## Introduction: Planck Constant Apparatus and Calculations

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.

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

## Supplies

- 300mm x 100mm x 3mm perspex

- 8mm OD Perspex tube (optional)

- A4 sticky label sheet

- IR 940 LED

- Equipment wire

Tools:

- 5V power supply

- Jigsaw

- Dril

- Voltmeter

- Ameter (optional)

- Soldering iron

- Equipment wire

- Ink/laser printer

- CO2 laser cutter (optional)

- 3D printer (optional)

- Wire strippers/cutters

## Step 1: Theory

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.

The energy produced by photons (hc/λ), is assumed to be equal to that lost by each electron, qV: where q is the charge on an electron (q = e = 1.6 x 10^-19 C), U is the turn-on voltage, λ is the wavelength of light emitted in metres, and c is speed of light 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.

NOTE: The accuracy of the measurements will depend on the eye's adaptation to light. A more accurate method is to use a light sensor measuring intensity which is good opportunity for future upgrades.

## Step 2: Assembly - Cutting and Drilling

- Use jigsaw to cut a perspex rectangle (about 300mm x 80mm)

- Print attached hole stencil and mark on the perspex all necessary holes

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

NOTE: You can order a custom size perspex from some suppliers to save cutting it yourself

## Step 3: Assembly - Component Mounting

- Mount the 4mm banana terminal as on the picture above

- Mount and secure potentiometer and the rotary switch

- Insert Blue, Cyan, Green, Orange, Red, IR 850, IR 940 LEDs into the drilled holes

- Bend all LEDs negative legs so they are all connected together

## Step 4: Assembly - Soldering

- Solder all inserted components together by following connection diagram above

- Glue rubber legs

NOTE: Make sure that you have fume extractor switched on while soldering. In case you burn yourself with hot soldering iron, immediately cool affected are under cold water.

## Step 5: Assembly - Labels

- Print attached PDF file with labels on sticky sheet

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

NOTE: You can edit labels by opening svg file in Inkscape (https://inkscape.org/release/inkscape-1.1/)

## Step 6: Assembly - 3D Printing and Laser Cutting

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

- Connect DC power supply using 4mm banana leads to the +5V and GND sockets

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

- Connect Ameter to the 4mm banana terminals marked as 'A' (this is optional for Planck constant calculations and if you do not wish to use Ameter simply connect 'A' terminals with the lead. This is important as the circuit need to be closed in order to work)

- Set rotary switch to first LED (Blue for example)

- Use 'Voltage adjust' potentiometer to increase voltage until you will see LED to light up (you can use perspex tube to increase accuracy or perform the experiment in a dark room)

- 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.

NOTE: If you don't have perspex tube you can use cheap pen case and wrap it with black insulation tape.

## Step 8: Planck Constant Calculations

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

- In addition you can connect Ameter to your setup and measure IV curves of each LED

- Above you can see IV curve of Red and Blue LED

CONCLUSIONS: As you can see from above calculations, the Planck constant is calculated with 11% error. When you compare our calculations with the Planck constant from the physics tables you can see that our calculations are more less within the error of 11%. It is quite significant error, but nonetheless we are able to calculate Planck constant at home.

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.

## Step 9: Upgrades

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

- First upgrade would be to add couple more LEDs: Yellow: 600nm & Purple: 400nm

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

NOTE: Above you can find stencil with 2 additional holes for the Yellow and Purple LED. As for the light sensor I would recommend to use arduino.

### Attachments

Second Prize in the
Explore Science Challenge