Introduction of Atom

The study of atoms leads to understanding the structure and behaviour of matter at the microscopic level. Atoms are the basic units of elements, consisting of a central nucleus surrounded by electrons.

The concept of atomic structure was developed over centuries, with key contributions from scientists such as Rutherford, Bohr, and de Broglie. Quantum mechanics further revolutionized our understanding of atomic behaviour, leading to insights into electron configuration, energy levels, and spectra.

Rutherford’s Nuclear Model of Atom

In 1909, Ernest Rutherford conducted the famous gold foil experiment, where he bombarded a thin gold foil with alpha particles (helium nuclei). The results led to the conclusion that:

• Most of the atom’s mass and all of its positive charge are concentrated in a very small nucleus at the centre of the atom.
• The rest of the atom is mostly empty space where electrons orbit the nucleus.
• Some alpha particles were deflected at large angles, which indicated the presence of a dense, positively charged nucleus.

This experiment led to the Rutherford nuclear model of the atom, where:

• The nucleus is small, dense, and positively charged.
• Electrons move around the nucleus in orbits, though the model did not explain their stability.

Atomic Spectra

When atoms absorb or emit energy, they release light in discrete wavelengths, forming an atomic spectrum. These spectra are unique to each element. There are two main types of spectra:

1. Emission Spectrum: The spectrum of light emitted by atoms when electrons jump from higher to lower energy levels.
2. Absorption Spectrum: The spectrum formed when atoms absorb specific wavelengths of light.

Line Spectra: Atomic spectra consist of specific wavelengths, leading to the formation of lines. This was puzzling to classical physics because it suggested quantization of energy levels.

The study of atomic spectra provided vital clues to the quantized nature of energy in atoms, leading to the development of quantum mechanics.

Bohr’s Model of Atom

In 1913, Niels Bohr proposed a new model for the hydrogen atom to explain the observed line spectra. Three postulates of the Bohr model:

1. Quantized Orbits: Electrons move in circular orbits around the nucleus without radiating energy, and these orbits have quantized radii.
2. Energy Quantization: Electrons can only occupy certain orbits corresponding to specific energy levels. The energy is quantized and given by:

Where n is the principal quantum number (n=1,2,3,…).

• Electron Transition: When an electron jumps between these orbits, it absorbs or emits a photon of energy equal to the difference between the initial and final orbits.

The Bohr model successfully explained the hydrogen spectrum but had limitations when applied to more complex atoms.

Line Spectra of the Hydrogen Atom

The hydrogen atom emits a line spectrum when its electrons transition between energy levels. The spectral lines are classified into series:

1. Lyman Series: Transitions to the n=1 orbit, emitting ultraviolet light.
2. Balmer Series: Transitions to the n=2 orbit, emitting visible light.
3. Paschen, Brackett, and Pfund Series: Transitions to n=3,4,5 orbits, emitting infrared light.

Bohr’s model explained the positions of these lines by quantizing the electron’s energy levels, which helped establish the Rydberg formula for the wavelengths of these spectral lines.

However, Bohr could not explain why electrons can exist only at a certain energy level around the nucleus.

De Broglie’s Explanation of Quantisation

Louis de Broglie tried to explain Bohr’s 2^nd Postulate which states that energy levels are quantised. He explained this by considering that particles behave like waves.

De Broglie proposed that matter (such as electrons) also behaves like waves, leading to the concept of matter waves. For an electron in orbit, de Broglie’s hypothesis suggests that the orbital angular momentum of the electron must be an integer multiple of the de Broglie wavelength. This leads to the quantization condition:

Where: m is the mass of the electron, v is the velocity, r is the radius of the orbit, h is Planck’s constant, and ‘n’ is an integer (the quantum number).

This wave nature of matter explains why only certain orbits are allowed, as they correspond to standing waves around the nucleus. This also justifies Bohr’s second postulate that the electron’s angular momentum is quantized, providing a deeper insight into atomic structure.

