Atomic Structure – Comprehensive Notes

Atomic structure is the foundational pillar of chemistry, providing insights into the composition, properties, and reactivity of all matter. A deep understanding of this topic is indispensable for mastering chemical bonding, periodicity, and various chemical phenomena, making it highly crucial for NEET and JEE Main.

1. Early Atomic Models and Discoveries

1.1. Discovery of Subatomic Particles

• Discovery of Electron (J.J. Thomson, 1897):
  • Experiment: Cathode Ray Tube (CRT) experiment.
  • Observations: Cathode rays (stream of negatively charged particles) traveled from cathode to anode, deflected by electric and magnetic fields.
  • Conclusion: Discovered electrons (negatively charged particles). Determined charge-to-mass ratio (e/m) of electron.
• Discovery of Proton (E. Goldstein, 1886; Rutherford, 1919):
  • Experiment: Modified CRT with perforated cathode (anode rays/canal rays).
  • Observations: Positively charged particles originated from the gas in the tube, passed through perforations.
  • Conclusion: Discovered protons (positively charged particles). Protons are about 1836 times heavier than electrons.
• Discovery of Neutron (James Chadwick, 1932):
  • Experiment: Bombarded beryllium with alpha particles.
  • Observations: Uncharged particles with mass slightly greater than protons were emitted.
  • Conclusion: Discovered neutrons (neutral particles).

1.2. Atomic Models

• Dalton’s Atomic Theory (1808):
  • Postulates:
    • Atoms are indivisible and indestructible particles.
    • Atoms of the same element are identical in mass and properties; atoms of different elements differ.
    • Atoms combine in simple whole-number ratios to form compounds.
    • Atoms are rearranged in chemical reactions, but never created or destroyed.
  • Limitations: Failed to explain the existence of subatomic particles, isotopes (atoms of same element with different mass), isobars (atoms of different elements with same mass), and why atoms combine to form molecules.
• J.J. Thomson’s Plum Pudding Model (1898):
  • Concept: Atom is a uniform sphere of positive charge within which electrons are embedded, resembling plums in a pudding. The positive and negative charges are equal in magnitude, making the atom electrically neutral.
  • Limitations: Could not explain the results of Rutherford’s alpha-scattering experiment (why most alpha particles passed through, but some were deflected at large angles).
• Rutherford’s Nuclear Model (1911):
  • Experiment: Alpha-particle scattering experiment (bombarded thin gold foil with high-energy alpha particles).
  • Observations:
    • Most alpha particles passed straight through the foil undeflected (over 99%).
    • A small fraction of alpha particles were deflected at small angles.
    • Very few alpha particles (about 1 in 20,000) were deflected back at large angles (nearly 180 degrees).
  • Conclusions:
    • Most of the atom’s volume is empty space.
    • A very small, dense, positively charged region, called the nucleus, exists at the center of the atom, containing almost all the atom’s mass.
    • Electrons revolve around the nucleus in definite circular paths.
  • Limitations (Major Drawbacks):
    • Stability of Atom: According to classical electromagnetic theory, an accelerating charged particle (like an electron revolving around the nucleus) should continuously emit radiation and lose energy, eventually spiraling into the nucleus. This would make the atom unstable, but atoms are stable.
    • Line Spectra: Could not explain the observed line spectra of elements (why atoms emit light at only specific discrete wavelengths, rather than a continuous spectrum).

2. Nature of Electromagnetic Radiation (EMR)

2.1. Wave Nature of EMR

• EMR (e.g., light, radio waves, X-rays) travels as waves.
• Wavelength (λ): The distance between two consecutive crests or troughs of a wave.
  • Units: meters (m), nanometers (nm, 10−9 m), Angstroms (Å, 10−10 m).
• Frequency (ν): The number of waves passing a given point in one second.
  • Units: Hertz (Hz) or per second (s−1).
• Velocity (c): The speed at which electromagnetic waves travel. In vacuum, c=3.0×108 m/s.
• Relationship: c=νλ
• Wave Number (νˉ): The number of wavelengths per unit length.
  • νˉ=1/λ=ν/c
  • Units: m−1 or cm−1.
• Amplitude (A): The height of the crest or depth of the trough from the mean position. It determines the intensity or brightness of the radiation.
• Electromagnetic Spectrum: The arrangement of various types of electromagnetic radiation in order of increasing wavelength (or decreasing frequency/energy).
  • Order: Gamma rays < X-rays < Ultraviolet (UV) < Visible < Infrared (IR) < Microwaves < Radio waves.

