Improved Millikan oil drop experiment device

Abstract

An improved Millikan oil drop experiment device comprises an oil drop ionization module and a temperature control assembly, and the temperature control assembly is attached to the outer side of the oil drop ionization module. The temperature control assembly is a groove body with an upper opening, and cold source substances are contained in the groove body. Or the temperature control assembly is in a cavity shape, and cold source materials are stored in an inner cavity. Or the temperature control assembly is a semiconductor cooler, and the cold end of the semiconductor cooler is attached to the outer side of the oil drop ionization module. According to the utility model, the temperature control assembly tightly attached to the oil drop ionization chamber is designed, the temperature of an experimental oil drop environment is reduced through heat conduction, the temperature change caused by long-time work of an infrared light source in the oil drop ionization chamber is reduced, and the Brownian motion of oil drops is reduced. Meanwhile, the temperature control assembly can cover the gap part of the oil drop ionization chamber, so that the air tightness of the experimental device is improved, and the influence of air flow on the lateral deviation of the experimental oil drops is reduced.

Description

Technical Field

[0001] This invention relates to the field of physical experimental apparatus, specifically an improved Millikan oil drop experimental apparatus. Background Technology

[0002] The Millikan oil drop experiment is a physics experiment for measuring the charge of an electron. By observing the motion of charged oil droplets in electric and gravitational fields, it measures the charge and mass of the droplets to verify the fundamental unit of charge, determine the precise value of the fundamental charge, measure the mass of the electron, and confirm that the charge of any charged body is an integer multiple of the fundamental charge, revealing the quantum nature of the electron. With the continuous development of technology, researchers have continuously improved the Millikan oil drop experiment apparatus to enhance its precision and accuracy and make it suitable for measuring more samples. Wang Zikang et al. developed an intelligent instrument for the Millikan oil drop experiment based on the Android embedded system. Huang Xiaoyuan et al. designed an automatically adjustable image acquisition system for the Millikan oil drop experiment based on LabVIEW. Zhang Qingfan et al. designed an intelligent testing device for the Millikan oil drop experiment by automatically capturing appropriate oil droplets using a high-voltage square wave signal testing method, proposing a new and more effective testing method for the Millikan oil drop experiment. Zhou Haitao et al., using VB as the main development tool and combining CCD, microcontroller, and serial port technologies, designed and developed an intelligent Millikan oil drop experimental system, making data processing more convenient and representing an intelligent improvement over the traditional Millikan oil drop experiment. Cai Xuhong et al., based on VC++, employed a cyclic trial-and-error method for data processing to improve the accuracy of calculating oil drop charge. V. Halyo, Peter C. Kim et al. used an automated Millikan oil drop method to search for free fractionally charged elementary particles and calculate charged electrons. GDPutt et al. used an improved Millikan oil drop device to search for fractionally charged particles in tungsten, enabling the exploration of other particles. Gordon L. Shaw et al. used an automated Millikan instrument to detect free quarks generated by the collision of GeV / nuclear oxygen nuclei with a BNL heavy target, achieving exploration at the molecular level. Michael A. Lindgeren et al. captured charged particles generated by a 1.9 GeV / nucleon iron beam incident on a lead target (i.e., heavy ion collision), and used Millikan's automated oil drop apparatus to detect the fractional charge of two samples, greatly improving the accuracy of the experiment. These studies all improved and innovated experimental methods and equipment, making the measurement of electron charge more precise. However, some problems still exist in the experiments, such as the influence of oil droplet vibration and air resistance on the measurement results, and the complexity of experimental operations. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides an improved Millikan oil drop experimental apparatus, namely, a Millikan oil drop experimental apparatus that reduces the influence of Brownian motion.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] An improved Millikan oil drop experiment apparatus includes an oil drop ionization module and a temperature control component, wherein the temperature control component is tightly fitted and wrapped around the outside of the oil drop ionization module.

[0006] Furthermore, the temperature control component is a tank with an opening at the top, and the tank contains a cold source substance.

[0007] Furthermore, the temperature control component is cavity-shaped, with the inner cavity storing cold source material.

[0008] Furthermore, the temperature control component is provided with a cold source material inlet and a cold source material outlet.

