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<title>DP Chemistry: Convergence limits</title>
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<meta name="description" content="In sub-topic 12.1 Electrons in atoms underneath "Applications and skills" it states "Calculation of the value of the first ionization energy from spectral data which gives the wavelength or frequency of the convergence limit". It is not that easy for teachers to find a good source of spectral data which gives the convergence limit. For example an internet search for the emission spectrum of sodium gives several images...">
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<meta itemprop="description" content="In sub-topic 12.1 Electrons in atoms underneath "Applications and skills" it states "Calculation of the value of the first ionization energy from spectral data which gives the wavelength or frequency of the convergence limit". It is not that easy for teachers to find a good source of spectral data which gives the convergence limit. For example an internet search for the emission spectrum of sodium gives several images...">
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<meta name="twitter:description" content="In sub-topic 12.1 Electrons in atoms underneath "Applications and skills" it states "Calculation of the value of the first ionization energy from spectral data which gives the wavelength or frequency of the convergence limit". It is not that easy for teachers to find a good source of spectral data which gives the convergence limit. For example an internet search for the emission spectrum of sodium gives several images...">
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fuels</a></li><li><a href="../19411/nuclear-fusion-nuclear-fission-reactions-1.html">Nuclear fusion & nuclear fission reactions</a></li><li><a href="../19429/solar-energy-1.html">Solar energy</a></li><li><a href="../19437/environmental-impact-global-warming-1.html">Environmental impact - global warming</a></li><li><a href="../19453/electrochemistry-rechargeable-batteries-fuel-cells-1.html">Electrochemistry, rechargeable batteries & fuel cells</a></li><li><a href="../19458/nuclear-fusion-fission-hl--1.html">Nuclear fusion & fission (HL) </a></li><li><a href="../19470/photovoltaic-cells-and-dsscs-1.html">Photovoltaic cells and DSSCs</a></li></ul></li><li><a href="../19078/option-d-1.html" class="father">Option D</a><ul class="level-2"><li><a href="../19079/pharmaceutical-products-drug-action--1.html">Pharmaceutical products & drug action </a></li><li><a href="../19158/aspirin-penicillin--1.html">Aspirin & penicillin </a></li><li><a href="../19174/opiates-1.html">Opiates</a></li><li><a href="../19184/ph-regulation-of-the-stomach-1.html">pH regulation of the stomach</a></li><li><a href="../19194/antiviral-medications--1.html">Antiviral medications </a></li><li><a href="../19211/environmental-impact-of-some-medications-1.html">Environmental impact of some medications</a></li><li><a href="../19254/taxol-a-chiral-auxiliary-case-study-1.html">Taxol - a chiral auxiliary case study</a></li><li><a href="../19258/nuclear-medicine--1.html">Nuclear medicine </a></li><li><a href="../19273/drug-detection-analysis--1.html">Drug detection & analysis </a></li></ul></li></ul></li><li><a href="../16592/practical-scheme-of-work-ia--1.html">Practical scheme of work & IA </a><ul class="level-1"><li><a href="../16682/internal-assessment-1.html" class="father">Internal Assessment</a><ul class="level-2"><li><a href="../18892/scaffolding-the-investigation-1.html">'Scaffolding' the investigation</a></li><li><a href="../18896/timing-organisation--1.html">Timing & organisation </a></li><li><a href="../18905/choosing-the-research-question-1.html">Choosing the research question</a></li><li><a href="../18946/personal-engagement-1.html">Personal engagement</a></li><li><a href="../18950/exploration-1.html">Exploration</a></li><li><a href="../18957/analysis-1.html">Analysis</a></li><li><a href="../18965/evaluation-1.html">Evaluation</a></li><li><a href="../18966/communication-1.html">Communication</a></li><li><a href="../19882/internal-standardization-of-the-ia-1.html">Internal standardization of the IA</a></li><li><a href="../19901/submitting-the-samples-for-moderation-2.html">Submitting the samples for moderation</a></li><li><a href="../33754/ten-suggestions-for-ias-using-secondary-data-1.html">Ten