11.5. PHOTOELECTRIC EFFECT AND WAVE THEORY OF LIGHT

The wave nature of light was well established by the end of the nineteenth century. The phenomena of interference, diffraction and polarisation were explained in a natural and satisfactory way by the wave picture of light. According to this picture, light is an electromagnetic wave consisting of electric and magnetic fields with continuous distribution of energy over the region of space over which the wave is extended. Let us now see if this wave picture of light can explain the observations on photoelectric emission given in the previous section.

The wave theory of light describes light as an electromagnetic wave that propagates through space. In this theory, light does not consist of particles but rather fields that oscillate. This model explains various phenomena, such as interference patterns and the bending of light (diffraction). However, when scientists observed the photoelectric effect—where light shining on a metal surface caused the emission of electrons—the wave theory faced challenges. The theory predicted that the energy absorbed by electrons would correlate with light intensity and that any sufficiently intense light could cause emission, irrespective of frequency. However, this was not supported by experimental evidence.

Think of a wave in the ocean—when waves hit the shore, they can wash away small pebbles. If you throw larger waves (higher intensity), you may expect to move larger rocks—but that’s not the case with the photoelectric effect where only certain frequencies of light can 'move' the electrons, much like how only specific tides can wash away bigger objects.

According to the wave picture of light, the free electrons at the surface of the metal (over which the beam of radiation falls) absorb the radiant energy continuously. The greater the intensity of radiation, the greater are the amplitude of electric and magnetic fields. Consequently, the greater the intensity, the greater should be the energy absorbed by each electron. In this picture, the maximum kinetic energy of the photoelectrons on the surface is then expected to increase with increase in intensity. Also, no matter what the frequency of radiation is, a sufficiently intense beam of radiation (over sufficient time) should be able to impart enough energy to the electrons, so that they exceed the minimum energy needed to escape from the metal surface. A threshold frequency, therefore, should not exist. These expectations of the wave theory directly contradict observations.

According to wave theory, increasing light intensity means more energy is imparted to the electrons. This should, in principle, lead to higher kinetic energy for the electrons released from the metal surface. However, experiments showed that only light of certain frequencies could release electrons, regardless of how intense the light was. This indicated that there was a minimum frequency (threshold frequency) below which no electrons were emitted, contradicting the continuous absorption concept of wave theory.

Imagine soaking a sponge with water. If you pour water slowly (low intensity), it takes time for the sponge to become saturated. But if you pour water with a high flow rate, you expect the sponge to absorb quickly. However, if you only pour a certain type of liquid that the sponge doesn't absorb, neither high nor low flow will help. This reflects how not all light can 'saturate' or energize the electrons in metals.

Further, we should note that in the wave picture, the absorption of energy by electron takes place continuously over the entire wavefront of the radiation. Since a large number of electrons absorb energy, the energy absorbed per electron per unit time turns out to be small. Explicit calculations estimate that it can take hours or more for a single electron to pick up sufficient energy to overcome the work function and come out of the metal. This conclusion is again in striking contrast to observation (iv) that the photoelectric emission is instantaneous.

Wave theory implies that electrons take time to gather enough energy to be emitted from the surface of a metal. Calculation in wave theory suggested long time periods (like hours) for significant energy absorption by the electrons. However, experiments found that electrons could be emitted almost instantaneously after light of a suitable frequency struck the metal. This contradiction points to a fundamental problem in the continuity assumption of the wave model.

Consider a faucet dripping water into a container. It takes time to fill the container. If you switch to a hose, water fills up almost instantly. In the electron scenario, the slow filling represents wave theory; the instant fill-up represents the reality of the photoelectric emission.

In short, the wave picture is unable to explain the most basic features of photoelectric emission.

The wave theory of light does not adequately describe phenomena such as the existence of a threshold frequency or the instantaneous nature of electron emission. This led to the realization that light must also possess characteristics associated with particles. The inability of wave theory to explain these observations necessitated a new understanding of light and its interaction with matter.

Imagine trying to solve a puzzle with only one piece when the picture on the box shows it should have multiple pieces. Just like that, wave theory failed to provide all the pieces needed to understand the photoelectric effect, prompting scientists to explore particle models.

--