Experimental Study on Visualisation of the Zeeman Effect Based on Flame Shadows

Experimental Study on Visualisation of the Zeeman Effect Based on Flame Shadows | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Experimental Study on Visualisation of the Zeeman Effect Based on Flame Shadows Yuchen Bai, Zhaohui Chen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8619400/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract When sodium chloride granules are introduced into a flame illuminated by a sodium lamp, a shadow forms behind the flame. Under the influence of an externally applied steady magnetic field, the Zeeman effect can be directly observed through changes in the shadow's brightness. This experimental design demonstrates that the Zeeman effect causes the shadow's colour to lighten as the degree of energy level splitting increases, thereby achieving a visualisation of the Zeeman effect. This experimental approach enables visual observation of the Zeeman effect using low-cost apparatus, thereby resolving the issue of expensive traditional experimental equipment. Theoretical Physics flame shadow sodium ion energy level splitting experimental observation of the Zeeman effect Figures Figure 1 Figure 2 Figure 3 Introduction The Zeeman effect describes the splitting of energy levels under the influence of an applied steady magnetic field. As a pivotal experiment in undergraduate quantum mechanics teaching, it plays a crucial role in students' comprehension and mastery of quantum mechanics. Traditional experiments primarily employ Fabry-Perot gratings, converging lenses, polarising filters and other auxiliary instruments to observe the Zeeman effect [1] - [2] . These methods suffer from drawbacks including the complex adjustment of precision optical components and the high cost of key equipment, presenting significant challenges for experimental operation, instrument procurement and maintenance. The 37th International Young Physicists' Tournament (IYPT) problem ‘Quantum Dimmer’ proposed the physical concept of using magnetic fields to modulate light source brightness. Its core principle lies in altering atomic energy level structures and absorption characteristics via the Zeeman effect. This concept offers a novel perspective for re-examining the classical ‘flame shadow’ phenomenon, namely by applying an external magnetic field to modulate the shadow's brightness, thereby developing it into an intuitive method for studying the Zeeman effect. Based on this, a visualisation experiment of the Zeeman effect using flame shadows was designed. By introducing a small quantity of sodium chloride particles into the flame, and illuminating this flame with a sodium lamp, a shadow appears behind the flame and the flame's colour turns black, with a distinct shadow forming behind it, as shown in Figure 1. Upon applying a uniform, stable magnetic field around the flame, the shadow behind it is observed to fade. As the magnetic induction strength increases, the degree of shadow fading progressively intensifies. This enables analysis of the shadow's generation mechanism and the factors influencing its brightness due to the Zeeman effect, thereby achieving the visualisation objective for experimental Zeeman effect studies. This experiment offers advantages including low cost and ease of operation. 1 Experimental Principle When sodium chloride granules are introduced into a flame, the high temperatures cause the chloride to decompose and vaporise, producing free, dispersed chloride and sodium ions. The flame—particularly its inner, incompletely combusted reducing zone—is filled with various reactive particles such as free radicals and electrons. These reducing agents can donate an electron to sodium ions, reducing them to neutral sodium atoms. As sodium lamps emit yellow light at a wavelength of 589.3nm, when sodium atoms are exposed to this light, their electrons absorb photons of this wavelength, transitioning from the ground state to an excited state. Upon returning to the ground state, these electrons emit photons into the surrounding medium. The absorbed energy is thus ultimately released as photons, thereby diminishing the transmitted light. Under these conditions, observing the reverse side of the flame reveals a distinct black shadow behind it. Upon introduction of a steady magnetic field, the energy levels of sodium atoms undergo splitting, giving rise to the Zeeman effect [3] - [5] . When an external magnetic field is applied, the single absorption line of sodium atoms at 589 nm splits into multiple spectral lines. These split lines increase the likelihood of electrons in sodium atoms absorbing stray light from the flame, thereby reducing absorption by the sodium light source. Consequently, the sodium light passing through the flame increases, Consequently, the brightness of the flame shadow also increases, rendering the shadow lighter. This effect renders the experimental phenomena arising from the Zeeman effect more pronounced. Altering the mass of sodium chloride granules introduced changes the total number of sodium atoms in the ground state within the flame. As the mass of sodium chloride particles increases, more sodium atoms capable of absorbing 589 nm photons become available, enhancing absorption of incident light and reducing transmitted light. Consequently, the flame shadow darkens. Therefore, under constant external magnetic field conditions, the flame shadow becomes more pronounced with increased sodium chloride particles. 