suggestions for IAs using secondary data</a></li><li><a href="../37544/gaining-full-marks-for-a-databased-ia--1.html">Gaining full marks for a databased IA </a></li><li><a href="../19506/ia-example-marking-exercise--1.html">IA example & marking exercise </a></li><li><a href="../23929/genuine-examples-of-moderated-ia-reports-1.html">Genuine examples of moderated IA reports</a></li><li><a href="../25234/examples-of-teacher-marked-ia-reports--1.html">Examples of teacher-marked IA reports </a></li><li><a href="../37542/history-of-internal-assessment-1.html">History of Internal Assessment</a></li></ul></li><li><a href="../16598/mandatory-laboratory-components-1.html" class="father">Mandatory laboratory components</a><ul class="level-2"><li><a href="../16613/formula-of-magnesium-oxide--1.html">Formula of magnesium oxide </a></li><li><a href="../16612/determining-the-mr-of-an-unknown-gas-1.html">Determining the <i>M</i><sub>r</sub> of an unknown gas</a></li><li><a href="../16615/acid-base-titrations--1.html">Acid-base titrations </a></li><li><a href="../16616/a-green-acid-base-practical-1.html">A green acid-base practical</a></li><li><a href="../16617/analysis-of-aspirin-tablets-1.html">Analysis of aspirin tablets</a></li><li><a href="../16618/caco3-in-egg-shells-1.html">CaCO<sub>3</sub> in egg shells</a></li><li><a href="../16644/enthalpy-changes-1.html">Enthalpy changes</a></li><li><a href="../16631/reaction-rates-1.html">Reaction rates</a></li><li><a href="../16635/rate-dependent-factors-1.html">Rate-dependent factors</a></li><li><a href="../16636/determining-ea-for-a-reaction-1.html">Determining <i>E</i><sub>a</sub> for a reaction</a></li><li><a href="../16637/iodination-of-propanone-1.html">Iodination of propanone</a></li><li><a href="../18144/titrations-with-a-ph-meter-1.html">Titrations with a pH meter</a></li><li><a href="../18355/redox-titration-with-kmno4--1.html">Redox titration with KMnO<sub>4</sub> </a></li><li><a href="../16640/voltaic-cells-1.html">Voltaic cells</a></li><li><a href="../16659/3-d-molecular-modelling--1.html">3-D molecular modelling </a></li></ul></li><li><a href="../17168/other-good-practicals-1.html" class="father">Other good practicals</a><ul class="level-2"><li><a href="../17196/common-chemical-reactions-1.html">Common chemical reactions</a></li><li><a href="../227/elements-oxides-of-the-third-period--1.html">Elements & oxides of the third period </a></li><li><a href="../17239/the-halogens-1.html">The halogens</a></li><li><a href="../17162/boiling-points-of-mixtures-1.html">Boiling points of mixtures</a></li><li><a href="../17170/polarity-of-molecules-1.html">Polarity of molecules</a></li><li><a href="../18083/le-chateliers-principle--1.html">Le Chatelier's principle </a></li><li><a href="../19582/determining-kc-for-an-esterification-reaction-1.html">Determining <i>K</i><sub>c</sub> for an esterification reaction</a></li><li><a href="../18164/redox-reactions-of-vanadium--1.html">Redox reactions of vanadium </a></li><li><a href="../18351/chlorine-in-swimming-pools--1.html">Chlorine in swimming pools </a></li><li><a href="../18178/analysis-of-cuii-ions-in-solution--1.html">Analysis of Cu(II) ions in solution </a></li><li><a href="../18179/percentage-of-copper-in-brass-1.html">Percentage of copper in brass</a></li><li><a href="../18356/electrolytic-cells--1.html">Electrolytic cells </a></li><li><a href="../18598/reactions-of-organic-compounds-1.html">Reactions of organic compounds</a></li><li><a href="../18752/hydrolysis-of-halogenoalkanes-1.html">Hydrolysis of halogenoalkanes</a></li><li><a href="../18784/preparation-of-13-dinitrobenzene--1.html">Preparation of 1,3-dinitrobenzene </a></li><li><a href="../19022/determination-of-an-organic-structure-1.html">Determination of an organic structure</a></li><li><a href="../19887/preparation-of-nylon-66-1.html">Preparation of nylon 6,6</a></li><li><a href="../19343/determination-of-vitamin-c-content--1.html">Determination of vitamin C content </a></li><li><a href="../19342/hydrolysis-of-starch--1.html">Hydrolysis of starch </a></li><li><a href="../19159/preparation-purification-of-aspirin--1.html">Preparation & purification of aspirin </a></li></ul></li><li><a href="../18851/ict-in-practical-work-1.html" class="father">ICT in practical work</a><ul class="level-2"><li><a href="../18852/data-logging--1.html">Data logging </a></li><li><a href="../18853/software-for-graph-plotting--1.html">Software for graph plotting </a></li><li><a href="../18854/spreadsheets-for-data-processing--1.html">Spreadsheets for data processing </a></li><li><a href="../18855/databases-1.html">Databases</a></li><li><a href="../18856/computer-modelling-simulations--1.html">Computer modelling & simulations </a></li></ul></li><li><a href="../16594/group-4-project-1.html" class="father">Group 4 Project</a><ul class="level-2"><li><a href="../16595/practicalities-1.html">Practicalities</a></li><li><a href="../16596/reflective-statement--2.html">Reflective statement </a></li></ul></li><li><a href="../16666/a-new-laboratory-1.html">A new laboratory?