[0009] Furthermore, the temperature control component is a semiconductor cooler.

[0010] Furthermore, the cold end of the semiconductor cooler is attached to the outside of the oil droplet ionization module.

[0011] Furthermore, the oil droplet ionization module includes an upper chamber, a lower chamber, and an electric field generating module.

[0012] The electric field generating module is installed in the lower chamber. The electric field generating module includes a lower electrode, an annular partition, and an upper electrode. The annular partition is installed between the lower electrode and the upper electrode. The cavity between the lower electrode, the annular partition, and the upper electrode is an oil droplet movement chamber.

[0013] The upper chamber wall is provided with an oil droplet injection through hole, the top of the lower chamber is provided with a first oil droplet through hole, the upper electrode is provided with a second oil droplet through hole, the lower chamber wall is provided with a lens mounting through hole, and the annular partition is provided with an observation through hole.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] This invention comprehensively considers the Brownian motion of tiny oil droplets, the influence of air buoyancy and air discontinuity on the oil droplet's air viscosity coefficient, and the significant deviations in experimental droplet radii. A temperature control component is designed to fit closely to the oil droplet ionization chamber. This component can store ice or other cold sources to lower the temperature of the experimental oil droplet environment through heat conduction, reducing temperature changes caused by prolonged operation of the infrared light source in the ionization chamber and thus reducing the Brownian motion of the oil droplets. Simultaneously, because the temperature control component covers the gaps in the ionization chamber, it increases the airtightness of the experimental device and reduces the lateral influence of airflow on the experimental oil droplets. For data analysis and processing, Origin is used for data analysis and fitting to analyze the influence of different oil droplet radii on the charge q, providing a range reference for selecting suitable oil droplets for this experiment. The oil droplet radius and charge e are calculated using MATLAB's GUI, and the charge e is calculated using the positive integer average method. The results show that by reducing the influence of external factors and analyzing and fitting the data, more accurate experimental results can be obtained, providing a new approach for studying and measuring the charge of other particles. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of a charged oil droplet between two parallel plates.

[0017] Figure 2 This is a schematic diagram of the force equilibrium of an oil droplet.

[0018] Figure 3 This is a schematic diagram of the overall experimental setup.

[0019] Figure 4 This is a schematic diagram of the assembly of the temperature control component and the oil droplet ionization module.

[0020] Figure 5 The graph shows the relationship between the oil droplet's falling time t and its radius r.

[0021] Figure 6 This is a schematic diagram of oil droplets of different radii falling.

[0022] Figure 7 This is a diagram showing the Brownian motion trajectory of a tiny oil droplet.

[0023] Figure 8 The graph shows the relationship between the experimental radius r of the oil droplet and its charge q.

[0024] Figure 9 The figure shows the fitted curve of the oil droplet's experimental radius r versus its charge q.

[0025] Figure 10 The graph shows the relationship between the experimental radius r of the oil droplet and the charge e.

[0026] Figure 11This is a comparison chart of the charge e at room temperature and the charge e at low temperature with the standard charge value e (orange: charge e at room temperature; green: standard charge value e; purple: charge e at low temperature).

[0027] Figure 12 This is a comparison chart of the charge e at room temperature and the charge e at low temperature with the standard value e (orange: charge e at room temperature; green: standard value e; purple: charge e at low temperature).

[0028] Figure 13 This is a comparison diagram of the Brownian motion of oil droplets under low temperature and normal temperature conditions.

[0029] Figure 14 Comparison of Brownian motion of oil droplets at different temperatures under conditions where air buoyancy is ignored (orange: charge e at room temperature; green: standard charge e; purple: charge e at low temperature).

[0030] Figure 15 A comparison of Brownian motion of oil droplets at different temperatures under the condition of considering air buoyancy (orange: charge e at room temperature; green: standard charge e; purple: charge e at low temperature).

[0031] Figure 16 This is a comparison chart of the charge e of five sets of experiments on the same oil droplet and different oil droplets at room temperature (orange: charge e at room temperature; green: standard charge value e; purple: charge e at low temperature).

[0032] Figure 17 This is a schematic diagram of the oil droplet ionization module.