2.2. Particle Nature of EMR (Planck’s Quantum Theory)

• Problem Statement: Classical physics failed to explain phenomena like black-body radiation and the photoelectric effect.
• Planck’s Postulate (1900): Energy is not radiated or absorbed continuously but discontinuously, in the form of small, discrete packets called quanta. In the case of light, a quantum of energy is called a photon.
• Energy of a photon (E): The energy of each quantum is directly proportional to its frequency.
  E=hν Where:
  • h = Planck’s constant (6.626×10−34 J s or 6.626×10−27 erg s).
  • ν = frequency of radiation.
• Extended Formula: Since c=νλ, we can write ν=c/λ.
  E=hc/λ=hcνˉ This explained the quantization of energy and was a revolutionary concept.

3. Bohr’s Model of Atom (for Hydrogen and Hydrogenic Species)

Niels Bohr (1913) modified Rutherford’s model by incorporating Planck’s quantum theory to explain the stability of atoms and the line spectrum of hydrogen.

• Postulates:
  1. Fixed Orbits/Stationary States: Electrons revolve around the nucleus in specific, definite circular paths called orbits or stationary states. Each orbit is associated with a fixed amount of energy.
  2. Non-radiating Orbits: As long as an electron remains in a particular orbit, it does not lose or gain energy. Hence, these orbits are called non-radiating or stationary orbits.
  3. Energy Transitions: Electrons can move from a lower energy orbit to a higher energy orbit by absorbing a definite amount of energy. Conversely, they can move from a higher energy orbit to a lower energy orbit by emitting a definite amount of energy. The energy difference between the two orbits corresponds to the energy of the photon absorbed or emitted.
     ΔE=Efinal​−Einitial​=hν
  4. Quantization of Angular Momentum: The angular momentum of an electron in any stationary orbit is quantized (i.e., it can only have certain discrete values). It is an integral multiple of h/2π.
     mvr=n(h/2π) Where:
     • m = mass of electron
     • v = velocity of electron
     • r = radius of the orbit
     • n = principal quantum number (an integer: 1, 2, 3, …) representing the orbit number or energy level.
• Formulas Derived from Bohr’s Model (for Hydrogenic Species like H, He+, Li2+): (Z = atomic number)
  • Radius of the nth orbit (rn​):
    rn​=0.529×(n2/Z) A˚=0.0529×(n2/Z) nm
    • For Hydrogen atom (Z=1), r1​=0.529 Å (Bohr radius). Radius increases with n2.
  • Energy of electron in the nth orbit (En​): The energy is negative, indicating that the electron is bound to the nucleus.
    En​=−13.6×(Z2/n2) eV/atomEn​=−2.18×10−18×(Z2/n2) J/atom
    • As n increases, the energy becomes less negative (closer to zero), meaning the electron is less tightly bound.
    • Ionization Energy of H-atom (removing electron from n=1 to n=infinity) = +13.6 eV.
  • Velocity of electron in the nth orbit (vn​):
    vn​=2.18×106×(Z/n) m/s
    • Velocity decreases as n increases.
• Limitations of Bohr’s Model:
  • Single-electron Species Only: Successfully explained the spectra of hydrogen and hydrogen-like ions (He+, Li2+, etc.) but failed for multi-electron atoms.
  • Fine Spectrum: Could not explain the fine structure of spectral lines (i.e., splitting of a single line into multiple closely spaced lines when observed with a high-resolution spectroscope). This suggested sub-energy levels.
  • Zeeman Effect: Failed to explain the splitting of spectral lines in the presence of an external magnetic field.
  • Stark Effect: Failed to explain the splitting of spectral lines in the presence of an external electric field.
  • Chemical Bonding: Could not explain the ability of atoms to form molecules (chemical bonding).
  • Heisenberg’s Uncertainty Principle: It violates this fundamental principle of quantum mechanics (discussed next) by assuming definite orbits and precise position and momentum for electrons.