</a></li></ul></li><li><a href="../16284/exams-1.html">Exams</a><ul class="level-1"><li><a href="../16286/essential-facts-1.html" class="father">Essential Facts</a><ul class="level-2"><li><a href="../16287/objectives-command-terms-1.html">Objectives & command terms</a></li><li><a href="../16288/grade-descriptors-1.html">Grade descriptors</a></li><li><a href="../16289/grade-boundaries-1.html">Grade boundaries</a></li></ul></li><li><a href="../16302/paper-1-multiple-choice-1.html" class="father">Paper 1 (Multiple Choice)</a><ul class="level-2"><li><a href="../16303/advice-to-students-paper-1-1.html">Advice to students (Paper 1)</a></li><li><a href="../31515/practice-paper-1-exams-1.html">Practice Paper 1 exams</a></li></ul></li><li><a href="../16305/paper-2-1.html" class="father">Paper 2</a><ul class="level-2"><li><a href="../16306/advice-to-students-paper-2-1.html">Advice to students (Paper 2)</a></li><li><a href="../16307/areas-of-difficulty-1.html">Areas of difficulty</a></li></ul></li><li><a href="../16313/paper-3--1.html" class="father">Paper 3 </a><ul class="level-2"><li><a 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href="../16323/retaking-the-exam-1.html">Retaking the exam</a></li></ul></li><li><a href="../16325/faqs-1.html">FAQs</a></li></ul></li><li><a href="../3147/ib-core-1.html">IB Core</a><ul class="level-1"><li><a href="../3149/learner-profile-1.html">Learner Profile</a></li><li><a href="../21735/extended-essays--1.html" class="father">Extended Essays </a><ul class="level-2"><li><a href="../21736/overview--1.html">Overview </a></li><li><a href="../21780/responsibilities-1.html">Responsibilities</a></li><li><a href="../21790/resources-1.html">Resources</a></li><li><a href="../21800/research-1.html">Research</a></li><li><a href="../21804/writing-the-essay-1.html">Writing the essay</a></li><li><a href="../21810/assessment-1.html">Assessment</a></li><li><a href="../22434/summary-of-advice--1.html">Summary of advice </a></li><li><a href="../25272/faqs--1.html">FAQs </a></li></ul></li><li><a href="../307/theory-of-knowledge-tok-1.html" class="father">Theory of Knowledge (TOK)</a><ul 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options</a></li><li><a href="../24897/sl-quizzes-on-option-sub-topics--1.html">SL Quizzes on option sub-topics </a></li><li><a href="../17785/hl-multiple-choice-tests-on-individual-topics-1.html">HL Multiple choice tests on individual topics</a></li><li><a href="../24352/hl-multiple-choice-quizzes-on-sub-topics-1.html">HL Multiple choice 'quizzes' on sub-topics</a></li><li><a href="../31520/hl-practice-paper-1-exams--1.html">HL Practice Paper 1 exams </a></li><li><a href="../17787/hl-questions-on-each-sub-topic--1.html">HL Questions on each sub-topic </a></li><li><a href="../20428/hl-paper-3-section-a-questions-1.html">HL Paper 3 Section A questions</a></li><li><a href="../17793/hl-questions-on-the-options-1.html">HL Questions on the options</a></li><li><a href="../24973/hl-quizzes-on-option-sub-topics-1.html">HL Quizzes on option sub-topics</a></li><li><a href="../41573/printable-versions-of-written-tasks--1.html">Printable versions of written tasks </a></li></ul></li><li><a 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</div><section id="main-content"><h1>Background</h1><p>In sub-topic <a href="../16946/electrons-in-atoms-1.html" title="Core & AHL » Teaching each topic & sub-topic » Topics 2 & 12 » Electrons in atoms">12.1 Electrons in atoms</a> underneath 'Applications and skills' it states "Calculation of the value of the first ionization energy from spectral data which gives the wavelength or frequency of the convergence limit". It is not that easy for teachers to find a good source of spectral data which gives the convergence limit. For example an internet search for the emission spectrum of sodium gives several images that all appear different and seem to depend upon the pressure under which the spectrum was taken. The example below is from <a href="http://www.differencebetween.net/science/difference-between-emission-and-absorption-spectra/">The difference between.net.