2.2.1 The Photoelectric Effect

Understanding the Photoelectric Effect

The photoelectric effect is the process in which photoelectrons are emitted from the surface of a metal when light of a certain frequency is shone on it. However, light below a specific frequency fails to emit photoelectrons, regardless of its intensity. This specific frequency is known as the threshold frequency, and it varies depending on the type of metal.

Wave Theory vs Photon Theory

The wave theory of light suggested that any frequency of light should eventually provide enough energy to release an electron if it is intense enough, but experiments showed this was not the case. The photon model of light, however, provides a solution to this observation. According to this model:

1. Photons: Light consists of discrete packets of energy called photons.

• The energy of each photon is proportional to its frequency $( E = hf )$, where $h$ is Planck's constant $($approximately 6.63 × 10^-34 J s $)$.

2. Absorption of Photons by Electrons: Each electron can absorb only one photon at a time.

• If the photon's energy (related to its frequency) is above the threshold frequency for that metal, the electron absorbs this energy and is emitted as a photoelectron.
• If the frequency of light is below the threshold frequency, no photoelectrons are emitted, regardless of the intensity.

3. Effect of Light Intensity: If the intensity of light is increased (more photons per second), and the frequency is above the threshold, more photoelectrons are emitted per second. However, the maximum kinetic energy of each photoelectron depends only on the frequency, not the intensity.

Key Terms in the Photoelectric Effect

1. Work Function $( \phi)$:

• The work function is the minimum energy required to remove an electron from the surface of a metal. It is unique to each material.
• If the photon energy (determined by its frequency) is greater than the work function, electrons can be emitted.

2. Stopping Potential $( V_s)$:

• The stopping potential is the voltage needed to stop the emitted photoelectrons with maximum kinetic energy.
• By applying a stopping potential, we can measure the maximum kinetic energy of the photoelectrons:

$$E_{k(\text{max})} = e V_s$$

where $e$ is the charge of an electron $( :highlight[1.6 × 10^-19 C]$) and $V_s$ is the stopping potential. This relationship is derived from the formula $\text{energy} = \text{charge} \times \text{voltage}$.

The Photoelectric Equation

The photoelectric equation relates the energy of the incident photon, the work function of the material, and the kinetic energy of the emitted photoelectrons:

$$E = hf = \phi + E_{k(\text{max})}$$

where:

• $E$ is the photon energy,
• $hf$ represents the photon energy (with $f$ being the frequency of light),
• $\phi$ is the work function of the metal,
• $E_{k(\text{max})}$ is the maximum kinetic energy of the emitted photoelectron.

Understanding the Equation:

• If $hf = \phi$ , the photon has just enough energy to release an electron, but the electron will have zero kinetic energy.
• If $hf > \phi$ , the excess energy $( hf - \phi )$ appears as the kinetic energy of the emitted electron.