4. Dual Nature of Matter and Heisenberg’s Uncertainty Principle

4.1. de Broglie Hypothesis (Dual Nature of Matter)

• Concept: Louis de Broglie (1924) proposed that, like light, matter (electrons, protons, atoms, molecules, etc.) also exhibits both particle and wave properties.
• de Broglie Wavelength (λ): The wavelength associated with a particle is inversely proportional to its momentum.
  λ=h/mv=h/p Where:
  • h = Planck’s constant
  • m = mass of the particle
  • v = velocity of the particle
  • p = momentum of the particle
• Significance:
  • The wave nature is significant only for microscopic particles (like electrons) due to their extremely small mass. For macroscopic objects (e.g., a cricket ball), the wavelength is too small to be detected.
  • This hypothesis provided a theoretical basis for Bohr’s quantization of angular momentum (an electron can exist only in orbits where its wavelength forms a standing wave, i.e., circumference = nλ).
• Experimental Verification: The wave nature of electrons was experimentally confirmed by Davisson and Germer (1927) and G.P. Thomson (1928) through electron diffraction experiments.

4.2. Heisenberg’s Uncertainty Principle

• Concept: Werner Heisenberg (1927) stated that it is impossible to simultaneously and precisely determine (measure) both the position and momentum (or velocity) of a subatomic particle (like an electron) with perfect accuracy. If one quantity is measured more precisely, the other becomes less precise.
• Mathematical Expression:
  Δx⋅Δp≥h/4π or, since p=mv (and mass m is constant):
  Δx⋅mΔv≥h/4π Where:
  • Δx = uncertainty in position
  • Δp = uncertainty in momentum
  • Δv = uncertainty in velocity
• Implication: This principle directly contradicts Bohr’s model, which assumes that an electron revolves in a well-defined orbit with a known radius and velocity. The uncertainty principle suggests that electrons cannot have fixed, well-defined orbits, but rather exist in regions of probability.

5. Quantum Mechanical Model of Atom (Wave Mechanical Model)

This is the most accepted and advanced model of the atom, developed by Schrödinger.

• Basis: It is based on the solutions to the Schrödinger Wave Equation (a complex mathematical equation that describes the wave nature of electrons in atoms).
• Concept of Orbitals: This model replaces the concept of fixed, definite “orbits” with orbitals.
• Orbital: A three-dimensional region (or space) around the nucleus where the probability of finding an electron is maximum (typically 90-95%). It does not represent a definite path.
• Electron Density: The probability of finding an electron at a particular point in space. It is proportional to ∣Ψ∣2 (square of the wave function).

5.1. Quantum Numbers

A set of four unique numbers that completely and precisely describe the energy, size, shape, and spatial orientation of an electron in an atom, as well as its spin orientation. No two electrons in an atom can have the same set of all four quantum numbers (Pauli’s Exclusion Principle).

1. Principal Quantum Number (n):
   • Determines: The main energy shell or principal energy level to which the electron belongs. It also primarily determines the size and energy of the orbital.
   • Values: Positive integers: 1, 2, 3, … (corresponding to K, L, M, … shells).
   • Properties:
     • Higher the ‘n’ value, larger the size of the orbital.
     • Higher the ‘n’ value, higher the energy of the orbital (for hydrogenic species).
     • Maximum number of electrons in a main shell = 2n2.
2. Azimuthal (Angular Momentum) Quantum Number (l):
   • Determines: The subshell within a main energy shell and the shape of the orbital. Also known as subsidiary or orbital angular momentum quantum number.
   • Values: Integers from 0 to (n-1).
   • Subshell Notation:
     • l=0 corresponds to s-subshell (spherical shape).
     • l=1 corresponds to p-subshell (dumbbell shape).
     • l=2 corresponds to d-subshell (double dumbbell or complex shape).
     • l=3 corresponds to f-subshell (more complex shape).
   • Properties:
     • Number of subshells in a main shell = n.
     • Maximum number of electrons in a subshell = 2(2l+1).
     • Orbital angular momentum = l(l+1)​(h/2π).
3. Magnetic Quantum Number (ml​):
   • Determines: The orientation of the orbital in three-dimensional space relative to a strong external magnetic field.
   • Values: Integers from −l to +l, including 0. (i.e., (2l+1) values).
   • Properties:
     • For l=0 (s-subshell): ml​=0 (only 1 s-orbital).
     • For l=1 (p-subshell): ml​=−1,0,+1 (3 p-orbitals: px, py, pz).
     • For l=2 (d-subshell): ml​=−2,−1,0,+1,+2 (5 d-orbitals: dxy, dyz, dzx, dx2-y2, dz2).
4. Spin Quantum Number (ms​):
   • Determines: The intrinsic spin orientation of the electron around its own axis. This creates a magnetic moment.
   • Values: Only two possible values: +1/2 (spin-up, usually denoted by ↑) or −1/2 (spin-down, usually denoted by ↓).

