Walk the Planck

Wenjun Li II
Department of Physics, University of Wisconsin-Parkside
900 Wood Road, Kenosha, Wisconsin 53141 USA
Douglas Richmond Jr.
Department of Physics, University of Wisconsin-Parkside
900 Wood Road, Kenosha, Wisconsin 53141 USA

March 22, 2036

Abstract

On the eve of the 30^th anniversary of our father’s joint Nobel-Prize winning experiment, we re-analyze their data, and corroborate their work. Download this report.

1 Introduction

There is a simple relationship between the minimal voltage bias V _min needed to light an LED and the frequency f of the emitted light

eVmin = h f

which we exploit in an experiment to determine Planck’s constant h.

2 Procedure

2.1 Instruments and materials

Six LEDs, emitting wavelengths λ = 480,560,590,635,665 and 950nm were examined with common laboratory volt and ammeters.

2.2 The Experiment

For each of the LED elements we ran an accelerating voltage through it’s relative circuit, and tested the current at a pre-decided threshold of 20.0 Volts. We then lowered the current until the LED turned off. Since we were looking for about 20 data points, we did a quick approximate division, and hence, had our average step voltage between data points. Repeating this for all of the LED elements we recovered the voltage, and the amperage at each step, and recorded them for data analysis.

3 Analysis and conclusions

We suspected that the current versus applied voltage bias for the LED follows a standard diode relation

( V-V ) I = I0 e---mαin - 1

and devised a means of determining the three parameters I₀,V _min and α that best ﬁt our data. Noting that

V -V -dI = I0e---αmin = 1I + 1I0 dV α α α

We performed a linear regression of the ﬁnite differences ΔI _ ΔV versus midpoint currents I for each LED, and from the slope determined the best-ﬁt α and I₀ in each case. We then performed a least squares ﬁt on each LED, with y = ln( I_ I₀ + 1) and x = V _ α using our previously determined α and I₀ values. The intercepts resulting in the best-ﬁt values of V _min listed below;


λ(nm)	V _min(V )

480	2.582527
560	1.799230
590	1.730158
635	1.633369
665	1.486527
950	1.012917

A linear regression of V _min versus λ^-1 results in

eVmin = 1444.9eV ⋅ nm λ- 1 + 0.6273 eV

from which we conclude that

(hc) = 1,444.9eV ⋅ nm exp

which compares quite well with the accepted value

(hc)acc = 1,239.8eV ⋅ nm

differing by only 16.5%.

4 Raw and processed data

We ﬁrst present the raw data at various stages of analysis, followed by the actual current versus voltage for each diode, in tabular form.

480 nm

560 nm

590 nm

635 nm

665 nm

950 nm

4.1 Raw data


480nm

V (volt)	I (mA)

2.60	0.090
2.81	0.172
3.06	0.338
3.20	0.459
3.45	0.722
3.61	0.940
3.82	1.259
4.05	1.673
4.25	2.095
4.42	2.496
4.63	3.129
4.83	3.795
5.02	4.542
5.21	5.329
5.40	6.300
5.62	7.544
5.82	8.849
6.03	10.518


560nm

V (volt)	I (mA)

1.80	0.413
1.83	0.676
1.86	1.031
1.89	1.493
1.92	2.004
1.95	2.617
1.98	3.331
2.01	4.070
2.03	4.615
2.06	5.481
2.09	6.311
2.12	7.261
2.15	8.224
2.18	9.302
2.21	10.270
2.24	11.453
2.27	12.575
2.30	13.907
2.33	15.010
2.36	16.454
2.39	17.866
2.42	19.064


590nm

V (volt)	I (mA)

1.79	2.836
1.80	3.340
1.81	3.750
1.82	4.276
1.83	4.812
1.84	5.436
1.85	6.204
1.86	6.828
1.87	7.644
1.88	8.382
1.89	9.394
1.90	10.467
1.91	11.197
1.92	12.332
1.93	13.468
1.94	14.620
1.95	15.790
1.96	16.884
1.97	17.978
1.98	19.558


635nm

V (volt)	I (mA)

1.664	1.328
1.681	1.770
1.708	2.684
1.725	3.443
1.743	4.189
1.764	5.280
1.780	6.258
1.807	7.960
1.822	9.054
1.844	10.685
1.865	12.344
1.881	13.613
1.904	15.620
1.922	17.259
1.946	19.470


665nm

V (volt)	I (mA)

1.51	0.803
1.52	1.020
1.53	1.399
1.54	1.800
1.55	2.234
1.56	3.016
1.57	3.538
1.58	4.667
1.59	5.816
1.60	7.239
1.61	9.400
1.62	11.270
1.63	13.657
1.64	16.641
1.65	19.669


950nm

V (volt)	I (mA)

1.03	0.583
1.04	0.735
1.05	1.062
1.06	1.355
1.07	1.793
1.08	2.325
1.09	2.833
1.10	3.956
1.11	5.336
1.12	6.423
1.13	8.850
1.14	11.650
1.15	14.700
1.16	17.627