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Photoelectric Effect Guide

PhysicsAdvancedReading time: 3 min

Overview

Is light a wave or a particle? In 1905, Einstein provided a world-shaking answer by explaining the "Photoelectric Effect": light has particle properties. This experiment simulates the process of photons bombarding a metal surface and ejecting electrons. By adjusting the light's frequency, intensity, and reverse voltage, you will personally experience the dawn of quantum mechanics and verify the famous Einstein photoelectric equation.

Background

  • In 1887, Heinrich Hertz first discovered the photoelectric effect in experiments, but he could not explain it using the electromagnetic wave theory of the time.
  • In 1902, Philipp Lenard discovered experimentally that the maximum kinetic energy of photoelectrons is independent of light intensity but depends on frequency, which contradicted the wave theory.
  • In 1905, Albert Einstein proposed the photon hypothesis, successfully explaining all experimental phenomena of the photoelectric effect, and was awarded the 1921 Nobel Prize in Physics for this.

Key Concepts

Photon

E=hfE = hf

Light energy comes in discrete packets, each called a photon. Its energy EE is determined by the frequency ff.

Work Function (Φ\Phi)

Φ=hf0\Phi = hf_0

The minimum energy required for an electron to escape from the surface of a metal. The work function varies for different metals and is usually denoted by Φ\Phi or WW.

Maximum Kinetic Energy (KmaxK_{\text{max}})

Kmax=hf−ΦK_{\text{max}} = hf - \Phi

The maximum kinetic energy possessed by a photoelectron as it escapes the metal surface. It equals the photon energy minus the work function.

Stopping Voltage (VsV_s)

eVs=Kmaxe V_s = K_{\text{max}}

The minimum reverse voltage required to reduce the photocurrent to zero. At this point, the negative work done by the electric field equals the maximum initial kinetic energy of the electrons.

Formulas & Derivation

Einstein's Photoelectric Equation

hf=Φ+Kmaxhf = \Phi + K_{\text{max}}
Part of the incident photon's energy hfhf is used to overcome the metal's binding force (Work Function Φ\Phi), and the remainder is converted into the electron's kinetic energy KmaxK_{\text{max}}.

Experiment Steps

  1. 1

    Find the Cutoff Frequency

    Select a metal (e.g., Sodium). Set the voltage to 0V0V. Starting from long wavelengths (red light), gradually decrease the wavelength (increase frequency) and observe at what wavelength electrons begin to be ejected. The frequency corresponding to this critical point is the cutoff frequency f0f_0.
  2. 2

    Explore the Effect of Intensity

    With photocurrent being generated, keep the wavelength constant and adjust the "Interval". Observe any changes in the number (density) of ejected electrons and their speed. What does light intensity represent?
  3. 3

    Measure Stopping Voltage

    Keep light intensity and frequency constant, and adjust the battery voltage to a negative value (reverse voltage). Observe how electrons are decelerated. Record the voltage value when the current just drops to 00. This is the stopping voltage VsV_s.
  4. 4

    Verify Einstein's Equation

    Change the frequency of the incident light and repeat step 3 to measure the stopping voltage at different frequencies. Consider whether there is a linear relationship between stopping voltage (representing measurement of maximum kinetic energy) and frequency.

Learning Outcomes

  • Confirm that the occurrence of the photoelectric effect depends on light frequency, not intensity
  • Master the proportional relationship between photocurrent magnitude and incident light intensity
  • Verify the law that maximum initial kinetic energy increases linearly with incident light frequency
  • Understand the "particle" characteristic of the wave-particle duality of light

Real-world Applications

  • Photocells: Used in automatic doors and street light sensors to generate current and control circuits when illuminated.
  • Solar Cells: Utilize the photovoltaic effect to convert light energy directly into electrical energy, a key component of clean energy.
  • Photomultiplier Tubes: Detect weak light signals in nuclear physics and medical imaging (like PET scans).
  • Digital Cameras (CCD/CMOS): Use the photoelectric effect to convert photon signals entering the lens into electronic signals for imaging.

Common Misconceptions

Misconception
As long as the light is bright enough, even red light can eject electrons from a zinc plate
Correct
Incorrect. If the photon energy hfhf is lower than the work function Φ\Phi, no matter how high the intensity (number of photons), a single photon cannot "kick" out an electron. This proves that energy is quantized.
Misconception
Increasing reverse voltage causes the photocurrent to increase infinitely
Correct
Incorrect. Increasing reverse voltage hinders electrons from reaching the anode, reducing the photocurrent. Increasing forward voltage increases current until it reaches saturation.
Misconception
The maximum kinetic energy of photoelectrons is proportional to light intensity
Correct
Incorrect. Maximum kinetic energy depends only on the frequency of light. Increasing intensity only adds more photons, thereby increasing the number of ejected electrons (photocurrent), but does not change the energy of individual electrons.

Further Reading

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