2 Design and Experimental Procedure of a Low-Cost Experimental Apparatus Based on the aforementioned experimental principle, an apparatus was constructed for experimentation, with specific equipment details outlined in Table 1 . Table 1 Experimental Apparatus Laboratory apparatus number Explanation Neodymium magnet several Diameter 80mm, edge magnetic field ≈ 0.22 T Sodium chloride granules several Analytical grade Sodium lamp 1 Wavelength: 589.3 nm Power: 100 W Multimeter 1 Measuring range: 0–200 M photoresistor 1 Illuminance range: 1-100000lx Slotted cardboard 1 The slit width is approximately 20mm Wet wipes several Encapsulate magnets to prevent demagnetisation from reflections and high temperatures. 3D-printed mounting base several Fixed magnet for convenient measurement of spacing Backdrop 1 White Alcohol lamp 1 None To detect the brightness of the flame shadow, a photoresistor was introduced for measurement, represented by the bright yellow rectangular device on the right in Fig. 2 . The specific principle is as follows: when sodium chloride particles are added to the flame core of an alcohol burner, and an external steady magnetic field is applied via a magnet to induce the Zeeman effect, the single absorption spectral line of sodium atoms at 589 nm splits into multiple spectral lines. This deviation from the peak of the sodium lamp emission spectrum results in reduced absorption of the light source by the flame. Consequently, increased light transmission through the flame reduces the photoresistor's resistance. As magnetic induction strengthens, the degree of energy level splitting becomes progressively more pronounced, causing the resistance value to decrease continuously. The experimental procedure is as follows: 1) In a relatively dark environment, switch on the sodium lamp and allow it to warm up for 10 minutes to enhance its performance [ 6 ] . 2) Cut a narrow slit approximately 20 millimetres wide in opaque thick cardboard. Position the alcohol burner within this slit, placing the cardboard between the sodium lamp and the burner so that light is directed solely through the slit onto the burner's flame. 3) Mark the origin on graph paper, aligning the centre of the alcohol burner as closely as possible with this point. Position the powerful magnet, wrapped in a damp cloth, onto the 3D-printed mounting base placed on the graph paper. Ensure it sits at the same height as the flame. Record the distance d from the origin at intervals of 250 mm, 200 mm, 150 mm, 100 mm, and 50 mm. 4) Place pre-weighed and moistened sodium chloride granules into the combustion spoon to prevent high-temperature splatter. 5) Secure the photoresistor onto the white background board. Adjust its position to maximise coverage by the flame's shadow. Once the flame shape stabilises, use a mobile phone to record the multimeter readings every second. Take three readings, calculate the average, and record it. 6) Keeping the position of the strong magnet constant, vary the mass of added sodium chloride granules between 0 and 6g in 1g increments. Conduct experiments and record data for each mass, as shown in the table below. 7) Introduce other substances into the flame and repeat the above steps to enhance the accuracy of the experiment. 3 Data Analysis and Research Findings Table 2 Record of Substances Generating Flame Shadows Substances added to the flame calcium chloride Potassium chloride Lithium chloride sodium carbonate sodium chloride Does it produce shadows? No No No Yes Yes As shown in Table 2 , under the experimental conditions set forth, only sodium ions were capable of absorbing energy and producing observable phenomena, thereby ruling out the possibility of interference from other elements. Further experiments were conducted by varying the concentration of sodium chloride, with the results recorded in Table 3 . Table 3 Data Record Sheet for the Effect of Sodium Chloride Concentration on Flame Shadowing in the Absence of Magnetic Fields Sodium chloride content (g) First Resistance measurement (kΩ) Second resistance measurement(kΩ) Third resistance measurement(kΩ) Average resistance value(kΩ) 0 19.3 20.1 19.6 19.7 1.0 62.3 61.8 61.9 62.0 2.0 68.6 69.3 68.4 68.8 3.0 74.9 74.7 75.2 74.3 4.0 81.4 81.0 81.3 81.2 5.0 86.1 86.4 86.1 86.2 6.0 92.3 91.5 92.1 92.3 By altering the magnitude of the magnetic field at different sodium chloride concentrations—that is, by adjusting the distance between the magnets—the recorded data are presented in Table 4 . Table 4 Data Record Sheet for the Effect of Sodium Chloride Content and Magnet Spacing on Flame Shadowing Sodium chloride content(g) Average resistance at different distances from the magnet(kΩ) 250mm 200mm 150mm 100mm 50mm 0 19.7 19.2 20.0 18.9 19.1 1.0 54.9 43.3 39.1 32.9 27.3 2.0 56.6 48.2 42.4 38.1 34.4 3.0 69.2 57.9 51.1 43.4 39.7 4.0 76.6 68.5 