Animated Solution for Physics - Dual Nature of Matter and Radiation: Photoelectric effect supports quantum nature of light because

The photoelectric effect is one of the most beautiful and revolutionary phenomena in modern physics. It single-handedly shattered the classical wave theory of light and paved the way for quantum mechanics.

Imagine you are standing in front of a metal surface. When you shine a light on it, something magical happens: electrons start popping out! But the rules governing how they pop out completely baffled scientists in the late 19th century. Let's dive into the mystery and see how Albert Einstein solved it.

According to the classical wave theory, light is a continuous wave of energy. If you shine a light on a metal, the energy should spread out evenly over the surface.

If the light is very dim, the wave theory predicts that an electron would have to "wait" and accumulate energy over time until it has enough to break free. Furthermore, if you increase the intensity (brightness) of the light, the wave theory says the electrons should come out with more kinetic energy.

But experiments showed the exact opposite!

Einstein proposed a radical idea: light is not a continuous wave. Instead, it is made of tiny, discrete packets of energy called photons.

Each photon carries a specific amount of energy given by the equation: where $h$ is Planck's constant and $ u$ is the frequency of the light.

When a photon hits the metal, it doesn't spread its energy around. It acts like a billiard ball. It hits a single electron and transfers all of its energy to that electron instantaneously.

Let's use Einstein's brilliant insight to analyze the options in our question.

Option (a): The Threshold Frequency For an electron to escape the metal, it must overcome the attractive forces holding it inside. This minimum energy required is called the work function ($\Phi$).

If the incoming photon's energy ($h u$) is less than the work function ($\Phi$), the electron simply cannot escape, no matter how bright the light is or how long you wait. This means there must be a minimum frequency, called the threshold frequency ($ u_0 = \frac{\Phi}{h}$), below which no emission occurs. This perfectly supports the quantum nature of light!

Option (b): Kinetic Energy vs. Intensity Einstein's photoelectric equation is beautifully simple:

This equation tells us that the maximum kinetic energy ($K_{\max }$) of the ejected electron depends only on the frequency of the light ($ u$) and the nature of the metal ($\Phi$).

What happens if we increase the intensity of the light? In the quantum world, higher intensity just means more photons are hitting the surface per second. More photons mean more electrons are ejected, but the energy of each individual photon remains exactly the same. Therefore, the maximum kinetic energy does not change. This is another massive win for the quantum theory!

Option (c): Instantaneous Emission Because the interaction is a one-to-one collision between a photon and an electron, the energy transfer happens in a fraction of a nanosecond.

Even if the light is incredibly faint (low intensity), as long as the frequency is above the threshold, the very first photon that strikes an electron will eject it immediately. There is no "waiting time" for energy to build up. This instantaneous emission is a direct consequence of the particle nature of light.

Option (d): Quantization of Charge This option states that the electric charge of photoelectrons is quantized ($q=ne$). While this is a fundamental truth of the universe, it has absolutely nothing to do with the quantum nature of light. The quantization of charge is a property of matter, famously proven by Millikan's oil drop experiment. Therefore, it is not the reason why the photoelectric effect supports the quantum theory of light.

The photoelectric effect is the ultimate proof that light behaves as a stream of particles. The existence of a threshold frequency, the independence of kinetic energy from intensity, and the instantaneous emission of electrons all point directly to the photon model.

Therefore, the correct options are (a), (b), and (c).