Particle	Discovered by (in the year)
Electron:	Discovered in 1897 by J.J. Thomson, a physics professor at Cambridge University. Thomson used cathode ray tubes to show that cathode rays are negatively charged as they were deflected by electric and magnetic fields like a negatively charged particle would behave. He was awarded the Nobel Prize in 1906.
Alpha particle:	Discovered in 1899 by Ernest Rutherford.
Photon:	Discovered in 1905 by Albert Einstein.
Proton:	Discovered in 1919 by Ernest Rutherford, and named in 1920. Rutherford observed that when alpha particles were fired into the air (composed of mainly nitrogen), scintillation detectors detected hydrogen nuclei. He then fired alpha particles into pure nitrogen gas and observed that more hydrogen nuclei were produced. He thus concluded that the hydrogen nucleus was a part of all other atoms. He called it Proton.
Neutron:	Discovered in 1932 by James Chadwick. Chadwick discovered neutrons by bombarding a thin sheet of beryllium with alpha particles. Chadwick fired alpha particles at a beryllium sheet. The alpha particles caused an unknown radiation to accelerate out of the beryllium. Chadwick then directed this radiation at paraffin wax, which ejected protons. He measured the range of the Protons and concluded that the radiation was made up of uncharged particles with a mass similar to a proton, which he named neutrons.
Quark:	In 1963, Murray Gell-Mann proposed the quark theory, which states that protons and neutrons are made up of three quarks.

Heisenberg’s Uncertainty Principle

The uncertainty Principle was Formulated by the German physicist and Nobel laureate Werner Heisenberg in 1927.

The Heisenberg uncertainty principle states that we cannot know both the position and speed of a particle, such as a photon or an electron, with perfect accuracy; the more we nail down the particle’s position, the less we know about its speed and vice versa.

It gives the following uncertainty relation:

Here  is the uncertainty in the position and  is the uncertainty in the momentum (Remember p = mv?).

Microscopic v/s Macroscopic level

In classical physics, the uncertainties are so small that they are not noticeable, but at the quantum scale, they are crucial.

• The uncertainty principle is significant at the microscopic scale (for example, with particles like electrons and photons), but it doesn’t have observable effects at macroscopic scales (like the motion of everyday objects).
• At the macroscopic scale, the mass is so huge that the momentum becomes high, increasing the momentum . When is high, the  becomes low. It means that for the larger objects uncertainty in position () is high.

Implications of the Uncertainty Principle

• Limits on Measurement: The principle fundamentally challenges the classical notion that with enough tools, we can measure a particle’s properties with precision. In the quantum world, there are intrinsic limits to such measurements. No matter how advanced the technology becomes, some uncertainty will always exist.
• Limits of Determinism: Unlike classical mechanics, which operates on deterministic laws (where future states of a system can be predicted exactly if initial conditions are known), quantum mechanics is inherently probabilistic. The uncertainty principle emphasizes that we can’t predict with certainty the exact state of a quantum system—only the probabilities of different outcomes.
• Wave-Particle Duality: It supports the idea of wave-particle duality, where particles like electrons exhibit both wave-like and particle-like properties. For instance, trying to measure a particle’s position precisely (like locating it as a “point” in space) leads to increased uncertainty in its momentum, which reflects its wave nature.
• Quantum superposition— Quantum superposition is a fundamental principle of quantum mechanics that describes how a quantum system can exist in multiple states simultaneously. It’s a combination of wavelike properties of objects, such as electrons and photons, that can be difficult to visualize.
• Quantum Tunneling: Particles can “pass through” energy barriers that they shouldn’t be able to according to classical physics. Because of uncertainty in position and momentum, particles have a probability of existing on the other side of the barrier, even if they don’t have enough energy to surmount it classically.
• Quantum Entanglement: Quantum entanglement is a phenomenon where two or more particles become linked, such that the state of one particle directly affects the state of the other, regardless of the distance between them. When particles are entangled, measuring one particle’s properties (e.g., spin or polarization) instantly determines the corresponding properties of the other, even if they are light-years apart.