57.3 50.9 46.1 5.0 80.2 76.7 65.3 57.7 51.2 6.0 83.7 77.4 71.1 63.6 59.0 From the experimental data above, Fig. 3 can be derived. The horizontal axis represents the distance between the magnet and the flame centre, while the vertical axis denotes the resistance value of the photoresistor. The different curves from top to bottom illustrate the variation in photoresistor resistance caused by changes in the distance from the magnet for different masses of sodium chloride. The graph reveals that when sodium chloride mass is 0g, the resistance value remains unchanged regardless of the magnet's distance. For sodium chloride masses ranging from 1.0g to 6.0g, the resistance decreases as the magnet's distance diminishes. It is also evident that, with the distance of the strong magnet remaining constant, increasing the mass of added sodium chloride particles progressively diminishes the brightness of the shadow cast by the flame. This causes the photoresistor's resistance to rise continuously. For other substances lacking sodium ions, no significant experimental phenomena occur, thereby ensuring the accuracy of the experiment. 4 Experimental Influencing Factors and Apparatus Improvements The individual data points displayed in Fig. 3 deviate from theoretical values. An error analysis is therefore conducted as follows: Firstly, both inadequate preheating of the sodium lamp and frequent switching on of the lamp can adversely affect the light source. The sodium lamp primarily consists of a bulb casing and an internal narrow arc tube. This arc tube is typically filled with a mixture of sodium and mercury vapour. Upon switching on the lamp, an electric arc between the electrodes heats the sodium vapour within the tube, and mercury within the arc tube into a gaseous state [ 6 ] . Electrons emitted from the cathode end of the tube collide with atoms as they travel towards the anode, imparting energy to these atoms and raising them to an excited state. When these atoms return to their ground state, the excess energy is released in the form of light [ 7 ]−[ 8 ] . Frequent switching and insufficient preheating both reduce luminous efficiency, diminishing the light emitted by the sodium lamp. This reduces the energy absorbed by sodium ions, thereby affecting the experimental data and conclusions obtained. Secondly, the measurement of sodium chloride mass lacks precision. This can be addressed by weighing sodium chloride granules using an electronic balance accurate to 0.01g, avoiding frequent switching of the sodium lamp, and ensuring thorough preheating during experiments to minimise error. Thirdly, uneven ion distribution occurs. Airflow disperses the sodium ion cloud generated within the flame, disrupting its stable distribution and trajectory within the magnetic field. This affects the contrast of shadows, introducing uncontrollable variables. The magnetic induction strength generated by the powerful magnet employed in the experiment at any given point in space can only be measured approximately. It is impossible to determine the specific range of magnetic induction strength required to produce distinct experimental phenomena, nor can a quantitative mathematical relationship between magnetic induction strength and the brightness of the flame shadow be established. Future experiments may utilise Helmholtz coils as an alternative to the powerful magnet [9]. Adjusting the current value via a PID controller would enable more precise determination of the minimum magnetic flux density required to observe the experimental phenomena, thereby improving the experimental outcomes. 5 Closing Remarks The experiment determines the occurrence of the Zeeman effect by observing changes in the brightness of the flame's shadow, characterised by low-cost apparatus and straightforward procedures. The shadow is produced because sodium ions, introduced into the flame, absorb sodium light, causing internal electron transitions that cast a shadow behind the flame. When a steady magnetic field is applied, the Zeeman effect occurs, causing the energy levels of sodium atoms to split. As the distance between the strong magnet and the flame's core decreases, the degree of energy level splitting increases. This causes the single absorption line of sodium atoms at 589 nm to split into multiple spectral lines. These split spectral lines exhibit centre frequencies displaced from the peak emission line of the sodium lamp. This displacement reduces the flame's absorption of the light source, increasing transmitted light and consequently decreasing the photoresistor's resistance, thereby lightening the shadow. Concurrently, while maintaining a constant magnetic field strength, increasing the quantity of sodium chloride particles added causes the flame shadow to gradually darken. This enables visual experimental investigation of the Zeeman effect. This flame shadow investigation not only deepens comprehension of the Zeeman effect but also offers straightforward procedures, simple operation, low cost, and reproducibility. Its suitability for widespread adoption makes it an ideal demonstration experiment for teaching the Zeeman effect in higher education institutions. References He Chenjuan L, Hongbo W, Haibo G, Wenping X, Jun (2024) Application and teaching of solid F-P etalon in Zeeman effect experiment [. J ] Phys Exp 44(08):53–61 Wang Jianchun Z, Wei (2022) The problem-oriented inquiry teaching practice of Zeeman effect in modern physics experiment [. J ] Phys Eng 32(03):46–49 Zeng Jinyan (2013) Quantum Mechanics: Volume I [ M ]. 