Experimental Observations and Findings

The study of the photoelectric effect began in the late 19th century with the pioneering work of Heinrich Hertz and Philipp Lenard. They conducted experiments to investigate the emission of electrons from a metal surface when exposed to light.

Key Observations:

1. Threshold Frequency: Lenard discovered that only light above a certain frequency, called the threshold frequency ($f_{\text{th}}$), would cause the emission of electrons. Light below this frequency did not produce any observable photoelectric effect.

   Formula:

   The threshold frequency is related to the work function ($\phi$) of the material by the equation:

   $$\begin{equation} f_{\text{th}} = \frac{\phi}{h} \end{equation}$$

   where $h$ is the Planck's constant.

2. Instantaneous Emission: As soon as the light of sufficient frequency strikes the metal surface, the electrons are instantaneously emitted. There is no time delay between the light exposure and the emission of electrons.

3. Kinetic Energy Dependence: The maximum kinetic energy ($E_{\text{max}}$) of the emitted electrons is directly proportional to the frequency ($f$) of light, while being independent of its intensity (intensity refers to the number of photons per unit area per unit time).

   Formula:

   The kinetic energy of the emitted electrons can be calculated using the equation:

   $$\begin{equation} E_{\text{max}} = hf - \phi \end{equation}$$

   where $h$ is Planck's constant, $f$ is the frequency of light, and $\phi$ is the work function of the material.

Challenges Faced:

The early researchers encountered several challenges in understanding the photoelectric effect.

1. Wave Theory Limitation: The wave theory of light, which was prevalent at that time, failed to explain the observations. According to this theory, increasing light intensity should lead to an increase in electron emission, regardless of frequency. However, this was not observed in the experiments.

2. Nature of Electrons: At the time, the nature of electrons was not well understood. It was unclear how light could cause the emission of electrons from a metal surface.

These challenges prompted further investigations, eventually leading to Albert Einstein's groundbreaking explanation of the photoelectric effect, which will be discussed in the next post.

Example:

To illustrate the observations, consider a metal surface with a work function of $\phi = 3.5\, \text{eV}$. When light with a frequency of $f = 5 \times 10^{14} \, \text{Hz}$ and an intensity of $I = 2 \, \text{W/m}^2$ is incident upon the surface, we can calculate the maximum kinetic energy of the emitted electrons using Equation 2.

Substituting the values into the equation, we have:

\begin{align*} E_{\text{max}} &= 6.63 \times 10^{-34} , \text{J s} \times 5 \times 10^{14} , \text{Hz} - 3.5 , \text{eV} \ &= 3.32 \times 10^{-19} , \text{J} - 5.60 \times 10^{-19} , \text{J} \ &= -2.28 \times 10^{-19} , \text{J} \end{align*}

Since the kinetic energy cannot be negative, we conclude that no electrons will be emitted from the metal surface under these conditions.