</a> </p><hr class="hidden"><p style="text-align: center;"><img alt="" class="noborder" src="../../../ib/chemistry/images/2014%20Core%20%26%20AHL/Topics-2-12/sodium-emission-spectrum.png" style="width: 493px; height: 103px;"></p><hr class="hidden"><p>Whilst most show the splitting of the two intense yellow lines it is almost impossible to determine where the convergence limit occurs.</p><hr class="hidden"><p>Probably the best source for the data is from <a href="http://physics.nist.gov/PhysRefData/Handbook/periodictable.htm">The National Institute of Science and Technology (NIST)</a>. If you click on one of the elements in the periodic table, e.g. sodium, you will see that it gives the ionization energy for sodium in its ground state (written as<sup> </sup> 1<em>s</em><sup>2</sup>2<em>s</em><sup>2</sup>2<em>p</em><sup>6</sup>3<em>s</em> <sup>2</sup>S<sub>1</sub><sub>/2</sub>) as 41449.451 cm<sup>-1</sup>. For chemists this is a strange unit for ionization energy. What it actually refers to is the wavenumber (i.e. 1/<em>λ</em>) of the relevant convergence limit. If you wish to use it to give to students then it would be more normal to convert it into a wavelength, i.e. 2.413 x 10<sup>-7</sup> m or 241 nm. To calculate the first ionization energy the students would then have to use the equation <em>E</em> =<em> hcL</em>/<em>λ</em>. Apart from having to convert wavenumber into wavelength (or frequency) there is another problem with the NIST data as students will need to be careful to choose the correct value. This is because the ionization energy for the removal of the second electron is also given (381390.2 cm<sup>-1</sup>) and rather confusingly they also call this the ground state and give the configuration as 1<em>s</em><sup>2</sup>2<em>s</em><sup>2</sup>2<em>p</em><sup>6</sup> <sup>1</sup>S<sub>0</sub>.</p><hr class="hidden"><p>In fact there is <strong>no</strong> need for <strong>any</strong> other sources such as NIST to solve these problems. <strong>All the information you require</strong> is easily available from the IB data booklet for first exams in 2016.</p><div class="blueBg"><h2><img alt="frown" height="24" src="../../../img/tib-icons/higher-level-24-1.png" title="frown" width="24"> Using the data booklet to obtain the wavelength of convergence limits</h2><p>For any element <em>E </em>= <em>hcL</em>/<em>λ</em>. Where <em>E</em> is the first ionization energy and <em>λ</em> is the wavelength of the relevant convergence limit. It is usual to solve this for hydrogen either to find the convergence limit or the ionization energy.<br><br>Since the ionization energy for hydrogen is given in the data booklet, as are the values for <em>h</em>, <em>c</em> and <em>L</em> it can easily be shown that the convergence limit occurs at 91.2 nm. To follow the instructions given in 12.1 students will normally be given the convergence limit and asked to find the ionization energy.</p><p>Since the equation is true for all elements and <em>hcL</em> is a constant it follows that:</p><hr class="hidden"><p style="text-align: center;">IE<sub>1</sub>(CL)<sub>1</sub> = IE<sub>2</sub>(CL)<sub>2</sub></p><hr class="hidden"><p>where IE<sub>1</sub> and IE<sub>2</sub> are the first ionization energies of two different elements and (CL)<sub>1</sub> and (CL)<sub>2</sub> are their respective relevant convergence limits.</p><hr class="hidden"><p>You can therefore easily find the convergence limit for each element simply from its ionization energy which is given in Section 8 of the IB data booklet. Just divide 1312 x 91.2 by the first ionization energy and it will give the convergence limit in nanometres.<br><br>For example, the first ionization energy of sodium is 496 kJ mol<sup>-1</sup>. By doing the sum (1312 x 91.2) / 496 the convergence limit comes out to be 241.4 nm. If you want to check that this is correct, convert it to centimetres and find the reciprocal to give a wavenumber of 4.14 x 10<sup>4</sup> cm<sup>-1</sup> which compares exactly with the NIST value of 4.14 x 10<sup>4</sup> cm<sup>-1</sup>. To check it also works for atoms with more than one electron in its outer shell I've randomly done the calculations for carbon (110 nm), fluorine (71.2 nm) and iron (157 nm). In each case the values agree extremely closely with the values given by the NIST source.