Determining Planck's Constant from an LED Lab

The purpose of this experiment is to successfully approximate Planck's constant while using different Light Emitting Diodes (LED).

Planck's constant is found in the expression which involves energy and frequency

E = hf = hc/λ

where the theoretical value of h is 6.626*10^-34 Js

In order to measure the electric field E, we can relate the concept of electric potential difference, or voltage;

E = qV, where q is the charge of an electron = 1.6*10^-19 C

Equating both Es, we can get the following formula

hc/λ = qV

and solving for h yields;    h = λqV/c

Voltage delivered by a power supply will be measured just when the LEDs are dimly  lit. This will be achieved by controlling the resistance of the circuit, avoiding the resistance to be zero since too much voltage would toast the LEDs.

λ is obtained using the method of spectrum lines through the formula:

λ = Dd/(L^2 +D^2 )^1/2

We then recorded the following data:

% error = |exp - act|/act *100 for Planck's constant in each of the LED lights:

Actual Value: 6.626*10^-34 Js

Green LED: 17.30%
Blue  LED: 22.88%
Yellow LED: 25.45%
Red LED: 21.52%

The percent error was moderately low giving the green LED the lowest percent error, where as the yellow LED threw the largest percent error out of the 4 samples.

One thing worth mentioning is that even though LEDs have a particular color, when they were seen through the diffraction grating, there was still a spectrum of different colors. This happened with all the 4 LEDs.

Also, when reading voltages, we saw that the blue LED particularly, changed to green if we varied the resistance. This means that wavelength is related to the voltage delivered to the LED.

Color and Spectra Lab

Part 1: The Spectrum of White Light

We began by using a light box and placing it a distance of 1.96+/-0.3 m away from the diffraction grating. A rainbow of colors could be observed through the grating.

The colors were blurry if the lights were on. However, the image became clearer once the lights were shut down. The closest color to the light source was violet, followed by blue, green, a slit of yellow and finally a red color.


Part 2: Measuring Wavelength - Theory

Part 3: Measuring Wavelength - Experimental



The following relationships will help to find the wavelenght of color as seen through the grating;

The grating used for this experiment had 500 groves per mm. This means that the distance, d, between the grove was found to be  2*10^-6 m.

The distance between the light source and the edge of each color were:

Violet: 36.7 +/- 0.5 cm
Blue: 45.5 +/- 0.5 cm
Green: 53.7 +/- 0.5cm
Red: 83.5 +/- 0.5 cm

The distance between the light source and the middle of each major color were:

Violet/Blue: 45.5 +/- 0.5 cm
Green: 53.7 +/- 0.5 cm
Red: 70.3 +/- 0.5 cm

All this values represent D in the equation.
L = 1.96 +/- 0.3 m
d = 2*10^-6 m

λ violet  = 368 +/- 5 nm              Shortest wavelength

λ blue = 460 +/- 4 nm

λ green = 540 +/- 5 nm

λ red = 784 +/- 4 nm                   Longest wavelength

Part 4: Spectra of a Single Element 

We took a hydrogen gas tube which substituted the light box, and then we did the same procedure as in the previous part.

 

We came up with the following data and the respective percent errors based on the calculated wavelengths from Part 2.

Identifying an unknown gas

Once we knew how to measure wavelengths of light through spectrum lines, we could now be able to identify an unknown gas from the light it emitted.

We were given unknown sample number 3:

 

The distances, D, between the gas tube and each spectrum line were the following:

Dviolet = 0.441 +/- 0.002 m

Dcyan = 0.500 +/- 0.002 m

D red = 0.693 +/- 0.002 m

Based on spectrum diagrams for different gases, we concluded that the closest gas whose wavelengths were close to the unknown, was Xenon gas.