Ways of experimentally determining h

Here is a brief overview of the various ways of determining $h$ experimentally, together with references to the literature:

Retarding-field method
With this method (described in the teaching text), difficulties can arise in detecting the photocurrent because of its low magnitude and the low intensity of the light falling on the cathode. Fritz Langensiepen discusses sources of error and improvements to the retarding-field method in his article: “Ein verbessertes Verfahren zur Bestimmung des Planckschen Wirkungsquantums mit in der Schule vorhandenen Mitteln”, in: Praxis der Naturwissenschaften-Physik 30 (1981)11, pp. 321-328.

Capacitor or charging method
In this measurement procedure the photocurrent of the vacuum photocell generates the counter-voltage itself by charging a capacitor. The terminals of the capacitor have to be connected to the anode and the cathode of the photocell respectively. The capacitor is charged up to the voltage that corresponds to the maximum energy of a photoelectron. By measuring or estimating the frequency of the light, Planck’s constant can be calculated using the equation $e \cdot \Delta U = h \cdot \Delta f$ .
Further information can be found in the following articles:
– Fiebich, R., Hartung, G.: Demonstrationsversuch zur Bestimmung des Planckschen Wirkungsquantums mit einfachen schulischen Mitteln, in: Physik in der Schule 33(1995) 11, p. 407, and
– Wilke, H-J., Patzi, W., Tronicke, G.: Bestimmung des Planckschen Wirkungsquantums mittels Leuchtdioden, in: Physik in der Schule 35(1997) 10, pp. 344-347.

Absorption of light in potassium dichromate solution
Light can be absorbed as it passes through a medium if it raises atoms or molecules into an excited state. Because of the quantization of the energy levels, only photons of a particular energy, or energy range (bands), can be absorbed. With a potassium dichromate solution the reaction energy can be determined experimentally. An equation for $h$ can then be calculated from the wavelength of the absorption edge.
More details can be found in the article “Das Plancksche Wirkungsquantum – einmal anders bestimmt” by Strahlke, W. and Siemon, H. in: Physik in der Schule 35(1997) 10, pp. 348-350.

Characteristic curves of light-emitting diodes
If light-emitting diodes of different colors are available, $h$ can also be determined from their characteristic curves. The forward voltage $U_{\mathrm{D}}$ of an LED depends on its color. If the forward voltage and the highest emitted frequency $f$ are determined for various LEDs, then the quotient $\dfrac{U_{\mathrm{D}}}{f}$ is almost constant, namely $\dfrac{U_{\mathrm{D}}}{f} = \dfrac{h}{e}$ .
Further information can be found in the following articles:
– Pitka, R.: Bestimmung von h/e mit Leuchtdioden, in: Didaktik der Physik Vorträge 1986 (1987), pp. 160-164,
– Hübel, H.: Leuchtdioden: annähernd monochromatische Lichtquellen für physikalische Schülerversuche zur Gitterbeugung und zum Planckschen Wirkungsquant, in: Praxis der Naturwissenschaften-Physik 3/1982, pp. 77-84,
– Schwarze, H.: Mit Leuchtdioden zu E = hf, in: Praxis der Naturwissenschaften-Physik 1/46 1997, pp. 34-36,
– Wilke, H-J., Patzi, W., Tronicke, G.: Bestimmung des Planckschen Wirkungsquantums mittels Leuchtdioden, in: Physik in der Schule 35(1997) 10, pp. 344-347.