Photoelectric Effect

What is the Photoelectric Effect?

The photoelectric effect is the emission of electrons from a metal surface when light (or electromagnetic radiation) of sufficiently high frequency falls on it. The emitted electrons are called photoelectrons. This phenomenon, first observed by Heinrich Hertz in 1887, could not be explained by classical wave theory, which predicted that the kinetic energy of emitted electrons should increase with light intensity, not frequency. In 1905, Albert Einstein provided a revolutionary explanation by proposing that light consists of discrete packets of energy called photons, each with energy E = hν, where h is Planck’s constant and ν is the frequency. Einstein’s theory earned him the Nobel Prize in Physics in 1921.

Where h = 6.626 × 10⁻³⁴ J·s, c = 3.0 × 10⁸ m/s (speed of light), λ = wavelength.

Interactive Photoelectric Effect Simulation

Adjust the light frequency (color) and intensity to see how photoelectrons are emitted from a potassium metal surface (work function = 2.30 eV). The simulation shows the photocurrent and kinetic energy of emitted electrons.

Graph of maximum kinetic energy vs frequency. The slope is h (Planck’s constant), and the x-intercept gives the threshold frequency.

Einstein’s Photoelectric Equation

Einstein proposed that a single photon transfers its entire energy to a single electron. The electron uses part of this energy to overcome the work function Φ (the minimum energy needed to escape the metal), and the remainder becomes its kinetic energy.

where Φ = hν_th (threshold frequency). The threshold frequency is the minimum frequency required to eject an electron. For frequencies below ν_th, no electrons are emitted regardless of intensity.

m_e = 9.11 × 10⁻³¹ kg (electron mass). The maximum kinetic energy K_max increases linearly with frequency, independent of intensity — a key prediction verified experimentally.

Work Function and Threshold Frequency

Above threshold (f > f_th), electrons are emitted with kinetic energy increasing linearly with frequency. Below threshold, no emission occurs.

Stopping Potential

The stopping potential V_s is the retarding voltage needed to stop the most energetic photoelectrons from reaching the anode. It is directly related to the maximum kinetic energy:

where e = 1.602 × 10⁻¹⁹ C (elementary charge). Combining with Einstein’s equation:

A plot of V_s versus ν gives a straight line with slope h/e, from which Planck’s constant can be determined. The intercept on the frequency axis gives the threshold frequency.

Stopping potential vs frequency. The linear relationship confirms Einstein’s equation and yields Planck’s constant from the slope.

Experimental Setup (Millikan’s Apparatus)

Robert Millikan conducted precise experiments to verify Einstein’s photoelectric equation. His apparatus consisted of:

• A clean metal surface (emitter) and a collector electrode in an evacuated glass tube.
• A monochromatic light source (mercury arc) with filters to select specific wavelengths.
• A variable voltage source to apply a retarding or accelerating potential between the electrodes.
• A sensitive galvanometer to measure photocurrent.

By measuring the stopping potential for different frequencies, Millikan obtained a straight-line graph, confirming Einstein’s equation and providing an accurate measurement of Planck’s constant.

Schematic of Millikan’s photoelectric effect apparatus. Light incident on the metal plate causes emission of electrons, and the stopping potential is measured to determine their maximum kinetic energy.

Properties of Photons

• Photons are massless, chargeless particles that travel at the speed of light in a vacuum.
• Energy of a photon: E = hν = hc/λ
• Momentum of a photon: p = h/λ = E/c
• Photons are not deflected by electric or magnetic fields.
• They exhibit both wave and particle properties (wave-particle duality).
• In interactions with matter, photons can be absorbed or scattered (e.g., photoelectric effect, Compton scattering).

Applications of the Photoelectric Effect

Contrast with Classical Wave Theory

Classical wave theory predicted that the kinetic energy of photoelectrons should increase with light intensity and that the effect should occur at any frequency if the intensity is high enough. The photoelectric effect contradicted both predictions:

Video Lecture: Photoelectric Effect in Urdu/Hindi

Summary & Key Takeaways

• The photoelectric effect is the emission of electrons from a metal surface when illuminated by light of sufficient frequency.
• Einstein proposed that light consists of photons with energy E = hν.
• The work function Φ is the minimum energy needed to remove an electron; it varies with the metal.
• Einstein’s photoelectric equation: K_max = hν – Φ.
• Threshold frequency ν_th = Φ/h; below this frequency, no electrons are emitted regardless of intensity.
• The stopping potential V_s is related to K_max: e V_s = hν – Φ.
• The photoelectric effect provided direct evidence for the quantum nature of light and confirmed Planck’s constant.