Pauli’s Exclusion Principle

Pauli’s Exclusion Principle states that no two electrons in the same atom can have identical values for all four of their quantum numbers.

• Philosophical Implications: The uncertainty principle has led to philosophical debates about the nature of reality. It suggests that reality at the quantum level is not deterministic but probabilistic, and that measurement itself plays a fundamental role in shaping the state of a system. It challenges the notion of objective reality, where properties exist independently of observation.

Quantum Technologies

The uncertainty principle also plays a role in the development of technologies such as quantum computing and quantum cryptography.

These systems often rely on the principles of superposition and entanglement, where the exact properties of quantum states cannot be known until measurement, offering both opportunities for computation and encryption that classical systems cannot achieve.

Potential applications include secure communication, fast computers that establish quantum supremacy, sensors and quantum-inspired devices.

Quantum computing

Quantum computing is a field of computing that leverages the principles of quantum mechanics to process information in fundamentally different ways than classical computers.

• Unlike classical bits, which represent either a 0 or 1, quantum bits or qubits can exist in multiple states simultaneously due to superposition.
• Additionally, qubits can be entangled, allowing for faster and more efficient problem-solving.
• Applications: Quantum computers can potentially solve complex problems, such as factoring large numbers or simulating molecular interactions, exponentially faster than classical computers. This has significant implications for fields like cryptography, drug discovery, optimization, and artificial intelligence.
• Computers: QSystem-1

Quantum Communication

It provides a secure method of communication that would not be vulnerable to attacks from any amount of computational power.

• Quantum Key Distribution (QKD): a technique that allows for secure distribution of keys to be used for encrypting and decrypting messages, through quantum entanglement.
• Several protocols such as the BB84 protocol have been developed in the field of Quantum communication.
• In QKD, two parties can exchange a secret key securely by encoding it in quantum states. If an eavesdropper tries to intercept the communication, the act of measurement disturbs the quantum states, revealing the presence of the eavesdropper and ensuring that the key is not compromised.
• ISRO demonstrated free-space QKD over 300 meters. ISRO has a goal of Satellite-Based Quantum Communication, where ISRO will demonstrate the technology between two Indian ground stations.

Quantum cryptography

Quantum cryptography is a method of secure communication that uses the principles of quantum mechanics to protect information. Unlike classical cryptographic systems, which rely on mathematical algorithms to encrypt data, quantum cryptography leverages the behaviour of quantum bits (qubits), such as superposition and entanglement, to ensure security.

• One of the most well-known techniques in quantum cryptography is Quantum Key Distribution (QKD),
• Quantum cryptography promises unconditional security, meaning that even with unlimited computational power, it is impossible to decrypt the communication without detection. This makes it a crucial component in the future of secure communications, especially for sensitive data exchanges and financial transactions.
• For Example, In June 2020, China demonstrated quantum communication technology using the satellite Micius, by conducting a secret conference between two ground stations about 1,120 km apart. They used the satellite not to transmit the entire communication, but to simultaneously send a pair of secret keys to the two ground stations. Each secret key is one of two strings of entangled photons.

Other Technologies

Quantum sensors: Various techniques can be used to make One common principle is quantum interference, where particles (e.g., photons or atoms) in superposition states interfere with each other in a way that allows precise measurements. For instance, in quantum interferometers, light or matter waves pass through different paths and recombine, with the interference pattern providing sensitive information about physical properties like magnetic fields, temperature, or gravitational forces.

Entanglement is another key feature, where pairs or groups of particles become correlated. Measuring one particle instantly affects the state of others, making these sensors highly sensitive to external changes.

Quantum metrology 

• Quantum simulation,
• Quantum imaging.

Opportunities:

• “The first mover has the advantage in garnering market share and technology supremacy.”
• In the international arena, huge investments, both public and private, are carried out to roll out quantum-based products.

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