[0033] Figure 18 This is a schematic diagram of the assembly of a cavity-shaped temperature control component and an oil droplet ionization module.

[0034] In the figure, the lower electrode is 1, the oil droplet movement chamber is 2, the lens mounting through hole is 3, the upper electrode is 4, the opening size switch of the first oil droplet through hole is 5, the upper chamber is 6, the first oil droplet through hole is 7, the oil droplet injection through hole is 8, the lower chamber is 9, the upper electrode compression spring is 10, the annular partition is 12, the temperature control component is 11, the observation through hole is 13, the second oil droplet through hole is 14, the cold source material outlet is 15, and the cold source material inlet is 16. Detailed Implementation

[0035] The technical solution of the present invention will be further illustrated below through embodiments.

[0036] Example 1

[0037] 1. Experimental Principle

[0038] 1.1 Charge of oil droplets when air buoyancy and discontinuity are neglected

[0039] Using the sprayer of a Millikan oil droplet apparatus, oil droplets are sprayed between two horizontally placed parallel charged plates spaced d apart. Figure 1 As shown.

[0040] Oil droplets become charged due to friction during spraying. Let the mass of the oil droplet be m, its charge be q, and the voltage between the two parallel charged plates be U. Then the oil droplet will experience two forces simultaneously between the plates. For example... Figure 1 As shown. When the voltage U between the two plates is adjusted, the two forces can be balanced, at which point:

[0041]

[0042] According to equation (1), measuring the electric charge q requires measuring U and d, as well as the mass m of the oil droplet. Since m is very small and cannot be measured directly, a special method is used for measurement.

[0043] The method is as follows: When no voltage is applied to the parallel plates, the oil droplets accelerate downwards due to gravity. Due to air resistance *f*, after falling a certain distance and reaching a certain velocity *v*, the resistance *f* balances with the gravity *mg*, as shown below. Figure 2 As shown (ignoring air buoyancy), the oil droplet will descend at a constant speed.

[0044] Under the influence of surface tension, the oil droplet takes the shape of a small sphere, i.e., the mass m of the sphere is:

[0045]

[0046] At this point:

[0047] f=6πrηv=mg (3)

[0048] Where η is the viscosity coefficient of air and r is the radius of the oil droplet.

[0049] The oil droplet radius r can then be expressed as:

[0050]

[0051] After transformation and modification, we can obtain Stokes' Law:

[0052]

[0053] Where b is a correction constant, b = 6.17 × 10 -6 m·cmHg, where p is atmospheric pressure in cmHg. Based on the modified viscous drag formula, the oil droplet radius r is:

[0054]

[0055] As for the velocity v of the oil droplet descending at a constant speed, it can be measured as follows: When the voltage U between the two plates is zero, let the distance the oil droplet descends at a constant speed be l, and the time be t, that is:

[0056]

[0057] Finally, the formula for calculating the charge of an oil droplet is obtained:

[0058]

[0059] 1.2 Calculation of the charge of oil droplets under air buoyancy and discontinuity

[0060] Since the experiment was conducted in an atmospheric environment, the oil droplets should be subject to buoyancy during their fall. Therefore, according to equations (1) and (3), the buoyancy force F is:

[0061]

[0062] Where ρ' is the mass density of air. It is easy to see that when the buoyancy of air on the oil droplets is taken into account, ρ in equation (8) needs to be corrected to ρ-ρ', that is, the increment of ρ before and after taking into account the buoyancy of air is Δρ=-ρ'. Therefore, the increment of q can be obtained by differentiating equation (8).

[0063]

[0064] Since the radius of the oil droplet is very close to the mean free path of air molecules at room temperature, air cannot be considered a continuous homogeneous medium at this point, and its viscosity coefficient η' is corrected as follows:

[0065]

[0066] The radius and charge of the oil droplet should then be corrected as follows:

[0067]

[0068] Under typical parameter settings, it can be found that the relative error caused by ignoring air buoyancy is no more than 0.1%, which has a relatively small impact on the experimental results. Therefore, the air buoyancy on the oil droplets can be ignored in both static and dynamic methods. However, when considering the discontinuity of air, it is necessary to fully consider the combination of air buoyancy and air discontinuity; otherwise, it will cause a large error.

