Unit 2: Structure of Atom

Introduction and Early Ideas

The diverse chemical behavior of elements is linked to differences in their atomic internal structure. Ancient Indian and Greek philosophers (around 400 B.C.) proposed that atoms are the fundamental building blocks of matter and are indivisible. The word 'atom' comes from the Greek 'a-tomio', meaning 'uncut-able' or 'non-divisible'. These early ideas were mere speculations without experimental testing.

John Dalton (1808), a British schoolteacher, first proposed the atomic theory on a firm scientific basis. Dalton's atomic theory considered the atom as the ultimate particle of matter. Dalton's theory successfully explained the law of conservation of mass, law of constant composition, and law of multiple proportion. However, Dalton's theory failed to explain phenomena like glass or ebonite getting electrically charged when rubbed with silk or fur.

2.1 Discovery of Sub-atomic Particles

Late 19th and early 20th-century experiments revealed that atoms are made of sub-atomic particles (electrons, protons, and neutrons), a concept very different from Dalton's. A basic rule for charged particles: Like charges repel, and unlike charges attract.

2.1.1 Discovery of Electron

Michael Faraday (1830) showed that passing electricity through an electrolyte solution caused chemical reactions at electrodes, suggesting the particulate nature of electricity. In the mid-1850s, scientists, notably Faraday, studied electrical discharge in partially evacuated tubes (cathode ray discharge tubes). When high voltage was applied, current flowed from the cathode to the anode as a stream of particles called cathode rays. The characteristics of these rays (electrons) are independent of the electrode material and the nature of the gas in the tube, leading to the conclusion that electrons are basic constituents of all atoms.

2.1.2 Charge to Mass Ratio of Electron (e/m_e)

In 1897, J.J. Thomson measured the ratio of electrical charge (e) to the mass of an electron (m_e) as e/m_e = 1.758820 × 10¹¹ C kg^-1.

2.1.3 Charge on the Electron

R.A. Millikan (1906-14) devised the oil drop experiment and determined the charge on the electron to be –1.6 × 10^-19 C. Combining this with Thomson's ratio gave the mass of an electron (m_e) as 9.1094 × 10^-31 kg.

2.1.4 Discovery of Protons and Neutrons

Protons: Electrical discharge in modified cathode ray tubes led to the discovery of canal rays, which carried positively charged particles. The smallest and lightest positive ion was obtained from hydrogen and named proton. Neutrons: Chadwick (1932) discovered neutrons by bombarding a thin sheet of beryllium with α-particles, identifying electrically neutral particles with a mass slightly greater than protons.

2.2.1 Thomson Model of Atom

J.J. Thomson (1898) proposed that an atom is a sphere (radius ≈ 10^-10 m) of uniformly distributed positive charge, with electrons embedded within it. Also called the plum pudding, raisin pudding, or watermelon model. It successfully explained the overall neutrality of the atom but was not consistent with later experimental results.

2.2.2 Rutherford’s Nuclear Model of Atom

Ernest Rutherford conducted the α-particle scattering experiment, directing a stream of α-particles at a thin gold foil. The unexpected observations were:

• Most α-particles passed through undeflected.
• A small fraction was deflected by small angles.
• A very few (≈1 in 20,000) bounced back, deflected by nearly 180°.

Rutherford's Nuclear Model (Postulates):

1. The positive charge and most of the atom's mass are densely concentrated in an extremely small region called the nucleus.
2. Electrons move rapidly in circular paths called orbits around the nucleus.
3. Electrons and the nucleus are held together by electrostatic forces of attraction.

2.2.3 Atomic Number and Mass Number

Atomic Number (Z): The number of protons in the nucleus. For a neutral atom, it also equals the number of electrons.

Mass Number (A): The total number of nucleons (protons + neutrons). A = Z + n.

2.2.4 Isobars and Isotopes

Isobars: Atoms with the same mass number (A) but different atomic numbers (Z).

Isotopes: Atoms with identical atomic numbers (Z) but different atomic mass numbers (A), due to a different number of neutrons. Since chemical properties are determined by electrons (and thus protons), isotopes of an element show the same chemical behavior.

2.2.5 Drawbacks of Rutherford Model

Problem with Stability: According to Maxwell's electromagnetic theory, an accelerated charged particle (like a revolving electron) should emit radiation, lose energy, and spiral into the nucleus. Rutherford's model cannot explain the stability of an atom.

Problem with Electron Distribution: The model said nothing about the distribution of electrons around the nucleus or their energies.

2.3.1 Wave Nature of Electromagnetic Radiation

James Clerk Maxwell (1870s) showed that light waves are associated with oscillating electric and magnetic fields. Key properties include frequency (ν), wavelength (λ), and their relation to the speed of light (c): c = νλ.

