MEASURING PLANCK’S CONSTANT

Joseph R. Groele

The Quantum Theory

There are five major ideas represented in the Quantum Theory:

Energy is not continuous, but comes in small but discrete units.

The elementary particles behave both like particles and like waves.

The movement of these particles is inherently random. It is physically impossible to know both the position

and the momentum of a particle at the same time. The more precisely one is known, the less precise the measurement of the other is.

The atomic world is nothing like the world we live in.

Planck’s Equation

E=hc/λ=eV0

Where: E is the energy of the photon (Joules) λ is the wavelength of light (nanometers) c is the speed of light (2.998 x108meters per

second) h is Planck’s constant (6.626 x 10-34 J-s) e is the charge of an electron (1.6022 x10-19

Coulomb) V0 is the threshold voltage for the LED (Volts) Linear equation (y=mx+b): V0 = (hc/e)(1/ λ)

The Methods

Method One is looking at the LED for the first sign of light. Turning the potentiometer gradually increases the voltage supplied to the LED. The threshold voltage is the drop in voltage across the LED when light first becomes visible.

Method Two measures the threshold voltage when current begins to flow through the LED. The supplied voltage is increased gradually until current begins to flow, which is measured by the voltage drop across a resistor. The threshold voltage is the drop in voltage across the LED when voltage is greater than zero. I will use a value of 0.3 millivolts.

In Method Three, I will graph voltage drop across the entire range of the supplied voltage. The threshold voltage will be measured by drawing a straight line through the last few points and continuing the line until it crosses the x-axis.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 20

500

1000

1500

2000

2500

3000

3500Description of the Three

Methods

Diode Voltage, Vd (Volts)

Volt

age a

(M

illivolt

s)

Method Two: Measure diode voltage when Va equals 0.3 milli-volts.

Method One: Measure diode voltage when the light is first visible.

Method Three: Draw a straight line between the last four points, and continue the line to the x-intercept.

Y-axis is the voltage measured at point a. This is proportional to the current flow through the LED.

X-axis is the voltage be-tween point b and point a. This is the voltage drop across the LED.

Purpose/Variables

The purpose of this experiment is to measure Planck’s constant and to compare the accuracies of three methods used to measure it.

Variables: Independent: wavelength of LED and supplied

voltage Constant: wavelength of the LED Dependent: voltage drop across the LED and

voltage drop across the resistor

Hypothesis

I hypothesize that Method Two will be the most accurate for measuring Planck’s constant. All the data required will come directly from the two multimeters, so human error should not present a problem. I think that Method One will be less accurate because it calls for human judgment as to when the LED first begins to emit light. In Method Three, a line needs to be made from the last few points of the Va and Vb-Va graph, which I believe will be curved like an exponential graph. The curve will make choosing points to make a line difficult and likely cause this method to be less accurate.

Materials

Wood base Battery holder D-cell battery Wire Wire strippers Solder Soldering iron Hot glue gun Potentiometer Switch Multimeters Banana clip Wire staples Resistors LEDs with various

wavelengths LED mount Microsoft Excel

Blue: 468 nmGreen: 574 nmYellow: 588 nmAmber Yellow: 595 nmYellow-Orange: 611 nmRed-Orange: 621 nmRed: 632 nmSuper Red: 639 nmInfrared: 940 nmInfrared: 880 nm (not shown)

Circuit Diagram

400000 600000 800000 1000000 1200000 1400000 1600000 1800000 2000000 2200000 24000000.000

0.500

1.000

1.500

2.000

2.500 Method One Graph

1/Lambda (meters-1)

Dio

de V

olt

age,

Vd (

Volt

s)

400000 600000 800000 1000000 1200000 1400000 1600000 1800000 2000000 2200000 24000000.000

0.500

1.000

1.500

2.000

2.500

Method Two Graph

1/Lambda (meters-1)

Dio

de V

olt

age ,

Vd (

Volt

s)

0.5 1 1.5 2 2.5 30

500

1000

1500

2000

2500

3000

3500

4000

Method Three Curves

632-1940-3468-1574-3595-3

Diode Voltage, Vd (Volts)

Volt

age a

(M

illivolt

s)

1000000 1200000 1400000 1600000 1800000 2000000 22000000.000

0.500

1.000

1.500

2.000

2.500

3.000

Method Three Graph

1/Lambda (meters-1)

Dio

de V

olt

age,

Vd (

Volt

s)

Results

Planck’s constant, current accepted value: 6.62607554E-34 J-s

Planck’s constant, Method One: 6.25181E-34 J-s Percent Deviation: 5.65%

Planck’s constant, Method Two: 6.79708E-34 J-s Percent Deviation: -2.58%

Planck’s constant, Method Three: 7.8694E-34 J-s Percent Deviation: -18.76%

Project Photos