[0069] Therefore, the buoyancy of the air and the discontinuity should be considered simultaneously, and the expression for the charge of the oil droplet is:

[0070]

[0071] Research has found that for a given oil droplet, if its charge q is changed, the voltage that allows the droplet to reach equilibrium must be a specific value U. n By studying the patterns of these voltage changes, we can find that they satisfy the following equation:

[0072]

[0073] In the formula, n = ±1, ±2..., while e is a constant value.

[0074] For different oil droplets, a common pattern emerges: e is a common constant. This shows that the charge q of all charged oil droplets is an integer multiple of the minimum charge e, proving the discontinuity of charge, and that the minimum charge e is the charge of an electron, i.e.:

[0075]

[0076] 2. Experimental Design

[0077] 2.1 Experimental Setup

[0078] This embodiment is based on the FB809 intelligent Millikan oil drop apparatus, and the overall experimental setup is designed as follows: Figure 3 As shown, it includes two main parts: a control panel and a display panel. To better measure the charge of the oil droplets, an arc-shaped cavity mold is used as a temperature control component 11. Figure 4 As shown. Specifically, it includes an oil droplet ionization module and a temperature control component 11. The temperature control component 11 is tightly fitted onto the outside of the oil droplet ionization module. The temperature control component 11 is a tank with an opening at the top, and the tank contains a cold source substance.

[0079] like Figure 17 As shown, the oil droplet ionization module includes an upper chamber 6, a lower chamber 9, and an electric field generating module. The electric field generating module is installed in the lower chamber 9. The electric field generating module includes a lower electrode 1, an annular partition 12, and an upper electrode 4. The annular partition 12 is installed between the lower electrode 1 and the upper electrode 4. The cavity between the lower electrode 1, the annular partition 12, and the upper electrode 4 is the oil droplet movement chamber 2. The upper chamber 6 has an oil droplet injection through hole 8 on its wall. The lower chamber 9 has a first oil droplet through hole 7 at its top. The upper electrode 4 has a second oil droplet through hole 14. The lower chamber 9 has a lens mounting through hole 3 on its wall. The annular partition 12 has an observation through hole 13.

[0080] The oil droplet ionization module is cylindrical in shape. Its outer diameter is measured and used as the inner diameter of the temperature control component. A 3D-printed arc-shaped cavity mold is then used. During the experiment, the arc-shaped cavity mold is fitted onto the oil droplet ionization module. Ice is placed inside the cavity of the arc-shaped cavity mold to lower the temperature of the experimental environment through heat conduction. This reduces temperature changes caused by prolonged operation of the infrared light source in the oil droplet ionization chamber, thus reducing the Brownian motion of the oil droplets. Furthermore, the mold can cover the gaps in the oil droplet ionization chamber, increasing the airtightness of the experimental setup and reducing the influence of airflow on the lateral displacement of the experimental oil droplets.

[0081] 2.2 Experimental methods and parameter settings

[0082] The initial experimental parameters are set as shown in Table 1:

[0083] Table 1. Setting the basic experimental parameters

[0084]

[0085]

[0086] The charge q of the oil droplet was calculated using the positive integer average method. See Table 2 for details.

[0087] Table 2. Example table of calculating oil droplet charge using the positive integer average method.

[0088]

[0089] 3. Data Analysis

[0090] 3.1 Analysis of Measurement Results

[0091] In this study, the standard electron charge was set at -1.6 × 10⁻⁶. -19 C is used to calculate the oil droplet radius and charge by substituting the measured voltage U, the required time t, and the charge q of the oil droplet into equations (8) and (14). The oil droplet radius and charge are calculated using MATLAB and summarized in Table 3. During the experiment, the charge q changes due to the influence of environmental factors (temperature, air buoyancy, air discontinuity) and the different oil droplet radii.

