Board exam focus — Structure of Atom (CBSE & HBSE)

This chapter traces the development of atomic structure from the discovery of subatomic particles through the Thomson, Rutherford and Bohr models to the modern quantum-mechanical picture. It covers electromagnetic radiation, Planck's quantum theory, the photoelectric effect, the hydrogen spectrum, the dual nature of matter (de Broglie), Heisenberg's uncertainty principle, quantum numbers, orbital shapes, and the rules governing electronic configuration. It is conceptually rich and a high-weightage area in both CBSE and HBSE examinations.

Subatomic Particles and Early Atomic Models

Discovery of Subatomic Particles

• Atomic number (Z) = number of protons = number of electrons in a neutral atom.
• Mass number (A) = number of protons + number of neutrons.
• Isotopes have the same Z but different A (e.g., protium, deuterium, tritium).
• Isobars have the same A but different Z (e.g., 40Ar, 40K, 40Ca).

Thomson's Model (Plum Pudding, 1898)

The atom is a uniform sphere of positive charge with electrons embedded in it, like seeds in a watermelon. Limitation: It could not explain the results of the gold-foil scattering experiment.

Rutherford's Nuclear Model (1911)

Based on the alpha-particle scattering experiment on gold foil:

1. Most alpha particles passed straight through -> the atom is mostly empty space.
2. A few were deflected at large angles -> a small, dense, positively charged nucleus exists.
3. Very few bounced back -> the nucleus is extremely small compared to the atom.

Electrons revolve around the nucleus like planets around the sun.

Limitation: According to classical electromagnetic theory, a revolving (accelerating) electron should continuously radiate energy, spiral into the nucleus, and make the atom unstable. This contradicts reality and could not be explained by Rutherford.

Quantum Theory, Photoelectric Effect, Hydrogen Spectrum & Bohr Model

Electromagnetic Radiation

Light is an electromagnetic wave characterised by:

• Wavelength (lambda): distance between successive crests.
• Frequency (nu): number of waves per second; nu = c / lambda, where c = 3 x 10^8 m s^-1.
• Wavenumber: 1/lambda.

Planck's Quantum Theory (1900)

Energy is emitted or absorbed not continuously but in discrete packets called quanta (photons for light):

$$E = h\nu = \frac{hc}{\lambda}$$

where h = Planck's constant = 6.626 x 10^-34 J s.

Photoelectric Effect (Einstein)

When light of sufficient frequency strikes a metal, electrons are ejected:

$$h\nu = h\nu_0 + \frac{1}{2}m v^2$$

• Threshold frequency (nu_0): minimum frequency to eject electrons.
• Below nu_0, no electrons are emitted however intense the light.
• Kinetic energy of ejected electrons depends on frequency, not intensity; intensity only affects the number of electrons.

Bohr's Model of the Hydrogen Atom (1913)

Postulates:

1. Electrons revolve only in certain permitted stationary orbits of fixed energy without radiating.
2. Angular momentum is quantised: mvr = nh / 2pi.
3. Energy is emitted/absorbed only when an electron jumps between orbits: Delta E = E_final - E_initial = h*nu.

Energy of nth orbit (hydrogen): E_n = -13.6 / n^2 eV.

Radius of nth orbit: r_n = 0.529 x n^2 angstrom.

Hydrogen Spectrum

Electron transitions give spectral series:

Rydberg equation: 1/lambda = R_H (1/n1^2 - 1/n2^2), R_H = 109677 cm^-1.

Limitation of Bohr's model: Works only for one-electron species (H, He+, Li2+); fails for multi-electron atoms, cannot explain fine spectral lines (Zeeman/Stark effects) or the dual nature of matter.

Dual Nature, Uncertainty Principle, Quantum Numbers & Electronic Configuration

de Broglie's Dual Nature (1924)

Matter, like light, has both particle and wave character. The wavelength associated with a moving particle is:

$$\lambda = \frac{h}{mv} = \frac{h}{p}$$

This wave nature is significant only for microscopic particles (small m).

Heisenberg's Uncertainty Principle (1927)

It is impossible to determine simultaneously, with absolute precision, both the position and momentum of a microscopic particle:

$$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$

This principle rules out fixed Bohr orbits and replaces them with probability regions called orbitals.

Quantum Numbers

Four quantum numbers describe each electron:

• l = 0 (s), 1 (p), 2 (d), 3 (f).
• Number of orbitals in a subshell = (2l + 1); each holds 2 electrons.

Shapes of Orbitals

• s orbital: spherical, non-directional.
• p orbital: dumb-bell shaped, three orientations (px, py, pz).
• d orbital: double dumb-bell (four lobes), five orientations.
• A node is a region of zero electron probability; radial nodes = n - l - 1.

Rules for Electronic Configuration

1. Aufbau principle: Orbitals fill in order of increasing energy (n + l rule; lower n+l fills first, ties broken by lower n).
2. Pauli exclusion principle: No two electrons in an atom can have all four quantum numbers identical; an orbital holds at most 2 electrons with opposite spins.
3. Hund's rule of maximum multiplicity: Electrons occupy degenerate orbitals singly first (with parallel spins) before pairing.

Stability trap: Half-filled (e.g., 3d5) and fully-filled (3d10) configurations have extra stability due to symmetry and exchange energy. This explains the anomalous configurations of Cr (3d5 4s1) and Cu (3d10 4s1).

Frequently asked questions

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