EVOLUTION OF PHYSICS: MODERN INTERPRETATIONS (2)
In our last discussion on this topic, we explored some of the early contributions made toward the development of atomic structure.
However, modern physics is not limited to atomic concepts alone. It also expands into entirely new branches of physics, such as electromagnetism, and explores advanced topics like Quantum Electrodynamics (QED), the Theory of Relativity, and much more.
In today’s blog, we will continue our discussion on the atom and learn about how modern scientists revolutionized our understanding by proposing radically new concepts of atomic structure. I am quite confident that after reading this, you might question your own common sense, because the modern picture of the atom is both strange and fascinating. You will also come to appreciate the incredible efforts made by scientists to expand our knowledge about something so small that it cannot be seen with the unaided eye.
''Everything we call real is made of things that cannot be regarded as real''
-Niels Bohr
HISTORICAL NOTE
During the time of Christiaan Huygens, it was widely believed that light behaved like a wave, a concept he strongly advocated in his Wave Theory.
However, Sir Isaac Newton was not ready to concede this debate so easily. Through his own experiments and observations, Newton became convinced that light was made up of tiny particles—a theory known as the Corpuscular Theory of Light.
This great dilemma kept physicists puzzled for years, as they worked relentlessly to uncover the true nature of light. After decades of intense research and debate, the mystery was finally unraveled, revealing that the nature of light is far more complex—and even more fascinating—than anyone had ever imagined.
Maxwell’s Electromagnetic Theory posed a serious challenge to Newton’s understanding of light. In his groundbreaking theory, Maxwell described light as a propagating electromagnetic wave, consisting of oscillating electric and magnetic fields.
Moreover, the particle theory of light struggled to explain certain well-documented phenomena like interference and diffraction, both of which were far better explained by the wave theory.
As a result, it was globally accepted for a time that light possessed a purely wavelike nature, with no particulate behavior.
However, this conclusion was soon overturned by the revolutionary findings of Max Planck, Heinrich Hertz, and Albert Einstein. Their experiments and theories revealed that light also exhibits particle-like properties. In fact, Einstein’s explanation of the photoelectric effect proved that light can behave both as a wave and as a particle, and sometimes it displays characteristics of both simultaneously.
This remarkable discovery laid the foundation for the wave-particle duality — a concept at the very heart of quantum physics.
PLANCK'S QUANTUM THEORY
Max Planck was a German Physicist who played a major role in the development of Bohr's Model of an Atom and subsequently the much discussed, Quantum Physics.
Figure 2: Max Planck
Max Planck published his theory in 1901, and the main postulates in the theory are as follows,
(1) Energy emitted or absorbed is not continuous but is in the form of small packets of energy called 'quanta' and in the case of light 'photons'.
(2) The photon carries energy which is directly proportional to the frequency of wavelength.
That is,
E∝𝛎
⇒ E=h𝛎
where, h is the Planck's Constant whose value is 6.634×10⁻³⁴ J-s
(3) The energy associated with a quanta is given by,
E=nh𝛎
where, n=1,2,3,...
PHOTOELECTRIC EFFECT: HERTZ AND EINSTEIN
Heinrich Rudolf Hertz performed the famous, 'Photoelectric Effect' in the year 1887.
Figure 3: Heinrich Rudolf Hertz
When certain metals like potassium (K), rubidium (Rb), caesium (Cs) are exposed to a light beam, then electrons are ejected from their surfaces. This phenomenon is called the 'Photoelectric Effect'.
They are as follows,
(1) Electrons are ejected from the metal surface as soon as the light beam strikes on it.
(2) For a given metal, there exists a characteristic minimum frequency called the threshold frequency (v₀), when the velocity v becomes greater than v₀ electrons get ejected from the metal surface.
(3) The number of electrons ejected is directly proportional to the intensity of the light beam.
Albert Einstein explained the 'Photoelectric Effect' using Planck's Quantum Theory, for which he won the Nobel Prize in Physics in 1921.
Einstein showed that the light beam consists of 'photons' (similar to quanta). The photons has some energy associated with it. When these photons strikes the metal surface it transfers its energy to the electrons present in the metal surface and this energy is used by the electron to overcome the threshold frequency and escape the metal surface. This proves Hertz's first observation...
Einstein postulated that the kinetic energy of the ejected electron is directly proportional to the frequency of the incident radiation.
He further added, 'as the intensity of the incident radiations increases the number of photons in the light beam also increases it means more electrons will receive the charges carried by these photons this means more electrons will be ejected from the metal surface...
LIGHT: WAVE OR PARTICULATE?
Planck's Quantum Theory and Photoelectric Effect followed 'particulate nature of light'. This meant that the wavy nature of light cannot explain photoelectric effect. Hence, wavy nature of light is not correct.
Then what is the nature of light???
Einstein proved that sometimes light behaves as wave, sometimes as particles and at times both as waves and particles...