[0092] Table 3 Summary of oil droplet measurement data under different conditions

[0093]

[0094]

[0095] 3.2 Investigating the effect of oil droplet falling time on experimental results

[0096] according to Figure 5The results show that, under conditions of sufficient triboelectric charging of the oil droplets, the droplet falling time t and the droplet radius r exhibit a certain regularity, that is, the longer the droplet falling time, the smaller the radius. For example... Figure 6 Using MATLAB to simulate the relationship between the falling time and height of different oil droplets, it can be seen that the larger the radius of the oil droplet, the shorter the falling time, indirectly indicating that the falling time of tiny oil droplets is longer. Furthermore, it is crucial to ensure the airtightness of the apparatus during the experiment to prevent lateral displacement of the oil droplets due to poor airtightness, which would increase the falling time. If the selected oil droplet is too small, Brownian motion becomes significant, such as... Figure 7 Therefore, in the experiment, to ensure the airtightness of the apparatus, the radius of the oil droplet should not be too small, so as to reduce the error of Brownian motion caused by poor airtightness of the apparatus and small oil droplet volume.

[0097] 3.3 Investigating the relationship between different oil droplet radii r and their charges q and e.

[0098] like Figure 8 As shown, there is a certain nonlinear relationship between the oil droplet radius *r* and its charge *q*. In the same set of experiments, the relationship between the oil droplet radius *r* and its charge *q*, after numerical fitting using Origin, exhibits a certain regularity: the oil droplet charge *q* increases with increasing oil droplet radius *r*, as shown below. Figure 9 This conforms to the variable relationship in equation (8). That is, the larger the radius, the greater the charge carried by the oil droplet during the process of full friction with the air.

[0099] Different oil droplet radii measured in the same group of experiments result in different calculated charges, e, on the oil droplet. Figure 10 Analysis shows that the radius is 0.8 × 10 -6 ~1.2×10 -6 The measured charge e of the oil droplets around m is close to the standard charge, with an error range of 0–1.88%, showing little difference from the standard value and relatively stable data. Therefore, a radius range of 1.0 × 10⁻⁶ should be selected. -6 Experiments using oil droplets near m will yield more accurate results.

[0100] 3.4 Investigating the effect of different temperatures on the charge e of oil droplets

[0101] according to Figure 11 As shown in Figure 12, this figure illustrates the relationship between the charge *e* measured at room temperature, the charge *e* measured at low temperature, and the standard charge *e*. The error between the charge *e* measured at room temperature and the standard charge *e* is relatively large, and the curve deviates significantly from the reference line of the standard value *e*. In contrast, the curve for the charge *e* measured at low temperature is closer to the reference line of the standard value *e*, with a smaller deviation. This indicates that measuring the charge *e* under low-temperature conditions can effectively reduce the influence of temperature on the Brownian motion measurement of oil droplets under room-temperature conditions, making the measurement results closer to the standard value. Figure 13By comparing the Brownian motion of 30 tiny oil droplets under low temperature and room temperature conditions using MATLAB simulations, it was found that the Brownian motion of oil droplets under room temperature conditions was more disordered than that under low temperature conditions, indicating that the Brownian motion of oil droplets under room temperature conditions was more intense than that under low temperature conditions.

[0102] 3.5 Investigating the Influence of Air Buoyancy and Discontinuity on the Charge E of Oil Droplets

[0103] according to Figure 14 Analysis 15 shows that, considering air buoyancy and air discontinuity, the charge e of the oil droplet is close to the standard value e, with a relatively small error; compared with normal temperature conditions, the charge e of the oil droplet is closer to the standard value e under low temperature conditions, with an error of 0 to 1.25%.

[0104] Millikan's oil drop experiment is conducted in an atmospheric environment, where oil droplets are inevitably affected by air buoyancy and air discontinuities. When these discontinuities and inhomogeneities are ignored, the resulting relative error is significant, leading to large deviations from standard values. Therefore, the effects of air buoyancy and air discontinuities must be considered.

[0105] Air buoyancy and air discontinuity affect the viscosity coefficient of air, which in turn affects the charge on oil droplets. Ignoring this effect will reduce the accuracy of oil droplet charge measurement. Under low-temperature conditions, the air density and viscosity inside the oil droplet chamber decrease, effectively reducing the influence of Brownian motion on the oil droplets, and the measurement results are closer to the standard value.