5, Beijing. Science Baojun Zhu ect Observation of Zeeman splitting effect in a laser-driven coil[J].Matter and Radiation at Extremes,2022(02):18–24 Wang Daqi Three methods for deriving Zeeman effect [J].Electronic technology,2021,50(03):40–42 Bao, Guanjia (2017) Design of high voltage sodium lamp electronic ballast based on SiC device [ D ]. Anhui University of Technology Chen Jingjing L, Jianke L, Shan H, Jianxin R Wenjie. Test analysis and modeling of typical lighting source load characteristics [J].Building electrical,2025,44(02):50–55 Wang T Application of electronic ballasts for high-pressure sodium and metal halide lamps [. J ] Application energy Technol, 2015(03):42–46 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8619400","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":575635656,"identity":"ea379674-519c-485b-8160-252aaea0bda2","order_by":0,"name":"Yuchen 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08:22:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":566073,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental Setup Diagram\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8619400/v1/513441a3519911111e92de31.png"},{"id":100532951,"identity":"79f7d775-83b2-4099-b4ed-f16851266f09","added_by":"auto","created_at":"2026-01-19 02:44:48","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":108947,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIlluminance values of flame shadows under different 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field. As a pivotal experiment in undergraduate quantum mechanics teaching, it plays a crucial role in students\u0026apos; comprehension and mastery of quantum mechanics. Traditional experiments primarily employ Fabry-Perot gratings, converging lenses, polarising filters and other auxiliary instruments to observe the Zeeman effect\u003csup\u003e[1]\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e\u003csup\u003e[2]\u003c/sup\u003e. These methods suffer from drawbacks including the complex adjustment of precision optical components and the high cost of key equipment, presenting significant challenges for experimental operation, instrument procurement and maintenance. The 37th International Young Physicists\u0026apos; Tournament (IYPT) problem \u0026lsquo;Quantum Dimmer\u0026rsquo; proposed the physical concept of using magnetic fields to modulate light source brightness. Its core principle lies in altering atomic energy level structures and absorption characteristics via the Zeeman effect. This concept offers a novel perspective for re-examining the classical \u0026lsquo;flame shadow\u0026rsquo; phenomenon, namely by applying an external magnetic field to modulate the shadow\u0026apos;s brightness, thereby developing it into an intuitive method for studying the Zeeman effect. Based on this, a visualisation experiment of the Zeeman effect using flame shadows was designed. By introducing a small quantity of sodium chloride particles into the flame, and illuminating this flame with a sodium lamp, a shadow appears behind the flame and the flame\u0026apos;s colour turns black, with a distinct shadow forming behind it, as shown in Figure 1. Upon applying a uniform, stable magnetic field around the flame, the shadow behind it is observed to fade. As the magnetic induction strength increases, the degree of shadow fading progressively intensifies. This enables analysis of the shadow\u0026apos;s generation mechanism and the factors influencing its brightness due to the Zeeman effect, thereby achieving the visualisation objective for experimental Zeeman effect studies. This experiment offers advantages including low cost and ease of operation.\u003c/p\u003e"},{"header":"1 Experimental Principle","content":"\u003cp\u003eWhen sodium chloride granules are introduced into a flame, the high temperatures cause the chloride to decompose and vaporise, producing free, dispersed chloride and sodium ions. The flame\u0026mdash;particularly its inner, incompletely combusted reducing zone\u0026mdash;is filled with various reactive particles such as free radicals and electrons. These reducing agents can donate an electron to sodium ions, reducing them to neutral sodium atoms. As sodium lamps emit yellow light at a wavelength of 589.3nm, when sodium atoms are exposed to this light, their electrons absorb photons of this wavelength, transitioning from the ground state to an excited state. Upon returning to the ground state, these electrons emit photons into the surrounding medium. The absorbed energy is thus ultimately released as photons, thereby diminishing the transmitted light. Under these conditions, observing the reverse side of the flame reveals a distinct black shadow behind it.