Structure of AtomNEET Chemistry · Class 11 · NCERT Chapter 2

Introduction

Every substance you study in chemistry is made of atoms. Understanding the inside of an atom, its electrons, protons, neutrons, and the rules governing their arrangement, is the key to explaining chemical reactivity, bonding, and the entire periodic table. Structure of Atom is one of the highest-weightage chapters in NEET Chemistry, delivering 3 to 4 questions most years.

The most tested areas are: electronic configurations (including exceptions for Cr and Cu), quantum numbers, Bohr model energy calculations, and de Broglie wavelength problems. This chapter is mathematical as well as conceptual, so you need to practise both.

Sub-atomic Particles

Three experiments revealed that atoms are made of smaller particles.

Discovery of Electron: Cathode Ray Experiment (J.J. Thomson, 1897)

When high voltage is applied across gas-filled tubes at low pressure, rays travel from the cathode to the anode. These cathode rays have these key properties:

• They travel in straight lines and cast shadows.
• They are deflected by electric and magnetic fields toward the positive plate, showing they are negatively charged.
• The charge-to-mass ratio (e/m) is constant regardless of the cathode material or gas used.
• This proved electrons are fundamental particles present in all matter.

Thomson measured e/m = 1.758820 × 10¹¹ C kg⁻¹. Millikan later determined e = 1.602 × 10⁻¹⁹ C, from which mass of electron = 9.11 × 10⁻³¹ kg.

Discovery of Proton: Canal Rays (Goldstein, 1886)

When a perforated cathode is used, rays also travel in the opposite direction (from anode toward cathode). These canal rays (or anode rays) are positively charged. The lightest canal ray particles had charge equal and opposite to the electron and much greater mass. These were protons. Mass of proton = 1.673 × 10⁻²⁷ kg = 1836 × mass of electron.

Discovery of Neutron (Chadwick, 1932)

When beryllium was bombarded with alpha particles, a highly penetrating radiation was produced that was not deflected by electric or magnetic fields. Chadwick showed these were neutral particles with mass approximately equal to the proton. These are neutrons. Mass of neutron = 1.675 × 10⁻²⁷ kg.

Properties of Sub-atomic Particles

Atomic Number, Mass Number, Isotopes, and Isobars

The atomic number (Z) = number of protons in the nucleus. It determines the identity of the element. The mass number (A) = number of protons + number of neutrons. Number of neutrons = A − Z.

Isotopes are atoms of the same element (same Z) but different mass number (different number of neutrons). Example: ¹H (protium), ²H (deuterium), ³H (tritium) are isotopes of hydrogen.

Isobars are atoms of different elements (different Z) but the same mass number (A). Example: ¹⁴₆C and ¹⁴₇N are isobars (both have A = 14).

Isotones are atoms with the same number of neutrons. Example: ¹⁴₆C and ¹⁵₇N both have 8 neutrons.

Early Atomic Models

Thomson's Plum-Pudding Model (1904)

Thomson proposed that an atom is a sphere of uniform positive charge (like pudding) with electrons embedded in it (like plums). The positive and negative charges balance, making the atom neutral. This model was abandoned when Rutherford's experiment showed the positive charge is concentrated in a tiny nucleus.

Rutherford's Nuclear Model (1911)

Geiger and Marsden, working under Rutherford, bombarded a thin gold foil with a beam of alpha particles (helium nuclei, charge +2, mass 4u) from a radioactive source. A circular fluorescent screen detected where the particles went.

Key Observations and Conclusions

Rutherford's Model of the Atom

• The atom has a tiny, dense, positively charged nucleus at the centre.
• Almost all the mass of the atom is in the nucleus.
• The electrons revolve around the nucleus in circular orbits (like planets around the sun).
• The size of the nucleus is about 10⁻¹⁵ m; the atom is about 10⁻¹⁰ m. So the nucleus is about 10⁵ times smaller than the atom.

Drawbacks of Rutherford's Model

• An electron moving in a circular orbit is accelerating. According to classical electromagnetic theory, an accelerating charged particle must continuously emit radiation and lose energy. So the electron should spiral inward and the atom should collapse in about 10⁻⁸ s. Atoms clearly do not collapse, so the model was incomplete.
• It could not explain the line spectrum of hydrogen. Classical theory predicts a continuous spectrum, but hydrogen emits only specific wavelengths of light.