2.3.2 Particle Nature of Electromagnetic Radiation: Planck’s Quantum Theory

Phenomena like black-body radiation and the photoelectric effect could not be explained by wave theory.

Planck's Quantum Theory (1900): Max Planck proposed that energy is emitted or absorbed in discrete quantities called quanta. The energy (E) of a quantum is proportional to its frequency: E = hν, where h is Planck's constant (6.626 × 10^-34 J s).

Photoelectric Effect: Explained by Einstein (1905) using Planck's theory. Light consists of particles called photons. The kinetic energy of an ejected electron is given by ½m_ev² = hν - hν₀, where hν₀ is the work function.

Dual Behaviour of Electromagnetic Radiation: Light possesses both particle and wave-like properties.

Postulates of Bohr’s Model:

1. The electron moves in circular paths of fixed radius and energy called orbits or stationary states.
2. The energy of an electron in an orbit does not change with time.
3. The frequency of radiation (ν) absorbed or emitted during a transition is given by ν = ΔE / h = (E₂ - E₁) / h.
4. The angular momentum of an electron is quantized: m_evr = n(h/2π), where n = 1, 2, 3... (Principal Quantum Number).

2.4.1 Explanation of Line Spectrum of Hydrogen

Bohr's model explains that each spectral line corresponds to a specific electron transition between energy levels. The energy difference is given by ΔE = R_H (1/n_i² - 1/n_f²), where R_H is the Rydberg constant (2.18 × 10^-18 J). This leads to different spectral series (Lyman, Balmer, Paschen, etc.).

2.4.2 Limitations of Bohr’s Model

• Fails to account for finer details (doublets) of the hydrogen spectrum.
• Unable to explain the spectrum of atoms other than hydrogen.
• Could not explain the Zeeman effect (splitting of lines in a magnetic field) or the Stark effect (in an electric field).
• Could not explain the ability of atoms to form molecules by chemical bonds.

2.5.1 Dual Behaviour of Matter

Louis de Broglie (1924) proposed that matter, like radiation, exhibits dual behavior. The de Broglie relation links wavelength (λ) to momentum (p): λ = h / p = h / mv. This was confirmed by the observation that electron beams undergo diffraction.

2.5.2 Heisenberg’s Uncertainty Principle

Werner Heisenberg (1927) stated that it is impossible to determine simultaneously the exact position and exact momentum (or velocity) of an electron. Mathematically: Δx ⋅ Δp_x ≥ h / 4π. This principle rules out the existence of definite paths or trajectories for electrons, invalidating Bohr's concept of fixed orbits.

Schrödinger Equation

The fundamental equation of quantum mechanics. Its solutions for the hydrogen atom give the possible energy levels (quantized) and the corresponding wave functions (ψ). The wave function itself has no physical meaning, but its square, |ψ|², gives the probability density of finding an electron at a point.

2.6.1 Orbitals and Quantum Numbers

An atomic orbital is a wave function (ψ) for an electron in an atom. Orbitals are distinguished by a set of three quantum numbers:

• Principal Quantum Number (n): A positive integer (1, 2, 3...). Determines the size and energy of the orbital and identifies the shell.
• Azimuthal Quantum Number (l): Values from 0 to n-1. Defines the shape of the orbital and identifies the sub-shell (l=0 is s, l=1 is p, l=2 is d, l=3 is f).
• Magnetic Orbital Quantum Number (m_l): Values from -l to +l. Gives the spatial orientation of the orbital.
• Electron Spin Quantum Number (m_s): Has two values, +½ (spin up, ↑) or –½ (spin down, ↓), describing the intrinsic spin of the electron.

2.6.2 Shapes of Atomic Orbitals

s-orbitals (l=0): Spherical. p-orbitals (l=1): Dumbbell-shaped (three orbitals: p_x, p_y, p_z). d-orbitals (l=2): More complex shapes (five orbitals).

2.6.3 Energies of Orbitals

In multi-electron atoms, energy depends on both n and l due to electron-electron repulsions and the shielding effect. The order of filling is generally given by the (n+l) rule.

2.6.4 Filling of Orbitals in Atom (Electronic Configuration)

Follows three principles:

1. Aufbau Principle: Orbitals are filled in order of increasing energy.
2. Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers. An orbital can hold a maximum of two electrons, and they must have opposite spins.
3. Hund's Rule of Maximum Multiplicity: Pairing of electrons in degenerate orbitals does not occur until each orbital is singly occupied.

2.6.6 Stability of Completely Filled and Half-filled Subshells

Configurations like p³, p⁶, d⁵, and d¹⁰ are exceptionally stable due to symmetrical distribution of electrons and greater exchange energy. This explains the anomalous configurations of elements like Chromium (Cr: [Ar] 3d⁵4s¹) and Copper (Cu: [Ar] 3d¹⁰4s¹).