E2-1. The Photoelectric Effect and Particle Nature of LightHL Only

1. The Photoelectric Effect

Definition and Core Concept

  • The photoelectric effect is the phenomenon in which electrons are emitted from the surface of a metal upon the absorption of electromagnetic radiation.
  • Electrons removed from the surface in this manner are known as photoelectrons.
  • This effect provides critical evidence that light behaves as a particle, meaning its energy is quantised and carried in discrete packets known as photons. Each electron can absorb only a single photon.

Threshold Frequency and Work Function

  • Threshold Frequency ($f_0$): The minimum frequency of incident electromagnetic radiation required to remove a photoelectron from the surface of a metal.
  • Work Function ($\Phi$): The minimum energy required to release a photoelectron from the surface of a metal.
  • Consider the electrons in a metal as trapped inside an "energy well". An electron can only escape from the surface of the metal if it absorbs a photon which has an energy equal to or higher than the work function.
  • Alkali metals (e.g., sodium) have weaker attractive forces between surface electrons and positive ions, giving them threshold frequencies in the visible light region. Transition metals (e.g., zinc) have much stronger attractive forces, requiring higher energy UV light.

2. Evidence for the Particle Nature of Light

The Gold Leaf Electroscope Experiment

The photoelectric effect is often demonstrated using a gold leaf electroscope. A metal plate (usually zinc) is given a negative charge, causing the attached gold leaf to be repelled. When UV light is shone onto the plate, photoelectrons are emitted, and the leaf falls as the plate becomes less negatively charged.

  • Instantaneous Emission: The gold leaf begins to fall instantly when illuminated with UV light, even at low intensities. This supports a one-to-one quantised energy transfer from photon to electron.
  • Frequency Dependence: The gold leaf does not fall when lower frequencies of light (like visible light) are used, indicating no electrons are emitted. This proves the existence of a threshold frequency and minimum energy (work function), which classical wave theory cannot explain.
  • Intensity Effect: At lower intensities of UV light, the gold leaf falls more slowly, demonstrating that the intensity of light affects the rate of photoelectric emission (the number of electrons emitted per second), not the kinetic energy of the electrons.

3. Examples

Example 1: The Particulate Nature of Light vs. Wave Theory

Problem: Using observations from the gold leaf electroscope experiment, explain why classical wave theory fails to explain the photoelectric effect and how the photon model successfully resolves these issues.

Solution:

Under classical wave theory, electromagnetic energy is delivered continuously over time. This implies that any frequency of light, given enough time, should eventually transfer enough energy for an electron to escape, and that there should be a noticeable time delay at low intensities as the energy "builds up."

However, experimental observations contradict this. Emission happens instantaneously with high-frequency UV light, proving that energy transfer occurs in singular, discrete quantum events. Furthermore, below a certain threshold frequency, emission never occurs, no matter how intense the light is or how long it shines. This is perfectly explained by Einstein's photon model: light consists of particles (photons) with energy $E = hf$. Because an electron can only interact with one photon at a time, it will only escape if that single photon possesses enough energy to overcome the metal's work function ($\Phi$).

Example 2: The Classical Time-Delay Paradox

Problem: Before Einstein’s photon model, classical physicists believed light was a continuous wave that distributed its energy evenly over a surface. Consider a dim UV light with an intensity of $1.0 \times 10^{-6} \text{ W m}^{-2}$ shining on a zinc plate (Work Function $\Phi = 4.3 \text{ eV}$). Assume a single zinc atom has a cross-sectional surface area of roughly $1.0 \times 10^{-19} \text{ m}^2$.
(a) Using classical wave theory, calculate how long it would take for a single electron to absorb enough energy to escape the metal.
(b) Explain how experimental observations of this scenario support the quantum photon model instead.

Solution:

Part (a): Classical calculation:
First, convert the work function to Joules: $$\Phi = 4.3 \text{ eV} \times (1.60 \times 10^{-19} \text{ J/eV}) = 6.88 \times 10^{-19} \text{ J}$$ Next, calculate the classical continuous power delivered to a single atom: $$\begin{aligned} P_{\text{atom}} &= \text{Intensity} \times \text{Area} = (1.0 \times 10^{-6} \text{ J s}^{-1} \text{ m}^{-2}) \times (1.0 \times 10^{-19} \text{ m}^2) \\ &= 1.0 \times 10^{-25} \text{ J s}^{-1} \end{aligned} $$ Determine the time ($t$) required to absorb the escape energy: $$t = \frac{\text{Energy Required}}{\text{Power}} = \frac{6.88 \times 10^{-19} \text{ J}}{1.0 \times 10^{-25} \text{ J s}^{-1}} = \mathbf{6.88 \times 10^6 \text{ s}}$$ Context: This is roughly 80 days! Classical theory predicts you would have to shine the light for months before a single electron pops off.

Part (b): The Quantum resolution:
Experimentally, photoelectrons are emitted instantaneously (within $10^{-9}$ seconds), even at exceptionally low intensities. This proves that energy is not absorbed continuously over an area, but rather delivered in concentrated, localised, quantised packets (photons). A single electron absorbs a single photon; if $hf > \Phi$, it escapes immediately.

Example 3: The Electroscope Charge Reversal Trick

Problem: A gold-leaf electroscope is fitted with a clean zinc plate. The threshold frequency of zinc corresponds to the UV spectrum.
(a) The electroscope is given a strong negative charge, and the leaf rises. What happens to the leaf when visible light is shone on it, and then when UV light is shone on it?
(b) The electroscope is discharged and then given a strong positive charge (the leaf rises again). High-intensity UV light is shone on the plate. Explain what happens to the gold leaf and why.

Solution:

Part (a): When visible light is used, the frequency is below the threshold frequency ($f < f_0$). No electrons are emitted, so the leaf remains raised. When UV light is used ($f > f_0$), photoelectrons are ejected. The electroscope loses its negative charge, and the gold leaf falls.

Part (b): When the electroscope is positively charged, the leaf is raised due to a deficit of electrons. If UV light shines on it, photons still hit the electrons with enough energy to overcome the zinc's work function. However, the moment an electron leaves the surface, it is overwhelmingly attracted back to the metal by the massive net positive electrostatic charge of the plate. It is immediately pulled back down. Therefore, the net charge of the electroscope does not change, and the gold leaf remains raised.