Planck’s constant from Stefan’s radiation law: a study of gray radiations of tungsten filament bulb

Abstract This study introduces a straightforward approach to determine Planck’s constant in an undergraduate course at the college or university level through the analyses the current–voltage ( I – V ) characteristic of a tungsten filament bulb. Unlike conventional methods, this analysis does not require the use of a color filter or an additional photodiode to select a specific wavelength or measure the emitted energy density from the filament. The temperature of the filament was computed by measuring the resistance of the filament. The obtained temperature and the input power of the filament are then used to estimate the emissivity of the filaments using Stefan–Boltzmann’s law, which is found to be lower than that of a perfect black body, i.e. unity. Therefore, the radiation emitted from the tungsten filament can be classified as gray radiation. The maximum energy density (intensity) of the emitted radiation is determined by calculating the consumed power of the filament. Finally, the obtained values of temperature, Stefan’s constant, and the intensity of the emitted radiations are used to calculate Planck’s constant. The calculated value of Planck’s constant is found to be 6.102 × 10 −34 Js, which closely matches the standard value of Planck’s constant (6.626 × 10 −34 Js). This close correlation between the two values validates the effectiveness of the present method.