5.2. Shapes of Atomic Orbitals

• s-orbital:
  • Shape: Spherical.
  • Directional property: Non-directional (electron density is uniformly distributed around the nucleus).
  • Size: Increases with increasing ‘n’ (1s < 2s < 3s).
  • Nodes: Has (n-1) radial (spherical) nodes.
• p-orbital:
  • Shape: Dumbbell-shaped.
  • Directional property: Directional (lobes are oriented along axes).
  • Types: Three degenerate p-orbitals (px, py, pz), oriented along the x, y, and z axes respectively.
  • Nodes: Has (n-2) radial nodes and 1 angular (planar) node.
• d-orbital:
  • Shape: Complex shapes.
  • Types: Five degenerate d-orbitals.
    • Four have a cloverleaf shape: dxy, dyz, dzx, dx2-y2.
    • One has a dumbbell with a donut shape: dz2.
  • Nodes: Has (n-3) radial nodes and 2 angular (planar) nodes.
• Nodes: Regions in space within an orbital where the probability of finding an electron is zero.
  • Total number of nodes = n-1
  • Number of radial (spherical) nodes = n-l-1
  • Number of angular (planar) nodes = l

5.3. Rules for Filling Electrons in Orbitals

1. Aufbau Principle: This principle states that in the ground state of an atom, electrons fill atomic orbitals in order of increasing energy. The orbital with the lowest energy is filled first.
   • (n+l) Rule (Bohr-Bury Rule / Madelung Rule): For multi-electron atoms, the energy of an orbital is primarily determined by the sum of its principal quantum number (n) and azimuthal quantum number (l).
     • The orbital with the lower (n+l) value has lower energy and is filled first.
     • If two orbitals have the same (n+l) value, the orbital with the lower ‘n’ value has lower energy and is filled first.
   • Order of filling orbitals: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s …
2. Pauli’s Exclusion Principle: This principle states that no two electrons in an atom can have the same set of all four quantum numbers (n,l,ml​,ms​).
   • Implication: An atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins. (e.g., one with ms​=+1/2 and the other with ms​=−1/2).
3. Hund’s Rule of Maximum Multiplicity: This rule applies to degenerate orbitals (orbitals within the same subshell that have the same energy, e.g., the three 2p orbitals or the five 3d orbitals).
   • It states that for degenerate orbitals, electrons will first occupy each orbital singly with parallel spins (same spin orientation) before any orbital is doubly occupied (i.e., pairing up).
   • This rule ensures that the total spin multiplicity (2S+1) is maximized, which leads to a more stable electronic configuration. For example, nitrogen (1s22s22p3) will have three electrons in the 2p subshell, each occupying a separate p-orbital with parallel spins (↑↑↑).

5.4. Electronic Configuration

• The distribution of electrons into the atomic orbitals of an atom in its ground state.
• General representation: Xvalenceelectrons (e.g., 1s22s22p6)
• Exceptions to Aufbau Principle (due to extra stability of half-filled and fully-filled orbitals):
  • Chromium (Cr, Z=24):
    • Expected configuration (by Aufbau): [Ar]3d44s2
    • Actual configuration: [Ar]3d54s1 (One electron from 4s shifts to 3d to achieve a more stable half-filled d-subshell).
  • Copper (Cu, Z=29):
    • Expected configuration (by Aufbau): [Ar]3d94s2
    • Actual configuration: [Ar]3d104s1 (One electron from 4s shifts to 3d to achieve a more stable fully-filled d-subshell).
  • Similar exceptions occur for other elements in transition series (e.g., Mo, Ag, Au).

