2. The Photoelectric Effect

Concept Explanation:

The photoelectric effect is a phenomenon where electrons are ejected from the surface of a metal when it is exposed to light of a certain frequency. Albert Einstein provided an explanation for this effect using Planck's quantum hypothesis. He proposed that light consists of particles called photons, and each photon carries energy proportional to its frequency.

For an electron to be ejected, the energy of the photon must be greater than the work function (φ) of the metal, which is the minimum energy required to remove an electron from the metal’s surface. The energy balance can be described as:

hν = φ + Kₑ

where:
hν is the energy of the photon,
φ is the work function of the metal,
Kₑ is the kinetic energy of the ejected electron.

Example Problem:

Light with a frequency of 7 × 10¹⁴ Hz is incident on a metal surface with a work function of 2.0 × 10⁻¹⁹ J. Calculate the kinetic energy of the ejected electron.

Solution:

First, calculate the energy of the incident photon:

E = hν = 6.626 × 10⁻³⁴ J·s × 7 × 10¹⁴ Hz = 4.638 × 10⁻¹⁹ J

The kinetic energy of the ejected electron is given by:

Kₑ = E − φ = 4.638 × 10⁻¹⁹ J − 2.0 × 10⁻¹⁹ J = 2.638 × 10⁻¹⁹ J