\u003c/p\u003e\n\u003cp\u003eUpon introduction of a steady magnetic field, the energy levels of sodium atoms undergo splitting, giving rise to the Zeeman effect\u003csup\u003e[3]\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e\u003csup\u003e[5]\u003c/sup\u003e. When an external magnetic field is applied, the single absorption line of sodium atoms at 589 nm splits into multiple spectral lines. These split lines increase the likelihood of electrons in sodium atoms absorbing stray light from the flame, thereby reducing absorption by the sodium light source. Consequently, the sodium light passing through the flame increases, Consequently, the brightness of the flame shadow also increases, rendering the shadow lighter. This effect renders the experimental phenomena arising from the Zeeman effect more pronounced.\u003c/p\u003e\n\u003cp\u003eAltering the mass of sodium chloride granules introduced changes the total number of sodium atoms in the ground state within the flame. As the mass of sodium chloride particles increases, more sodium atoms capable of absorbing 589 nm photons become available, enhancing absorption of incident light and reducing transmitted light. Consequently, the flame shadow darkens. Therefore, under constant external magnetic field conditions, the flame shadow becomes more pronounced with increased sodium chloride particles.\u003c/p\u003e"},{"header":"2 Design and Experimental Procedure of a Low-Cost Experimental Apparatus","content":"\u003cp\u003eBased on the aforementioned experimental principle, an apparatus was constructed for experimentation, with specific equipment details outlined in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental Apparatus\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLaboratory apparatus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003enumber\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExplanation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNeodymium magnet\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eseveral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDiameter 80mm, edge magnetic field\u0026thinsp;\u0026asymp;\u0026thinsp;0.22 T\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSodium chloride granules\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eseveral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnalytical grade\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSodium lamp\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWavelength: 589.3 nm Power: 100 W\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMultimeter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMeasuring range: 0\u0026ndash;200 M\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ephotoresistor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIlluminance range: 1-100000lx\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSlotted cardboard\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThe slit width is approximately 20mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWet wipes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eseveral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEncapsulate magnets to prevent demagnetisation from reflections and high temperatures.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3D-printed mounting base\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eseveral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFixed magnet for convenient measurement of spacing\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBackdrop\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWhite\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlcohol lamp\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNone\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo detect the brightness of the flame shadow, a photoresistor was introduced for measurement, represented by the bright yellow rectangular device on the right in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The specific principle is as follows: when sodium chloride particles are added to the flame core of an alcohol burner, and an external steady magnetic field is applied via a magnet to induce the Zeeman effect, the single absorption spectral line of sodium atoms at 589 nm splits into multiple spectral lines. This deviation from the peak of the sodium lamp emission spectrum results in reduced absorption of the light source by the flame. Consequently, increased light transmission through the flame reduces the photoresistor's resistance. As magnetic induction strengthens, the degree of energy level splitting becomes progressively more pronounced, causing the resistance value to decrease continuously.\u003c/p\u003e \u003cp\u003eThe experimental procedure is as follows:\u003c/p\u003e \u003cp\u003e1) In a relatively dark environment, switch on the sodium lamp and allow it to warm up for 10 minutes to enhance its performance \u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e2) Cut a narrow slit approximately 20 millimetres wide in opaque thick cardboard. Position the alcohol burner within this slit, placing the cardboard between the sodium lamp and the burner so that light is directed solely through the slit onto the burner's flame.