6. Photoelectric Effect

• Definition: The phenomenon of emission of electrons from the surface of a metal when light of a suitable frequency (or wavelength) strikes it.
• Key Observations (explained by particle nature of light):
  1. Threshold Frequency (ν0​): For each metal, there is a minimum characteristic frequency of incident light, below which no electrons are emitted, regardless of the intensity of the light.
  2. Kinetic Energy vs. Frequency: If the incident light’s frequency is above the threshold frequency (ν>ν0​), electrons are emitted, and their maximum kinetic energy (KEmax​) is directly proportional to the frequency of the incident light. It is independent of light intensity.
  3. Number of Electrons vs. Intensity: The number of electrons emitted per second is directly proportional to the intensity (brightness) of the incident light (for ν>ν0​).
  4. Instantaneous Emission: Electron emission is instantaneous. There is no time lag between the incidence of light and the emission of electrons, even at very low light intensities.
• Einstein’s Photoelectric Equation: Albert Einstein (1905) explained the photoelectric effect using Planck’s quantum theory.
  hν=hν0​+KEmax​ Where:
  • hν: Energy of the incident photon.
  • hν0​: Work function (Φ0​) – the minimum energy required to eject an electron from the surface of a specific metal. This is equivalent to the threshold energy.
  • KEmax​: Maximum kinetic energy of the emitted electron (1/2mv2).
  • This equation implies that a photon transfers all its energy to an electron. If this energy is greater than the work function, the excess energy is converted into the kinetic energy of the emitted electron.

7. Atomic Spectra (Hydrogen Spectrum)

When atoms absorb energy (e.g., by heating or passing electric current), their electrons get excited to higher energy levels. When these excited electrons return to lower energy levels, they emit radiation. This emitted radiation, when passed through a prism, forms a unique spectrum characteristic of the element.

• Emission Spectrum: Produced when radiation emitted by excited atoms passes through a prism, showing distinct bright lines against a dark background. Each line corresponds to a specific wavelength of light emitted.
• Absorption Spectrum: Produced when light from a continuous source passes through a substance. The substance absorbs specific wavelengths of light, resulting in distinct dark lines against a bright continuous background. The wavelengths of dark lines in an absorption spectrum correspond exactly to the bright lines in the emission spectrum of the same element.
• Line Spectrum of Hydrogen: The simplest atomic spectrum. When hydrogen gas is excited, it emits radiation at specific discrete wavelengths, resulting in several series of lines.
  • Rydberg Formula (for hydrogen-like species): This empirical formula describes the wavelengths of lines in the hydrogen spectrum.
    1/λ=νˉ=RH​(1/n12​−1/n22​) Where:
    • RH​ = Rydberg constant (1.09677×107 m-1 or 109677cm−1).
    • n1​ = lower energy level (final orbit to which electron falls).
    • n2​ = higher energy level (initial orbit from which electron falls; n2​>n1​).
  • Different Spectral Series of Hydrogen:
    • Lyman Series: Electron transitions to the first shell (n1​=1) from higher shells (n2​=2,3,4,…). Lies in the Ultraviolet (UV) region.
    • Balmer Series: Electron transitions to the second shell (n1​=2) from higher shells (n2​=3,4,5,…). Lies in the Visible region (and some lines in UV). This is the only series in the visible part of the spectrum.
    • Paschen Series: Electron transitions to the third shell (n1​=3) from higher shells (n2​=4,5,6,…). Lies in the Infrared (IR) region.
    • Brackett Series: Electron transitions to the fourth shell (n1​=4) from higher shells (n2​=5,6,7,…). Lies in the Infrared (IR) region.
    • Pfund Series: Electron transitions to the fifth shell (n1​=5) from higher shells (n2​=6,7,8,…). Lies in the Infrared (IR) region.
  • Series Limit: The shortest wavelength (highest energy) line in a series occurs when n2​=∞. The energy associated with this transition corresponds to the ionization energy from that particular shell.