Animated Solution for Chemistry - Atomic Structure: Given below are two statements : Statement I Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen atom. Statement II Bohr's model of hydrogen atom contradicts Heisenberg's uncertainty principle. In the light of the above statements, choose the most appropriate answer from the options given below :

The journey to understand the fundamental building blocks of matter is one of the most thrilling sagas in the history of science. It is a story of brilliant hypotheses, unexpected experimental results, and the constant shattering of old paradigms to make way for new, more profound truths. In this problem, we are asked to evaluate two critical statements that highlight the limitations of two of the most famous atomic models: Rutherford's planetary model and Bohr's quantized model.

Let's embark on this historical journey and dissect the physics behind these statements.

The Nuclear Dawn

Imagine you are Ernest Rutherford in 1911. You fire a beam of heavy, positively charged alpha particles at a ridiculously thin sheet of gold foil. You expect them to pass straight through, like bullets through tissue paper, based on J.J. Thomson's "plum pudding" model. But astonishingly, a tiny fraction of the alpha particles bounce right back at you!

Rutherford famously remarked that it was as if you fired a 15-inch naval shell at a piece of tissue paper and it came back and hit you. This led to a monumental breakthrough: the atom is mostly empty space, with almost all its mass and positive charge concentrated in a tiny, dense center called the nucleus. He proposed that electrons revolve around this nucleus much like planets revolve around the sun.

Why Rutherford Failed

While Rutherford's model was revolutionary, it harbored a fatal flaw. According to Maxwell's electromagnetic theory, any charged particle undergoing acceleration must continuously emit electromagnetic radiation. An electron moving in a circular orbit is constantly changing direction, meaning it is constantly accelerating.

If the electron is continuously radiating energy, it must lose kinetic energy. As it loses energy, its orbit should decay, causing it to spiral inward and eventually crash into the nucleus in a fraction of a second. This means Rutherford's atom should be highly unstable, which contradicts the very existence of stable matter!

Furthermore, if the electron spirals inward, it would emit radiation of continuously increasing frequency. This would produce a continuous spectrum. However, experimental evidence showed that atoms like hydrogen emit light only at specific, discrete wavelengths, creating a line spectrum. Rutherford's model was completely silent on why this happens. Therefore, Statement I is absolutely true.

To rescue the atom from classical collapse, Niels Bohr stepped in with a radical idea in 1913. He proposed that electrons do not radiate energy while revolving in certain special, "allowed" orbits. He introduced the concept of quantization, stating that the angular momentum of the electron is an integral multiple of $\frac{h}{2\pi }$.

In Bohr's model, an electron has a perfectly defined, exact radius ($r$) and a perfectly defined, exact velocity ($v$) in any given stationary state. It only emits or absorbs energy when it "jumps" between these fixed orbits, perfectly explaining the discrete line spectrum of hydrogen.

The Death of Determinism

Bohr's model was a triumph, but it was still a semi-classical patch. It treated the electron as a tiny billiard ball moving on a deterministic track. In 1927, Werner Heisenberg introduced a principle that shook the foundations of physics: the Uncertainty Principle.

Heisenberg mathematically proved that it is fundamentally impossible to simultaneously determine both the exact position ($\Delta x$) and the exact momentum ($\Delta p$) of a microscopic particle. The relationship is given by the famous inequality:

If you know exactly where an electron is, you have no idea how fast it is moving. If you know exactly how fast it is moving, you have no idea where it is.

Bohr's model, which assigns an exact radius (position) and an exact velocity (momentum) to the electron simultaneously, is in direct violation of this fundamental law of nature. The concept of a "fixed orbit" or a "trajectory" simply does not exist in the quantum realm. Instead, we must speak of "orbitals"—regions of probability where an electron is likely to be found. Therefore, Statement II is also absolutely true.

By tracing the historical evolution from classical electrodynamics to quantum mechanics, we can clearly see the stepping stones of scientific progress. Rutherford gave us the nucleus but failed the line spectrum. Bohr gave us quantized energy but failed the uncertainty principle. Both statements provided in the question accurately reflect the limitations of these historical models.

Thus, the most appropriate answer is that both Statement I and Statement II are true.