[0106] 3.6 Investigating the effect of different numbers of the same oil droplets on the charge e

[0107] Because different oil droplets are selected in different experiments within the same set of experiments, the charge of electrons will also change. Measurements were taken from five sets of experiments using the same oil droplet at room temperature and five sets of experiments using different oil droplets. The experiments were pre-designed to be conducted at room temperature. Figure 16 The charge values ​​of the five sets of data measured from the same oil droplet are close to the standard value e, which is 1.59 × 10⁻⁶. -19 C, 1.58 × 10 -19 C, 1.59 × 10 -19 C, 1.61 × 10 -19 C, 1.57 × 10 -19 C and 1.60×10 -19 C is similar, with an error ranging from 0.6% to 1.8%; the five sets of data measured for different oil droplets show significant differences from the standard value e, indicating instability. Figure 16 As shown.

[0108] Performing multiple measurements on the same oil droplet can improve experimental repeatability. Each measurement may be affected by random errors, but multiple measurements allow these errors to cancel each other out, improving the accuracy of the results. When using different oil droplets for measurement, the different sizes, shapes, and charges of these droplets can significantly affect the calculated charge e. When using the positive integer average method, the differences in oil droplets within each group lead to variations in the measurement data, significantly impacting the average value and resulting in a larger error.

[0109] 4. Conclusion

[0110] In the Millikan oil drop experiment, higher temperatures result in more pronounced Brownian motion and slower droplet descent. During the droplet's descent, the charge on the droplet changes due to factors such as ambient temperature and humidity. This study addresses the influence of Brownian motion on the Millikan oil drop experiment by designing an arc-shaped cavity mold that fits snugly against the oil droplet ionization chamber, effectively improving the airtightness of the experimental setup. Adding ice to the cavity to create low-temperature conditions effectively reduces the impact of Brownian motion on the oil droplet, and the measurement results are closer to the standard values ​​with a smaller relative error. To address the influence of air buoyancy and air discontinuity on the Millikan oil drop experiment, the calculation formula and air viscosity coefficient were modified, revealing that the calculated results are close to the standard values ​​with an error of 0–1.25%.

[0111] Example 2

[0112] The temperature control component is cavity-shaped, with the inner cavity storing the cold source material. The temperature control component has a cold source material inlet 16 and a cold source material outlet 15. To achieve a temperature lower than that of ice, the temperature control component is designed as a cavity-shaped container, using liquid nitrogen or liquid carbon dioxide as the cold source material. This material enters through the cold source material inlet 16 and flows out through the cold source material outlet 15, simultaneously carrying away heat from the oil droplet ionization module, thus maintaining the oil droplets at a low temperature and further reducing the influence of Brownian motion.

[0113] Example 3

[0114] The temperature control component is a thermoelectric cooler, and the cold end of the thermoelectric cooler is attached to the outside of the oil droplet ionization module. When the thermoelectric cooler is powered on, the cold end of the thermoelectric cooler lowers the temperature of the oil droplet ionization module, keeping the oil droplet ionization module in a low-temperature state, which can reduce the influence of Brownian motion.

Claims

1. An improved Millikan oil drop experiment apparatus, characterized in that, The device includes an oil droplet ionization module and a temperature control component. The temperature control component is wrapped around and installed on the outside of the oil droplet ionization module, covering the gaps in the oil droplet ionization module. The temperature control component is any one of the following: (a) A tank with an opening at the top, containing a cold source substance; (b) A cavity-shaped container, the inner cavity of which stores cold source material, and the cavity-shaped container is provided with a cold source material inlet and a cold source material outlet; (c) A semiconductor cooler, the cold end of which is attached to the outside of the oil droplet ionization module.

2. The improved Millikan oil drop experimental apparatus as described in claim 1, characterized in that, The oil droplet ionization module includes an upper chamber, a lower chamber, and an electric field generating module. The electric field generating module is installed in the lower chamber. The electric field generating module includes a lower electrode, an annular partition, and an upper electrode. The annular partition is installed between the lower electrode and the upper electrode. The cavity between the lower electrode, the annular partition, and the upper electrode is an oil droplet movement chamber. The upper chamber wall is provided with an oil droplet injection through hole, the lower chamber top is provided with a first oil droplet through hole, the upper electrode is provided with a second oil droplet through hole, the lower chamber wall is provided with a lens mounting through hole, and the annular partition is provided with an observation through hole.

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