\u003c/p\u003e \u003cp\u003e3) Mark the origin on graph paper, aligning the centre of the alcohol burner as closely as possible with this point. Position the powerful magnet, wrapped in a damp cloth, onto the 3D-printed mounting base placed on the graph paper. Ensure it sits at the same height as the flame. Record the distance d from the origin at intervals of 250 mm, 200 mm, 150 mm, 100 mm, and 50 mm.\u003c/p\u003e\n\u003cp\u003e4) Place pre-weighed and moistened sodium chloride granules into the combustion spoon to prevent high-temperature splatter.\u003c/p\u003e\n\u003cp\u003e5) Secure the photoresistor onto the white background board. Adjust its position to maximise coverage by the flame's shadow. Once the flame shape stabilises, use a mobile phone to record the multimeter readings every second. Take three readings, calculate the average, and record it.\u003c/p\u003e \u003cp\u003e6) Keeping the position of the strong magnet constant, vary the mass of added sodium chloride granules between 0 and 6g in 1g increments. Conduct experiments and record data for each mass, as shown in the table below.\u003c/p\u003e \u003cp\u003e7) Introduce other substances into the flame and repeat the above steps to enhance the accuracy of the experiment.\u003c/p\u003e"},{"header":"3 Data Analysis and Research Findings","content":"\u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRecord of Substances Generating Flame Shadows\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubstances added to the flame\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecalcium chloride\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePotassium chloride\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLithium chloride\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003esodium carbonate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003esodium chloride\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDoes it produce shadows?\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, under the experimental conditions set forth, only sodium ions were capable of absorbing energy and producing observable phenomena, thereby ruling out the possibility of interference from other elements.\u003c/p\u003e \u003cp\u003eFurther experiments were conducted by varying the concentration of sodium chloride, with the results recorded in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eData Record Sheet for the Effect of Sodium Chloride Concentration on Flame Shadowing in the Absence of Magnetic Fields\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSodium chloride content (g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFirst Resistance measurement\u003c/p\u003e \u003cp\u003e(kΩ)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSecond resistance measurement(kΩ)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eThird resistance measurement(kΩ)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAverage resistance value(kΩ)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e19.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e19.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e62.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e61.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e62.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e68.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e69.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e68.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e68.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e74.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e74.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e75.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e74.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e81.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e81.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e81.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e81.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e86.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e86.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e86.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e86.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e92.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e91.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e92.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e92.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBy altering the magnitude of the magnetic field at different sodium chloride concentrations\u0026mdash;that is, by adjusting the distance between the magnets\u0026mdash;the recorded data are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eData Record Sheet for the Effect of Sodium Chloride Content and Magnet Spacing on Flame Shadowing\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSodium chloride content(g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e \u003cp\u003eAverage resistance at different distances from the magnet(kΩ)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e250mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e200mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e150mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e100mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e50mm\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e19.