Bohr's Model of Hydrogen (1913)

Niels Bohr solved Rutherford's problems by incorporating quantum ideas. He proposed four postulates for the hydrogen atom:

1. Electrons revolve around the nucleus in fixed circular paths called stationary states or orbits. These are allowed orbits.
2. An electron in an allowed orbit does not radiate energy and does not spiral inward.
3. Only orbits where the angular momentum of the electron is a whole-number multiple of$h/2\pi$ are allowed:
   $$m_{e}vr=\frac{nh}{2\pi }$$
   where n = 1, 2, 3, ... is the principal quantum number, h is Planck's constant.
4. Energy is absorbed or emitted only when an electron jumps between allowed orbits. The energy of the photon equals the energy difference between the two states:
   $$\Delta E=E_2-E_1=h\nu$$
   where $\nu$ is the frequency of the emitted or absorbed photon.

Energy of Bohr's Orbits (for Hydrogen-like atoms)

The negative sign means the electron is bound to the nucleus (energy is negative for bound states). The ground state is n = 1 with E₁ = −13.6 eV. As n increases, the energy becomes less negative (higher, i.e., less stable). At n = ∞, E = 0 (electron is free).

Radius of Bohr's Orbits

For hydrogen: r₁ = 52.9 pm (= 0.529 Å, the Bohr radius, a₀). r₂ = 4 × 52.9 = 211.6 pm.

Velocity of Electron in Bohr's Orbits

Hydrogen Spectrum and Spectral Series

When hydrogen is excited (given energy), electrons jump to higher levels. When they fall back to lower levels, they emit photons of specific energy. Different series are named for the level they fall to:

The wavenumber ($\bar{\nu }$ = 1/λ) of a line in any series is given by Rydberg's formula:

where R_H= 1.097 × 10⁷ m⁻¹ (Rydberg constant), n₁ = lower level, n₂ = upper level (n₂ > n₁).

Limitations of Bohr's Model

• Works only for hydrogen and hydrogen-like ions (one electron). Fails for multi-electron atoms.
• Cannot explain the fine structure of spectral lines (Zeeman and Stark effects).
• Does not account for the wave nature of the electron (de Broglie).
• Violates the Heisenberg uncertainty principle by specifying exact orbits.

Dual Nature of Matter and Radiation

Planck's Quantum Theory (1900)

Energy is not emitted or absorbed continuously. It is emitted in discrete packets called quanta (plural) or a quantum (singular). The energy of one quantum is:

where h = 6.626 × 10⁻³⁴ J·s (Planck's constant) and ν is the frequency of radiation. Since c = νλ, we can write E = hc/λ.

Photoelectric Effect (Einstein, 1905)

When light of a certain minimum frequency (threshold frequency, ν₀) falls on a metal, electrons are ejected. Key observations:

• Electrons are ejected only if the frequency of light exceeds ν₀, regardless of intensity.
• The kinetic energy of emitted electrons increases with frequency, not intensity.
• Above ν₀, the number of electrons ejected increases with intensity.

Einstein explained this by treating light as particles (photons). Each photon carries energy hν. If hν ≥ hν₀ (the work function), the electron is ejected:

Incident light frequency

de Broglie's Wave-Particle Duality (1924)

If radiation (light) can behave as particles (photons), then matter (particles like electrons) can also behave as waves. de Broglie's wavelength for a particle of mass m moving with velocity v:

where p = mv is the momentum. The wave nature of electrons was confirmed by Davisson and Germer's electron diffraction experiment (1927).

For a particle accelerated through potential V, the kinetic energy is eV = ½mv², so:

Heisenberg's Uncertainty Principle (1927)

It is fundamentally impossible to simultaneously determine the exact position and exact momentum of a moving particle. The more precisely you know the position, the less precisely you can know the momentum, and vice versa.

Or in terms of energy and time:

This principle destroys the concept of definite orbits. An electron cannot have a known path. Instead, we can only speak of the probability of finding an electron in a given region of space.

Note: The uncertainty principle is not due to instrument limitations. It is a fundamental property of quantum systems.

Quantum Mechanical Model of the Atom

Erwin Schrödinger (1926) derived a wave equation for the electron in an atom. Solutions to the Schrödinger equation are called wave functions (ψ, psi). Each wave function describes a specific state of the electron.

Key idea: ψ² gives the probability density of finding an electron at a given point in space. The 3D region where ψ² is significant is called an orbital. An orbital is not a definite path; it is a probability cloud.

Radial probability distribution tells you the probability of finding the electron at various distances from the nucleus. For 1s, there is a maximum at r = 52.9 pm (the Bohr radius is the most probable distance for the 1s electron in hydrogen).