Niels Bohr used the particulate nature of light in his famous atomic theory...
Now let us explore more about atoms and dive into the mysterious structure if atoms...
BOHR'S CONTRIBUTIONS
We now know that Rutherford’s Model of the Atom was incomplete, and a more refined model was needed to explain the structure and behavior of atoms. This enormous challenge was confidently taken up by the Danish physicist, Niels Bohr. Interestingly, Bohr had previously worked with J.J. Thomson and Ernest Rutherford, both of whom were towering figures in the field of nuclear physics at the time.
Figure 4: Niels Bohr
Bohr worked tirelessly for years and eventually emerged with an elegant atomic model—but with one limitation: it was applicable only to hydrogen-like species (atoms or ions with a single electron).
Bohr’s Model was based on the following postulates:
Negatively charged electrons revolve around the positively charged nucleus in definite circular paths, called stationary orbits.
Each orbit has a specific, fixed amount of energy associated with it, and electrons do not radiate energy while moving through these well-defined orbits.
The orbits are numbered 1, 2, 3, ... or designated as K, L, M, ... shells. The lowest energy level an electron can occupy is called the ground state.
Electrons can move to higher energy levels if they absorb energy, and they can drop to lower energy levels by emitting energy, usually in the form of light (photon emission).
Bohr didn’t stop there. He went on to calculate the radius of the first orbit, which is now known as the Bohr Radius, named in his honor.
The Bohr Radius has a value of approximately 5.29 × 10⁻¹³ m.
Additionally, Bohr derived a generalized equation to calculate the radius of any orbit in his atomic model, providing a mathematical foundation for understanding the size and structure of atoms.
rₙ = a₀n²
where,
a₀= Bohr Radius
n= orbit (1,2,3...)
He then found frequency (v)of radiations absorbed or emitted when an electron jumps from one energy level to another...
where,
v = ΔE/h
ΔE= the difference in energy between the orbits
h= Planck's Constant
According to Bohr, electrons occupy specific energy levels (orbits) around the nucleus, and these levels have fixed energies. When an electron absorbs energy, it jumps to a higher energy level (excited state). However, this excited state is unstable, so the electron quickly falls back to a lower energy level, releasing the excess energy in the form of light (photons).
The energy of the emitted photon corresponds exactly to the difference between the two energy levels. Since only certain energy differences are allowed, only certain wavelengths (colors) of light are emitted, creating the distinct line spectrum of hydrogen. This elegant explanation successfully matched the experimental spectrum of hydrogen, giving strong support to Bohr’s model.
Figure 6: Hydrogen spectral lines, 400nm to 700nm. (1nm= 10⁻⁹m)
He postulated that the angular momentum of an electron is quantised, given by the equation.
mₑvr = n.h/2𝜋
where,
mₑ= mass of electron= 9.1×10⁻³¹kg
v = velocity of electron
r = radius of the required orbit
n = orbit (1,2,3...)
h = Planck's Constant
DOWNFALL OF BOHR MODEL
There were several reasons why Bohr’s Model was eventually proven to be incomplete. Some of the major limitations are discussed below:
- Bohr’s model could not explain the finer details of the hydrogen spectrum, known as fine structure.
- It could only account for hydrogen and hydrogen-like species (single-electron systems), but failed for multi-electron atoms.
- The model could not explain how atoms form chemical bonds, which is essential to understanding molecules.
- It failed to explain two important experimental observations — the Stark Effect and the Zeeman Effect.
Now, what are these effects?
- The Stark Effect refers to the splitting of spectral lines when the atom is placed in a strong electric field.
- The Zeeman Effect refers to the splitting of spectral lines when the atom is placed in a strong magnetic field.
At this point, it seemed like no theory was able to fully match the level of human experimentation and observation. Scientists were constantly pushing the boundaries, and existing models just couldn’t keep up.
But then…
Everything changed with the birth of Quantum Physics, one of the most sophisticated and revolutionary branches of physics.
One of the key principles that laid the foundation for Quantum Physics was the 'Dual Nature of Matter', an idea that would transform our understanding of the microscopic world forever.
DE-BROGLIE'S RELATIONSHIP
Louis de Broglie made deliberate and bold attempts to establish a relationship between mass and wavelength. After extensive research, he finally derived an equation that revolutionized our understanding of matter forever.
Figure 7: Louis Victor de-Broglie
λ=h/mv
where,
λ= de-Broglie wavelength
h = Planck's Constant
m = mass of the body
v = velocity of the body under consideration
Now, some of you might be wondering — what’s so special about this equation?
This equation was groundbreaking because it shattered the age-old belief that electrons were purely particulate in nature.
λ∝ 1/m
From this equation, it becomes clear that wavelength (λ) and mass (m) are inversely proportional. In simple terms, when the mass decreases, the wavelength increases. This is particularly important for electrons, which have extremely small mass, meaning they possess a relatively large wavelength. As a result, electrons show significant wave-like behavior.