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e54.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e43.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e39.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e32.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e27.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e56.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e42.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e38.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e34.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e69.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e43.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e39.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e76.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e68.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e57.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e46.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e76.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e65.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e57.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e51.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e83.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e77.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e71.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e63.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e59.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFrom the experimental data above, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e can be derived. The horizontal axis represents the distance between the magnet and the flame centre, while the vertical axis denotes the resistance value of the photoresistor. The different curves from top to bottom illustrate the variation in photoresistor resistance caused by changes in the distance from the magnet for different masses of sodium chloride. The graph reveals that when sodium chloride mass is 0g, the resistance value remains unchanged regardless of the magnet's distance. For sodium chloride masses ranging from 1.0g to 6.0g, the resistance decreases as the magnet's distance diminishes. It is also evident that, with the distance of the strong magnet remaining constant, increasing the mass of added sodium chloride particles progressively diminishes the brightness of the shadow cast by the flame. This causes the photoresistor's resistance to rise continuously. For other substances lacking sodium ions, no significant experimental phenomena occur, thereby ensuring the accuracy of the experiment.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4 Experimental Influencing Factors and Apparatus Improvements","content":"\u003cp\u003eThe individual data points displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e deviate from theoretical values. An error analysis is therefore conducted as follows: Firstly, both inadequate preheating of the sodium lamp and frequent switching on of the lamp can adversely affect the light source. The sodium lamp primarily consists of a bulb casing and an internal narrow arc tube. This arc tube is typically filled with a mixture of sodium and mercury vapour. Upon switching on the lamp, an electric arc between the electrodes heats the sodium vapour within the tube, and mercury within the arc tube into a gaseous state\u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e. Electrons emitted from the cathode end of the tube collide with atoms as they travel towards the anode, imparting energy to these atoms and raising them to an excited state. When these atoms return to their ground state, the excess energy is released in the form of light \u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u0026minus;[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e. Frequent switching and insufficient preheating both reduce luminous efficiency, diminishing the light emitted by the sodium lamp. This reduces the energy absorbed by sodium ions, thereby affecting the experimental data and conclusions obtained. Secondly, the measurement of sodium chloride mass lacks precision. This can be addressed by weighing sodium chloride granules using an electronic balance accurate to 0.01g, avoiding frequent switching of the sodium lamp, and ensuring thorough preheating during experiments to minimise error. Thirdly, uneven ion distribution occurs. Airflow disperses the sodium ion cloud generated within the flame, disrupting its stable distribution and trajectory within the magnetic field. This affects the contrast of shadows, introducing uncontrollable variables.\u003c/p\u003e \u003cp\u003eThe magnetic induction strength generated by the powerful magnet employed in the experiment at any given point in space can only be measured approximately. It is impossible to determine the specific range of magnetic induction strength required to produce distinct experimental phenomena, nor can a quantitative mathematical relationship between magnetic induction strength and the brightness of the flame shadow be established. Future experiments may utilise Helmholtz coils as an alternative to the powerful magnet [9]. Adjusting the current value via a PID controller would enable more precise determination of the minimum magnetic flux density required to observe the experimental phenomena, thereby improving the experimental outcomes.