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Approximation of Planck’s constant and work function using Photoelectric effect on the particle nature of light

This experiment aims to demonstrate the particle nature of light by photoelectric effect. Stopping potential was measured against different intensities of yellow (λ = 578 nm) and green (λ = 546 nm) light from first order spectral lines of mercury. No significant relationship was observed for stopping potential and percent transmission. However, charging time was inversely proportional to the percent transmission for the yellow light which implied more photoelectrons were emitted for greater intensity. Stopping potentials for green light was noted to be higher than of yellow light. Ratio of Planck’s constant to electron charge and work function of the photocathode were determined experimentally from the plot of frequency vs. stopping potential from the first and second orders of spectral lines of mercury. The h/e ratio from the plot was 2.345 × 10-15 eV•s with 43.29% error from the literature value and a work function of 0.439 eV. Linear relationship was observed from the plot of stopping potential vs. frequency.

Keywords: photoelectric effect, Planck’s constant, work function, stopping potential

1. Introduction
The emission of electrons in a solid surface such as metals when electromagnetic (EM) radiation (e.g. light) hits its surface is called photoelectric effect. This phenomenon was discovered in 1886 by Heinrich Hertz and was investigated further by Wilhelm Hallwachs and Philipp Lenard [1, 2] using a circuit similar to Figure 1. [pic]

Figure 1. A circuit for a photoelectric effect experiment. When enough energy is transferred to the electrons in the cathode from the photons on the EM radiation, the electrons maybe ejected from the cathode’s surface and a current is produced. The photoelectric effect can be understood clearly when light is viewed as a particle, rather than a wave. Einstein first used this concept to explain the results of Hallwachs’ and Lenard’s photoelectric effect experiment/s [1, 2]. He assumed that light consists of discrete quantities called photons, each with energy dependent on frequency, E=hf (1)

where E is the energy, f is the frequency of the radiation and h is Planck’s constant[3]. When the photons hit the cathode, there is either a total energy transfer from the photon to the electrons on the surface or none at all. When energy transfer does occur, the electrons maybe ejected from the surface when the work function (denoted as ϕ), the minimum amount of energy an electron must have to escape from a surface [1], is reached or exceeded. When exceeded, the excess energy from the emission becomes the electrons’ kinetic energy [3]. [pic]

Figure 2. A photoelectric experiment circuit with the E field reversed. Even when the E field is reversed, some electrons with enough kinetic energy will still be able to escape and go to the anode. The least voltage needed to stop the electrons from traveling into the anode is called V0 or the stopping potential. The maximum kinetic energy the emitted electrons depends on the stopping potential V0, KEmax=eVo (2)

where e is the charge of an electron.
With this, Einstein used the conservation of energy,
E=hf= KEmax + ϕ (3)
Substituting KEmax for eVo from equation (2) into equation (3), the resulting equation will be hf= eVo + ϕ (4)
Transforming the equation to solve for the Vo, equation (4) becomes

V0= (h/e)f – ϕ/e (5)

From the equation above, if a stopping potential vs. frequency graph is produced, the slope is equal to h/e while the y-intercept is equal to ϕ/e [3]. In this experiment, the photoelectric effect was studied more closely using a mercury lamp and an h/e apparatus. The effect of intensity and effect of wavelength on...
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