Building on Max Planck's attempt to reconcile classical physics with blackbody radiation, as well as the anomalous experimental observations made by Philipp Lenard, Albert Einstein proposed a radical explanation for the nature of light—thereby ushering in the concept of wave-particle duality.

The Classical Dilemma & Lenard's Observations

Under classical wave theory (Maxwell's equations), light is an electromagnetic wave. Classical physics made three key predictions regarding light striking a metal surface:

1. Intensity Dependence: Increasing the light intensity (brightness) increases the electric field amplitude, which should grant ejected photoelectrons greater maximum kinetic energy (K_max).
2. Frequency Independence: Light of any frequency should eventually eject electrons, provided the intensity is high enough or the light shines long enough.
3. Time Lag: For low-intensity light, there should be a measurable delay while electrons absorb enough continuous wave energy to break free.

However, Philipp Lenard’s vacuum tube experiments contradicted classical theory on every point:

• Increasing light intensity produced more photoelectrons per second (higher photocurrent), but did not increase their individual kinetic energy.
• Below a specific threshold frequency (f₀), no electrons were ejected, regardless of light intensity or exposure duration.
• Electron emission was instantaneous (≪ 1 ns) whenever f > f₀.

Einstein's Photon Model & The Photoelectric Equation

In 1905, Einstein proposed that light consists of localized quanta of energy called photons. Each photon carries an energy (E) directly proportional to its frequency (f):

When a photon strikes a metal surface, it transfers its energy to a single electron in a 1-to-1 interaction:

• A minimum amount of energy, called the work function (Φ or W), is required to overcome the electrostatic binding forces of the metal lattice.
• Any remaining energy becomes the electron's maximum kinetic energy (K_max):

Using the wave speed relationship c = f λ, this can also be expressed in terms of wavelength (λ) and threshold wavelength (λ₀):

Key Concepts to Remember

• Threshold Frequency (f₀ = Φ / h): Photons with f < f₀ lack sufficient energy to overcome the work function (Φ), explaining why no photocurrent flows regardless of intensity.
• Stopping Voltage (V_s): The maximum kinetic energy can be experimentally measured by applying a retarding electric potential until the photocurrent drops to zero:
  K_max = e V_s
• Slope of K_max vs. f: A plot of K_max (or V_s) against frequency yields a straight line where the slope is Planck's constant (h) and the x-intercept represents the threshold frequency (f₀).