Planck's Constant from an LED

We are going to determine the value of Planck's constant h.

We connect the LED to a power supply V.

We put one two meter stick perpendicular to the other one meter stick, and we one diffraction grating with 300 lines/mm at the end of two meter stick. We put the LED at the other end of the two meter stick, which is the same location of the intersection of two sticks.

We have the LED glow. We have the LED oriented right. We solder the resistor. We also screw the wires down in alligator clips. The battery "fresh" at least 9V.

We have the energy of one electron in a completed circuit E = qV, and we have the energy of one photon is E=hc/(wavelength)

We have the E=qV and E=hc/(wavelength)

we thus have h=qV(wavelength)/c and V=hc/q(wavelength)

We measure the voltage V across the LEDS with different color.

One student observe the fringe of different color of the LEDs through diffraction grating, and the other point the position of the fringes and mark the reading of that position.

We have the data below:

LED	Voltage (V)	Wavelength (m)	h(Js)	% Error (%)
RED	1.85	8.25083E-08	8.14081E-35	87.72124573
GREEN	2.57	1.415E-07	1.93949E-34	70.74672778
BLUE	2.67	1.20299E-07	1.71306E-34	74.16193823
YELLOW	1.9	9.33804E-08	9.46255E-35	85.72768391

We see there are mixture of color of LED through the spectroscope. All of the LED are mixture of color. It is because the LED is not made prefect, the electrons in the LED may jump to different levels that it is designed. The red LED gives the largest of error as the red LED is not made perfect. We can see the wavelength of the LEDs is proportional to potential. We have the voltage across the sky and earth is lower in the day time, as the voltage is smaller, we have the wavelength of the sky is shorter, the sky is blue. We have the voltage across the sky and earth is higher in the setting of sun, as the voltage is larger, we have the wavelength of the sky is longer, the sky is red.

LED	Voltage (V)	1/Wavelength (m^-1)
RED	1.85	12120000
GREEN	2.57	7067142.857
BLUE	2.67	8312593.22
YELLOW	1.9	10708887.22

The equation y = -2^-7 x + 3.93. The slope is -2 * -7, and it represents the value of hc/q. So we have the Planck's constant 3.616*10^-34 J/Hz.

We successfully measure the voltage across each led. We have the Planck's constant calculated that is same digital but half of the theoretical value 6.63*10^-34. There exists errors, for example, there is light come from background, which influence the pattern of light observed through the grating slit. We thus measure the wavelength inaccurate.

Measurement of wavelength of white light source, mercury gas and hydrogen gas

The purpose: We are going to measure the wavelength of a white light source, and we find the name of two unknown gases (mercury gas and hydrogen gas), by measuring their wavelength.

First of all, we put two meters sticks that one is 1 meter and the another is 2 meters perpendicular to other each, and we put a white light bulb at the intersection point of two meter sticks.


We use diffraction grating to see the diffraction pattern of the white pattern, and we draw the pattern from red color to violet color.

We measure the reading of 1 meter of both end of different color fringes, we subtract every value of end so we have the width of the fringe.

We use the equation λ= s*D/(d^2+D^2)^1/2, where s is 1.75975698*10^-6m.

Color	D (cm)	λ (m)
Violet	45.1	3.87*10^-7
Blue	51.3	4.37*10^-7
Green	59.9	5.05*10^-7
Yellow	66.5	5.55*10^-7
Red	78.1	6.40*10^-7

We offset the wavelength measured to match the actual wavelength by adding 30*10-9.

λ measured (m)	λ after offset (nm)
3.87*10^-7	417
4.37*10^-7	467
5.05*10^-7	535
5.55*10^-7	585
6.40*10^-7	670

After that, we measure the two gases, and we find out the gas by measuring their wavelength.

(Mercury gas)

We replace white source with mercury gas (we do not know yet).

We use the same equation to find the wavelength.

There are not blue and red fringes.

Color	D(m)	λ (m)
Violet	0.475	4.07E-07
Green	0.605	5.10E-07
Yellow	0.655	5.48E-07

We look at the spectrum to find the actual wavelength, and we compare the measured and actual wavelength.

λ (m)	λ Acutal(m)
4.07E-07	4.30E-07
5.10E-07	5.48E-07
5.48E-07	5.77E-07

We check that we measure the wavelength correct by multiple every measured wavelength by 1.0642, which is closed to the actual wavelength.

(Hydrogen)

We replace mercury gas with hydrogen gas(we do not know yet).

We use the same equation to find the wavelength.

There are not green and yellow fringes.

We also offset the measured wavelength by multiple 1.06 which is the ratio of measured wavelength and actual wavelength found in mercury gas part, and we compare the measured wavelength and actual wavelength.

Color	D(m)	λ (m)	λ offset (m)	λ Acutal(m)
Violet	0.482	4.12E-07	4.37E-07	4.34E-07
Blue	0.537	4.56E-07	4.83E-07	4.86E-07
Red	0.745	6.14E-07	6.51E-07	6.56E-07

The offset wavelength is closed to actual wavelength as the slope is 1.031 closed to 1.

We find the wavelength of the violet color (4.38E-7) that is closed to the energy for an electron moves from 5th to 2nd level (4.34E-7) in hydrogen atom.

We find the wavelength of the blue color (4.85E-7) that is closed to the energy for an electron moves from 4th to 2nd level (4.86E-7) in hydrogen atom.

We find the wavelength of the red color (6.53E-7) that is closed to the energy for an electron moves from 3th to 2nd level (6.56E-7) in hydrogen atom.

So we check that we measure the wavelength correctly.

As a result, we successfully measure the wavelength of a white light source, and we find the name of two unknown gases which are mercury gas and hydrogen gas by measuring their wavelength.