This equation is universal — it applies to objects with large mass too. For example, if we apply this equation to de Broglie himself, his large mass would result in an extremely tiny wavelength, meaning his wave nature would be negligible.
de Broglie’s key insight was that every object — from electrons to humans — exhibits both particle-like and wave-like behavior. However, for macroscopic objects (like us), the wave nature is so insignificant that it is practically undetectable.
So yes, we all have a wave nature — but it’s so tiny that we can’t see or feel it.
This revolutionary concept — known as wave-particle duality — earned Louis de Broglie the Nobel Prize in Physics in 1929, securing his place in history as a pioneer of quantum mechanics.
HEISENBERG'S UNCERTAINTY PRINCIPLE
Figure 8: Werner Heisenberg
Werner Heisenberg was a prominent physicist who made seminal contributions to the development of Quantum Physics. During his early career, he also worked closely with Niels Bohr in Copenhagen, where some of the most groundbreaking ideas in quantum mechanics were born.
One of Heisenberg’s most famous contributions is the uncertainty principle, which can be stated as follows:
STATEMENT 1: It is impossible to determine simultaneously the exact position and exact momentum or velocity of an electron.
Mathematically,
Δx × Δp ≥ h/4𝝅 ('Δx ' is the uncertainty in position of the particle and 'h' is the Planck's Constant)
We know that, Δp = Δ(mv), since momentum is equal to mass times velocity
Δx × Δ(mv) ≥ h/4𝝅
⇒ Δx× m Δv ≥ h/4𝝅 (as mass is constant)
⇒ Δx × Δv ≥ h/4𝝅m ('Δv ' is the uncertainty in velocity of the particle)
This is the mathematical expression for Heisenberg's Uncertainty Principle.
Heisenberg's Uncertainty Principle is applicable only to microscopic objects, such as electrons, protons, and atoms. This principle, in turn, completely rules out the existence of definite paths for electrons — a concept that Bohr had earlier proposed in his atomic model.
However, newer experiments have shown that 'quantum systems do not necessarily induce uncertainties' in the way Heisenberg originally predicted. This has led to refinements and reinterpretations of the uncertainty principle, suggesting that Heisenberg’s initial formulation was not entirely correct.
SCHRӦDINGER: Quantum Physics takes form...
'' If in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passes on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that all things are made up of atoms- little particles that move in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed to one another''
Richard P Feynman
Figure 9: Erwin Schrödinger
Erwin Schrödinger, an Austrian physicist, was a key figure in the development of Quantum Mechanics, a branch of physics that describes the behavior of matter and energy at the atomic and subatomic levels. His most famous contribution is the Schrödinger Equation, a mathematical equation that describes the evolution of a particle's wave function over time, given by:
Ĥ𝚿 = E𝚿
where,
Ĥ= Hamiltonian operator
𝚿 = Wave function
E= Energy
The wave function (𝚿) is a core concept in quantum mechanics — it’s essentially a mathematical description of all the possible states a quantum system can occupy. From this wave function, probabilities of different outcomes can be calculated. Schrödinger’s equation helps us predict how this wave function changes with time when a particle interacts with forces like electric fields, magnetic fields, or potential energy landscapes.
Before Schrödinger, Niels Bohr proposed his atomic model where electrons moved around the nucleus in fixed orbits. However, this "planetary model" could not explain all the complex behaviors of electrons, especially for atoms larger than hydrogen.
Schrödinger approached this problem by treating electrons not as tiny particles moving in fixed paths, but instead as wave-like entities. His equation described electrons as standing waves surrounding the nucleus — introducing the revolutionary concept of electron clouds or orbitals, which is the foundation of modern atomic theory.
SCHRÖDINDER AND HIS THOUGHTS
Despite his pioneering work, Schrödinger himself was troubled by the philosophical implications of quantum theory — particularly the weirdness of superposition (where particles can exist in multiple states simultaneously until observed).
This was explained by him through a thought experiment which we now famously refer to as Schrödinger's cat.
Figure 10: Illustration of Schrödinger's cat
Imagine you have a closed box. Inside the box, there’s a cat, a bottle of poison, and a tiny bit of radioactive stuff.
- If the radioactive stuff decays, the poison gets released and the cat dies.
- If the radioactive stuff doesn’t decay, the poison stays in the bottle and the cat stays alive.
Here’s the twist: Until you open the box and check, you have no way of knowing if the cat is alive or dead.
In quantum physics, the cat is actually considered to be both alive and dead at the same time until you look. This strange idea is called superposition — where something exists in multiple states at once.
Once you open the box and check, the cat becomes either alive or dead — but before that, it’s like the cat is in a weird mix of both!
REFERENCES:
1. All the images published in this blog were taken from Wikimedia Commons.
2. Class XI NCERT Textbook in Chemistry
*All the media published in this blog belongs to their original creators and 'Knowledge Through Science' does not claim any right over it.
Comments
Post a Comment