 10 electrons in Na).Explain why the relative orbital energies in the n = 3 shell for Na (and othermulti-electron atoms) are: 3s < 3p < 3d.BIBLIOGRAPHYBlitz J. P.; Sheeran D. J.; Becker T. L. “An Improved Flame Test for QualitativeAnalysis Using a Multichannel UV–Visible Spectrophotometer.” J. Chem. Educ. 2006 83 277.Waldron K. A.; Fehringer E. M.; Streeb A. E.; Trosky J. E.; Pearson J. J. “ScreeningPercentages Based on Slater Effective Nuclear Charge as a Versatile Tool for TeachingPeriodic Trends.” J. Chem. Educ. 2001 78 635-639.McSwiney H. D. “The Spectroscopy and Thermochemistry of Na and Na2.” J. Chem.Educ. 1989 66 857-860.Miller K. J. “The Spectrum of Atomic Lithium: An undergraduate laboratoryexperiment.” J. Chem. Educ. 1974 51 805.Hollenberg J. L. “The Spectrum of Atomic Hydrogen: A freshman laboratoryexperiment.” J. Chem. Educ. 1966 43 216.Stafford F. E.; Wortman J. H. “Atomic Spectra: A Physical Chemistry Experiment.” J.Chem. Educ. 1962 39 630-632.Postma J. M.; Roberts J. L.; Hollenberg J. L. Chemistry in the Laboratory: Experiment 17 6th Ed. W. H. Freeman and Company New York 2006.PRE-LAB CALCULATIONSThe ionization energy for potassium is 419 kJ/mol. The wavelength of light emittedwhen an excited K-atom undergoes the 4s ? 4p transition is approximately 769 nm.Using this information calculate the energies of the 4s and 4p orbitals in potassium.2 – 11