\u003c/p\u003e"},{"header":"5 Closing Remarks","content":"\u003cp\u003eThe experiment determines the occurrence of the Zeeman effect by observing changes in the brightness of the flame's shadow, characterised by low-cost apparatus and straightforward procedures. The shadow is produced because sodium ions, introduced into the flame, absorb sodium light, causing internal electron transitions that cast a shadow behind the flame. When a steady magnetic field is applied, the Zeeman effect occurs, causing the energy levels of sodium atoms to split. As the distance between the strong magnet and the flame's core decreases, the degree of energy level splitting increases. This causes the single absorption line of sodium atoms at 589 nm to split into multiple spectral lines. These split spectral lines exhibit centre frequencies displaced from the peak emission line of the sodium lamp. This displacement reduces the flame's absorption of the light source, increasing transmitted light and consequently decreasing the photoresistor's resistance, thereby lightening the shadow. Concurrently, while maintaining a constant magnetic field strength, increasing the quantity of sodium chloride particles added causes the flame shadow to gradually darken. This enables visual experimental investigation of the Zeeman effect.\u003c/p\u003e \u003cp\u003eThis flame shadow investigation not only deepens comprehension of the Zeeman effect but also offers straightforward procedures, simple operation, low cost, and reproducibility. Its suitability for widespread adoption makes it an ideal demonstration experiment for teaching the Zeeman effect in higher education institutions.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHe Chenjuan L, Hongbo W, Haibo G, Wenping X, Jun (2024) Application and teaching of solid F-P etalon in Zeeman effect experiment [. J ] Phys Exp 44(08):53\u0026ndash;61\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Jianchun Z, Wei (2022) The problem-oriented inquiry teaching practice of Zeeman effect in modern physics experiment [. J ] Phys Eng 32(03):46\u0026ndash;49\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZeng Jinyan (2013) Quantum Mechanics: Volume I [ M ]. 5, Beijing. Science\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBaojun Zhu ect Observation of Zeeman splitting effect in a laser-driven coil[J].Matter and Radiation at Extremes,2022(02):18\u0026ndash;24\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Daqi Three methods for deriving Zeeman effect [J].Electronic technology,2021,50(03):40\u0026ndash;42\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBao, Guanjia (2017) Design of high voltage sodium lamp electronic ballast based on SiC device [ D ]. Anhui University of Technology\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen Jingjing L, Jianke L, Shan H, Jianxin R Wenjie. Test analysis and modeling of typical lighting source load characteristics [J].Building electrical,2025,44(02):50\u0026ndash;55\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang T Application of electronic ballasts for high-pressure sodium and metal halide lamps [. J ] Application energy Technol, 2015(03):42\u0026ndash;46\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"flame shadow, sodium ion energy level splitting, experimental observation of the Zeeman effect","lastPublishedDoi":"10.21203/rs.3.rs-8619400/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8619400/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWhen sodium chloride granules are introduced into a flame illuminated by a sodium lamp, a shadow forms behind the flame. Under the influence of an externally applied steady magnetic field, the Zeeman effect can be directly observed through changes in the shadow's brightness. This experimental design demonstrates that the Zeeman effect causes the shadow's colour to lighten as the degree of energy level splitting increases, thereby achieving a visualisation of the Zeeman effect. This experimental approach enables visual observation of the Zeeman effect using low-cost apparatus, thereby resolving the issue of expensive traditional experimental equipment.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"Experimental Study on Visualisation of the Zeeman Effect Based on Flame Shadows","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-19 02:44:43","doi":"10.21203/rs.3.rs-8619400/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ce7bef76-5985-4281-98c9-a89484a68287","owner":[],"postedDate":"January 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61251162,"name":"Theoretical Physics"}],"tags":[],"updatedAt":"2026-01-19T02:44:43+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-19 02:44:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8619400","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8619400","identity":"rs-8619400","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}