Q.What is photoelectric effect? State the result of photoelectric effect experiment that could not be explained on the basis of laws of classical physics. Explain this effect on the basis of quantum theory of electromagnetic radiations.

Concept: Photoelectric effect and the quantum nature of light

The photoelectric effect is the phenomenon in which electrons are ejected from a metal surface when electromagnetic radiation (typically ultraviolet or visible light) of sufficiently high frequency strikes it.

Classical physics failure:

According to classical wave theory, the energy of a wave depends on its intensity (amplitude), not frequency. Classical physics predicted that:

• Any frequency of light should eject electrons if the intensity is high enough
• There should be a time lag between illumination and electron emission while the electron accumulates energy

The experiment showed instead that below a certain threshold frequency $\nu_0$, no electrons are emitted regardless of intensity, and above $\nu_0$ emission is instantaneous. This contradicted wave theory completely.

Quantum explanation (Einstein, 1905): …

The Photoelectric Effect

When electromagnetic radiation (light) of sufficiently high frequency strikes a metal surface, electrons are emitted from that surface. This phenomenon is called the photoelectric effect, and the emitted electrons are called photoelectrons.

Heinrich Hertz discovered it in 1887, and the systematic experimental study by Philipp Lenard in the early 1900s revealed several puzzling features that defied classical electromagnetic theory.

The Classical Physics Failure

Classical wave theory of light predicted that:

• The energy carried by a wave is proportional to its intensity (amplitude squared).
• A more intense light wave should deliver more energy to electrons, eventually giving them enough to escape.
• There should be no frequency dependence—only intensity should matter.
• There should be a time lag between when light strikes the surface and when electrons are emitted, as the electron gradually absorbs energy.

The Experimental Results That Contradicted Classical Physics

The experiments revealed three key observations that classical physics could not explain:

1. Existence of a threshold frequency ($\nu_0$): Below a certain frequency, no electrons are emitted no matter how intense the light. A very bright red light (low frequency) produces nothing, while a dim violet light (high frequency) immediately ejects electrons. Classical theory predicted that any frequency should work if the intensity is high enough.

2. Instantaneous emission: Photoelectrons are emitted essentially instantaneously (within $10^{-9}$ s) after light strikes the surface, even at very low intensities. Classical theory predicted a time delay during which the electron would accumulate enough energy to escape.

3. Kinetic energy depends on frequency, not intensity: The maximum kinetic energy of the emitted electrons increases linearly with the frequency of the incident light but is independent of its intensity. Increasing intensity only increases the number of electrons emitted, not their energy. Classical theory predicted that higher intensity should produce more energetic electrons.

Einstein's Quantum Explanation (1905)

Einstein extended Planck's quantum hypothesis to explain the photoelectric effect. He proposed that light itself is quantized—it consists of discrete packets of energy called photons.

The Photon Picture

Each photon carries energy:

where $h = 6.626 \times 10^{-34}$ J·s is Planck's constant and $\nu$ is the frequency of the light.

When a photon strikes the metal surface, it interacts with a single electron in an all-or-nothing collision. The photon transfers all its energy to that one electron. The electron uses part of this energy (the work function $\phi_0$) to escape the attractive forces binding it to the metal, and the remainder appears as the electron's kinetic energy.

Einstein's Photoelectric Equation

The energy conservation for this process is:

or equivalently,

where:

• $K_{\text{max}} = \frac{1}{2}m v_{\text{max}}^2$ is the maximum kinetic energy of the emitted electron,
• $\phi_0 = h\nu_0$ is the work function (minimum energy needed to free an electron),
• $\nu_0$ is the threshold frequency.

How Quantum Theory Explains the Observations …