Plank's Constant From An LED

Purpose:

            The primary purpose of this laboratory experiment is to determine the value of Plank’s constant using only a couple of LED lights with varying color. The lights will be turned down to as little a voltage as possible just so that the light is barely visible. After the voltage is found, the wavelength will need to be determined in order to determine the value of planks constant.

Procedure:

           

            First, the LED lights were distributed so that each group received red, green, blue, and yellow colored lights. These were then attached to a power supply and a resistor box. Once that was set up, the resistance across the circuit was increased to the point at which the light was barely visible in the casing. 

Once this was done, the voltage across the circuit was measured and recorded for a later calculation. This process was repeated for the remaining colors. Next, the lights were shined to a visible level and allowed to be beamed through a gradient.

 Similar to previous setups, the light was placed a distance “l” away from the observing gradient and another meter stick was placed perpendicular to the length so as to measure the distance away from the light source, “x”, that the spectrum lines were placed. 

This was done to achieve the wavelength. Once the line was found, it was marked and recorded to compute the necessary calculations at a later time. This process was repeated for the rest of the colors that were obtained.

Data Analysis:

            The following table contains the recorded voltage reading across the colored LEDs while the light was barely shining.

Color	Voltage (V)
Red	1.56
Green	1.87
Blue	2.25
Yellow	1.63

These numbers will be used at a later time, after the wavelengths are calculated.

The next table displays the recorded information obtained from the viewing of the lights through the gradient.

Color	l (cm)	x (cm)	λ (nm)
Red	90 ± 1	32 ± 1	673 ±20
Green	90 ± 1	28 ± 1	551 ±15
Blue	90 ± 1	25.8 ± 1	485 ±14
Yellow	90 ± 1	22.5 ± 1	594 ±14

The following shows the derivation of finding lambda:

λ/d = x/(x²+l²)^1/2

λ = dx/(x²+l²)^1.2

Once the wavelength was determined for each light, Plank’s constant can then be found using the following equation:

E=hc/λ=qV

h = qVλ/c

the following table depicts the calculated constants that are associated with the color:

Color	Value of h
Red	5.57 * 10-34
Green	5.50 * 10-34
Blue	5.82 * 10-34
Yellow	5.20* 10-34

The last chart pictured, displays the percent errors of each calculated value to the accepted value of Plank’s constant.

Color	Percent Error
Red	15.9%
Green	17.0%
Blue	12.1%
Yellow	21.5%

Conclusion:

            Although the theory was there, the results did not manage to produce the value of Plank’s constant to within a reasonable degree of error. This may have been as a result of an inaccurately measured voltage across the LED while the light was being viewed. The light continued to be seen even when the resistivity was turned extremely high. This led to a large uncertainty in the determination of the minimum voltage across the LED and thus led to an inaccurate calculation of the constant. Another source of error could have resulted from the measurement of the spectrum lines with the diffraction gradient. The lines were hard to see and may have led to a not so accurate measurement of x value. Given better conditions, it seems very likely that the value of Plank’s constant could me accurately measured by simply using a LED.