Quantum Numbers

Four quantum numbers completely describe the state of an electron in an atom. They arise naturally from the solution to the Schrödinger equation.

1. Principal Quantum Number (n)

Indicates the main energy level (shell) and the average distance of the electron from the nucleus.

• Allowed values: n = 1, 2, 3, 4, ... (positive integers)
• Shell designations: n = 1 (K), n = 2 (L), n = 3 (M), n = 4 (N)
• Maximum electrons in a shell: 2n²

2. Azimuthal (Angular Momentum) Quantum Number (l)

Indicates the subshell (shape of orbital) within a shell.

• Allowed values: l = 0, 1, 2, ..., (n−1)
• Subshell designations: l = 0 (s), l = 1 (p), l = 2 (d), l = 3 (f)
• Number of orbitals in a subshell: 2l + 1
• Maximum electrons in a subshell: 2(2l + 1)

3. Magnetic Quantum Number (m_l or m)

Indicates the orientation of the orbital in space.

• Allowed values: m_l = −l, ..., −1, 0, +1, ..., +l (total 2l + 1 values)
• For l = 1 (p): m_l = −1, 0, +1 (three p orbitals: p_x, p_y, p_z)
• For l = 2 (d): m_l = −2, −1, 0, +1, +2 (five d orbitals)

4. Spin Quantum Number (m_s or s)

Indicates the spin of the electron: either spin-up (+½) or spin-down (−½). Each orbital can hold at most 2 electrons with opposite spins.

• Allowed values: m_s = +½ or −½

Quick Summary Table

Shapes of Orbitals

s Orbitals (l = 0)

s orbitals are spherically symmetric: the probability of finding the electron is the same in all directions at a given distance from the nucleus. The size increases with n: 3s > 2s > 1s. The 2s orbital has one radial node (a spherical surface where ψ² = 0); 3s has two.

p Orbitals (l = 1)

There are three p orbitals (p_x, p_y, p_z), each shaped like a dumbbell (two lobes) along one axis. They have a nodal plane (a plane where ψ² = 0) passing through the nucleus. For example, p_x has its lobes along the x-axis and a nodal plane in the yz plane. The three p orbitals are degenerate (have the same energy) in a free atom.

d Orbitals (l = 2)

There are five d orbitals. Four of them (d_xy, d_xz, d_yz, and d_x²-y²) have four lobes arranged between or along the axes. The fifth (d_z²) has two lobes along the z-axis and a doughnut-shaped ring in the xy plane. All five are degenerate in a free atom.

Number of Nodes

Total nodes in any orbital = n − 1. These are split into angular nodes (l) and radial nodes (n − l − 1).

Rules for Filling Orbitals

1. Aufbau Principle

Electrons fill orbitals in order of increasing energy. The (n + l) rule: the orbital with lower (n + l) has lower energy. If two orbitals have the same (n + l), the one with lower n has lower energy.

Filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, ...

2. Pauli Exclusion Principle

No two electrons in an atom can have the same set of all four quantum numbers. This means each orbital can hold at most two electrons, and they must have opposite spins (+½ and −½).

3. Hund's Rule of Maximum Multiplicity

When filling orbitals of equal energy (degenerate orbitals, e.g., three p orbitals or five d orbitals), electrons fill each orbital singly before any orbital is doubly occupied. All singly-occupied orbitals have parallel spins.

Example for carbon (Z = 6): configuration is 1s² 2s² 2p². The two 2p electrons go into two different 2p orbitals with parallel spins, not both into the same orbital.

Electronic Configurations

Use the Aufbau principle, Pauli exclusion principle, and Hund's rule together to write electronic configurations.

Key Configurations to Memorise

Stability of Half-filled and Fully-filled Subshells

Certain electron configurations have extra stability because of two factors:

• Symmetry: Half-filled (d⁵, f⁷) and fully-filled (d¹⁰, f¹⁴) subshells have spherically symmetric electron distributions, which lowers the energy.
• Exchange energy: Electrons with parallel spins can exchange positions. More parallel spins means higher exchange energy, which stabilises the configuration.

This is why chromium (Cr, Z = 24) has [Ar] 3d⁵ 4s¹ instead of the expected [Ar] 3d⁴ 4s². One electron moves from 4s to 3d to give the half-filled 3d⁵ configuration. Copper (Cu, Z = 29) has [Ar] 3d¹⁰ 4s¹ instead of [Ar] 3d⁹ 4s² for similar reasons.

These two exceptions (Cr and Cu) are the most tested in NEET. Memorise them.

Worked NEET Problems

Summary Cheat Sheet