Animated Solution for Physics - Dual Nature of Matter and Radiation: Match List I (fundamental experiment) with List II (its conclusion) and select the correct option from the choices given below the list. $\begin{array}{ll}\text{List I}& \text{List II}\\ \text{A. Franck-Hertz experiment}& \text{1. Particle nature of light}\\ \text{B. Photo-electric experiment}& \text{2. Discrete energy levels of atom}\\ \text{C. Davisson-Germer experiment}& \text{3. Wave nature of electron}\\ & \text{4. Structure of atom}\end{array}$

Imagine the early 20th century. Classical physics, which had beautifully explained the macroscopic world for centuries, was suddenly struggling to make sense of the microscopic realm. The universe was not as continuous and predictable as Newton and Maxwell had thought. It was chunky, probabilistic, and deeply weird.

To understand this transition, we look at three monumental experiments that acted as the pillars of modern quantum mechanics. Let's decode them one by one.

Staircases of Energy

In 1914, James Franck and Gustav Hertz set out to probe the internal structure of the atom. They designed an elegant experiment where they fired electrons through a vacuum tube filled with mercury vapor.

According to classical physics, an electron should be able to transfer any arbitrary amount of its kinetic energy to a mercury atom during a collision. But that's not what happened. Franck and Hertz observed that the electrons would bounce off the mercury atoms elastically, losing almost no energy, until they reached a very specific kinetic energy threshold: exactly $4.9\text{ eV}$.

At exactly $4.9\text{ eV}$, the electrons suddenly lost all their energy. Why? Because the mercury atom could only absorb energy in specific, quantized chunks. This was the first direct experimental proof of Niels Bohr's radical idea: atoms possess discrete energy levels. The atom is like a staircase; you can stand on step 1 or step 2, but you cannot hover in between. Thus, the Franck-Hertz experiment perfectly matches with the conclusion of discrete energy levels of an atom.

Light as Bullets

While atoms were revealing their discrete nature, light was also undergoing an identity crisis. For decades, light was universally accepted as a continuous electromagnetic wave. But the photoelectric effect threw a wrench into this theory.

When high-frequency light shines on a metal surface, it ejects electrons. Classical wave theory predicted that if you shine a very bright, low-frequency light (like intense red light) for a long enough time, the energy would eventually "build up" and knock an electron loose. But experiments showed that no matter how intense the red light was, or how long you waited, no electrons were ever ejected. However, even a very dim blue light would eject electrons instantaneously.

In 1905, Albert Einstein solved this mystery by proposing that light is not a continuous wave, but a stream of discrete energy packets, now called photons. The energy of each photon is given by $E = h u$. A single photon of blue light has enough energy to knock out an electron, while a photon of red light does not. This brilliant insight firmly established the particle nature of light.

Matter Rides the Wave

If light, which was thought to be a wave, could act like a particle, could a particle act like a wave? In 1924, Louis de Broglie made this bold hypothesis, suggesting that all matter has an associated wavelength given by $\lambda =\frac{h}{p}$.

Three years later, Clinton Davisson and Lester Germer accidentally proved him right. They were firing a beam of electrons at a piece of nickel. After a vacuum tube broke and they had to heat the nickel to clean it, the nickel formed large crystal domains. When they resumed firing electrons, they didn't see the electrons bouncing off randomly like billiard balls. Instead, they observed a distinct diffraction pattern.

Diffraction is a hallmark property of waves! The electrons were interfering with each other just like ripples in a pond. The spacing of the nickel atoms acted as a diffraction grating, and the observed diffraction peaks perfectly matched the wavelength predicted by de Broglie's formula. This groundbreaking experiment undeniably confirmed the wave nature of electrons.

Matching the pieces of this quantum puzzle: - A. Franck-Hertz experiment $\to$ 2. Discrete energy levels of atom - B. Photo-electric experiment $\to$ 1. Particle nature of light - C. Davisson-Germer experiment $\to$ 3. Wave nature of electron

This corresponds to the combination A-2, B-1, C-3, making option (c) the correct choice. These three experiments collectively shattered classical mechanics and built the foundation of the quantum world we study today.