The Photoelectric Effect – Experimental Confirmation Concerning a Widespread Misconception in the Theory

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The Photoelectric Effect – Experimental confirmation concerning a widespread Misconception in the Theory Gao Shenghan 1, Huan Yan Qi 1, Wang Xuezhou 1, Darren Wong 2, Paul Lee 2 and Foong See Kit 2

1 Raffles Institution, One Raffles Institution Lane, Singapore 575954 2 Natural Sciences and Science Education, National Institute of Education, Nanyang Technological University, Singapore 637616

Abstract
The photoelectric effect is a well-known and widely taught field in many schools and institutions, yet it has been shown through theoretical arguments that there is a common error in the theory in which this topic is learnt and taught. The common theory is that the energy of the incoming photons must be greater than the work function of the emitter, and also that the difference between the energy of the photon and the work function of the emitter must be greater than the voltage applied between the emitter and collector multiplied by the elementary charge. This paper provides experimental evidence for the correct interpretation of the photoelectric effect in order to correct the misconception. In this paper, it was experimentally determined that both the work functions of the emitter and the collector metals must be taken into account in order for a current to be detected, contrary to conventional theory. Introduction

The photoelectric effect is the phenomenon in which electrons are liberated from matter as a result of electromagnetic radiation being shone onto it. Generally, the phenomenon is only investigated in metals as they require lower energy from the radiation.

The photoelectric effect was first discovered by Heinrich Hertz in 1887 and was explained by Albert Einstein in 1905.

Einstein’s model quantized light as photons, each with energy E=hν where h is the Planck’s constant and ν is the frequency. Einstein also introduced the work function ϕ of a material, defined as the minimum amount of energy needed in order to liberate an electron from the material. Through this model, the characteristic photoelectric equation eVs=hν-ϕ can be derived where Vs is the stopping voltage.

Eisntein’s explanation and relations of the photoelectric effect, shown below, has been taught in many schools all around the world today and is widely known.

Theory
In this section we present the derivation of the photoelectric equation eVs=hν-ϕ.

From the definition of ϕ, it follows that once an electron has been liberated, it has a maximum possible kinetic energy of hν-ϕ. This also implies that hν>ϕ for a liberation of electron.

When an external voltage V is applied across the metals, there is a potential difference between the plates and thus when the electron needs KE>eV in order to to reach the collector plate.

Combining the two relations, we get hν-ϕ>eV. In the equality case, we call the voltage Vs, which is the is the minimum amount of voltage needed to be applied such that no current is recorded. ‘Conventional’ understanding of the photoelectric effect:

‘Alternative’ understanding of the photoelectric effect:

The above section uses the work function ϕe referred to that of the emitter material, even when the emitter and collector are made of different materials. However, this is incorrect, and the derivation is shown below:

When an electron is just emitted from surface of the emitter, it has potential energy ϕe above the ground energy state. Conversely, when an electron is just emitted from surface of the collector, it has potential energy ϕc. Hence, if ϕe≠ϕc, we note that there will be a potential energy difference of ϕc-ϕe, even if there is no external voltage applied. This is known as the contact potential.

ϕc

ϕe

ϕc-ϕe

Potential Energy
Emitter
Collector
Figure 1: Energy diagram without an external voltage
ϕc

ϕe

ϕc-ϕe

Potential Energy
Emitter
Collector
Figure 1: Energy diagram without an external voltage

Once a potential difference of V is applied between...
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