Planck Constant Apparatus and Calculations

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5

简介:普朗克常数仪器和计算

关于:我拥有物理学硕士学位,我的爱好是:3D打印、CAD设计、arduino、天文学、天体摄影、宇宙学和科幻:)

Planck constant (h) is one of the fundamental physics constants and the most important constant in quantum mechanics. When I was studying physics years ago, I fall in love with Quantum Mechanics and now I have decided to conduct simple experiment to calculate Planck constant at home.

In this instructables I will show you how to make an apparatus that can be used to calculate Planck constant and, also how to measure the turn-on voltage and IV characteristic for different colour LEDs. This time I only used hand tools so anyone can make it at home.

注:Optionally I have included files for 3D printing and laser cutting in case you have an access to any of that equipment.

Supplies

-220欧姆0.5W电阻器

-2k欧姆电位计

-12-way rotary switch (1P12T)

-6 x 4mm香蕉端子(3个黑色,3个红色)

-三x 4mm banana leads

-电位计旋钮(可选)

-旋转开关旋钮(可选)

-300mm x 100mm x 3mm有机玻璃

-4 rubber feet

-8mm外径有机玻璃管(可选)

-A4粘性标签纸

-红、橙、黄、Green, Blue, Purple LEDs

-Cyan LED

-IR 850 LED

-红外940发光二极管

-设备线


工具:

-5V电源

-拼图

-德里尔

-Voltmeter

-Ameter (optional)

-Soldering iron

-设备线

-Ink/laser printer

-CO2激光切割机(可选)

-三D printer (optional)

-剥线器/切割机

第一步:理论

Light-emitting diodes (LEDs) convert electrical energy into light energy. They emit radiation (photons) of visible wavelengths when they are forward biased. This is caused by electrons from the `N' region in the LED giving up light as they fall into holes in the `P' region. The graph above shows the current-voltage curve (IV curve) for a typical LED. The 'turn-on' voltage Ut is about the same as the energy lost by an electron as it falls from the N to the P region. In this experiment you will find the point at which the light `goes on' by gradually adjusting the voltage.

光子产生的能量(hc/λ), 假设等于每个电子的损耗,qV:其中q是电子上的电荷(q=e=1.6x10^-19c),U是开启电压,λ 是以米为单位发出的光的波长,c是光速c=3.0 X10^8 m/s。

Above you can also see calculation for the measurement error. LED manufacturers state the wavelength of the LEDs with the precision about Δλ = 20nm - 30nm and the precision of my voltmeter is ΔU = 0.01V.

注:测量的准确性将取决于眼睛对光线的适应能力。更准确的方法是使用光传感器测量强度,这是未来升级的好机会。

第2步:装配-切割和钻孔

-使用拼图切割有机玻璃矩形(约300mm x 80mm)

-打印附带的孔模板,并在有机玻璃上标记所有必要的孔

-德里尔l holes in perspex sheet (you will need 5mm, 7mm and 10mm drill bits)

注:你可以从一些供应商订购定制尺寸的有机玻璃,省得自己切割

步骤3:装配-部件安装

-如上图所示安装4毫米香蕉端子

-安装并固定电位计和旋转开关

-将蓝色、青色、绿色、橙色、红色、IR 850、IR 940 LED插入钻孔

-弯曲所有的脚,使它们连接在一起

第4步:组装-焊接

-按照上面的连接图将所有插入的组件焊接在一起

-胶皮腿

注:确保在焊接过程中已打开抽油烟机。如果你用热烙铁烫伤了自己,立即用冷水冷却。

步骤5:部件-标签

-Print attached PDF file with labels on sticky sheet

-Cut the labels and glue them on the apparatus accordingly (see picture above)

注:您可以通过在Inkscape中打开svg文件来编辑标签(https://inkscape.org/release/inkscape-1.1/)

第6步:装配-3D打印和激光切割

This step is optional. Below you will find .stl files ready for 3D printing or .pdf / .svg files ready for laser cutting.

Step 7: Taking Readings

-使用4毫米香蕉引线将直流电源连接到+5V和GND插座

-Connect Voltmeter to the 4mm banana terminals marked as 'V'

-将安培表连接到标有“A”的4mm香蕉端子上(这对于普朗克常数计算是可选的,如果您不想使用安培表,只需将“A”端子与导线连接即可。这一点很重要,因为电路需要闭合才能工作)

-将旋转开关设置为第一个LED(例如蓝色)

-使用“电压调整”电位计增加电压,直到您看到LED亮起(您可以使用有机玻璃管提高精度或在暗室中进行实验)

-Repeat the process for all LEDs and record the turn-on voltage for each colour

-For Infrared LEDs (IR850 & IR940) you need to use mobile phone camera. The IR light is invisible for human eye but you can clearly see it through your camera.

注:如果你没有有机玻璃管,你可以用便宜的笔套,用黑色绝缘胶带包起来。

第8步:普朗克常数计算

-使用Excel电子表格进行阅读

-Calculate Planck constant and the error using formulas (see above picture)

-此外,您可以连接Ameter到您的设置和测量每一个LED的IV曲线

-上面你可以看到红色和蓝色LED的IV曲线

CONCLUSIONS:从上面的计算可以看出,普朗克常数的计算误差为11%。当你把我们的计算与物理表中的普朗克常数比较时,你会发现我们的计算在11%的误差范围内要小得多。这是一个相当严重的错误,但我们仍然能够计算普朗克常数在家里。

As for IV cure we can clearly see that Red LED is achieving maximum brightness before Blue LED. This makes sense as the red light has longer wavelength therefore lower energy photons.

步骤9:升级

I have decided to leave some room for upgrades, especially if you decide to use as a project at school.

-第一个升级将是添加更多的发光二极管:黄色:600nm和紫色:400nm

-Second upgrade would be to add light sensor to take the readings

注:在上面你可以找到另外两个孔的黄色和紫色发光二极管模具。至于光传感器,我建议使用arduino。

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    3条评论

    0
    奈尔

    三天前

    干得好:)
    我也很欣赏细节。
    (since the uncertainty in U and lambda are independent you probably want to calculate the root of the squared uncertainties [Pythagoras] , not their sum)
    谢谢分享!

    0
    1982年

    3天前回复

    嗨,是的,你是对的,也许这是计算误差的更好方法。我会做数学,看看我会得到什么:)
    Thanks

    0
    奈尔

    2天前回复

    there's absolutely no need! :)
    thanks again!