<br><br>What concerns me a little is that all students are being asked to do is manipulate the two equations <em>E</em> = <em>hf</em> and <em>c</em>=<em>λf</em> without really having to show they understand the underlying chemistry. I would ask them which electron is being removed from the sodium atom and therefore which convergence limit is the relevant one. Hopefully they would give the answers 3s<sup>1</sup> and the relevant convergence limit is for the series n = 3 to n = 4, n = 5, n = 6 ...... n = infinity. This then begs the Objective 3 question "Suggest why this convergent limit is in the ultraviolet-region of the spectrum when for the hydrogen atom the convergence limit for the n = 3 to n = 4, n = 5, n = 6 ...... n = infinity series is in the infrared region of the spectrum".</p><p>There is also a good opportunity to explore some Nature of Science here. Would you mark as correct a student who worked out an enthalpy change and gave the answer in cm<sup>-1</sup>? The IB Chemistry programme places great emphasis on using the correct terminology and units and yet real scientists, i.e. those people who work at The National Institute of Science and Technology, are quite happy to quote an ionization energy in cm<sup>-1</sup> and also not include mol<sup>-1</sup>. Clearly frequency and wavenumber etc. are all related to energy but they are not an actual recognised unit of energy - at least not as the IB sees it.</p><hr class="hidden"></div></section></article><section id="media-extras"><div class="page-actions no-print navbar inline hidden-desktop"><div class="navbar-inner"><ul class="nav"><li><a class="presentation" href="#" onclick="return false;"><i class="fa fa-desktop"></i></a></li><li><a class="print-section-blog" href="#" onclick="return false;"><i class="fa fa-print"></i></a></li><li><a class="page-bookmarker" data-ticket="IB Docs (2) Team" data-pid="17791" href="#" onclick="return false;"><i class="fa fa-star"></i></a></li><li><a class="personal-notes" href="#" onclick="return false;"><i class="fa fa-file-text"></i></a></li><li><a class="" data-toggle="modal" href="#modal-feedback" onclick="return false;"><i class="fa fa-envelope-o"></i></a></li><li class="dropdown"><a class="dropdown-toggle" data-toggle="dropdown" data-target="#" href="#"><i class="fa fa-share-alt"></i></a><ul class="dropdown-menu" role="menu"><li><a class="" target="_blank" title="Share on Twitter" href="https://twitter.com/share?text=%22Convergence+limits%22+-+via+%40InThinker+%23chemistry%0A&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17791%2Fconvergence-limits"><i class="fa fa-twitter-square"></i><span>Twitter</span></a></li><li><a class="" target="_blank" title="Share on Facebook" href="https://www.facebook.com/sharer.php?u=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17791%2Fconvergence-limits&t=Convergence+limits"><i class="fa fa-facebook-square"></i><span>Facebook</span></a></li><li><a class="" href="http://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17791%2Fconvergence-limits"><i class="fa fa-linkedin-square"></i><span>LinkedIn</span></a></li><li><a class="" href="https://plus.google.com/share?url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17791%2Fconvergence-limits"><i class="fa fa-google-plus-square"></i><span>Google +</span></a></li><li><a class="" href="mailto:?subject=Convergence limits&body=In sub-topic 12.1 Electrons in atoms underneath 'Applications and skills' it states " calculation="" of="" the="" value="" of="" the="" first="" ionization="" energy="" from="" spectral="" data="" which="" gives="" the="" wavelength="" or="" frequency="" of="" the="" convergence="" limit"....%0ahttps%3a%2f%2fwww.thinkib.net%2fchemistry%2fpage%2f17791%2fconvergence-limits"=""><i class="fa fa-envelope"></i><span>Email</span></a></li></ul></li><li><a class="" href="chemistry/teaching-materials"><i class="fa fa-puzzle-piece colored"></i></a></li></ul></div></div><div style="border-top: solid 1px #eee;border-bottom: solid 1px #eee;padding: 4px 0 4px 0;line-height: 1em;color: #666;font-size: .8em"><small><em>All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. 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