Structure of Atom Class 11 Chapter Notes

Key points

• Atom contains a tiny, dense, positively charged nucleus and negatively charged electrons around it; most atomic mass is in the nucleus.
• Cathode rays proved the existence of electrons; canal rays led to the discovery of positive particles. Charge of electron = -1.602 × 10^-19 C.
• Rutherford model explained nuclear atom but failed to explain atomic stability and line spectra.
• Bohr model works well for hydrogen and hydrogen-like species such as He+, Li2+, Be3+; it is not valid for multi-electron atoms.
• Electromagnetic radiation has both wave and particle character: c = νλ and energy of photon E = hν = hc/λ.
• Hydrogen spectrum follows Rydberg formula: wave number = RH Z^2(1/n1^2 - 1/n2^2), where n2 > n1.
• de Broglie relation connects matter and wave nature: λ = h/mv = h/p. Smaller mass gives more noticeable wavelength.
• Heisenberg uncertainty principle: Δx × Δp >= h/4π; exact position and momentum cannot be known simultaneously.
• Four quantum numbers describe an electron: n, l, m_l and m_s. No two electrons in an atom can have all four identical.
• Electronic configuration follows Aufbau principle, Pauli exclusion principle and Hund rule; important exceptions include Cr and Cu.

Must-know definitions

Atomic number

Number of protons present in the nucleus of an atom. For a neutral atom, it is also equal to the number of electrons.

Mass number

Total number of protons and neutrons present in the nucleus of an atom.

Isotopes

Atoms of the same element having the same atomic number but different mass numbers due to different numbers of neutrons.

Isobars

Atoms of different elements having the same mass number but different atomic numbers.

Photon

A packet or quantum of electromagnetic radiation with energy E = hν.

Wave number

Number of waves per unit length; it is the reciprocal of wavelength and is commonly expressed in m^-1 or cm^-1.

Orbital

A three-dimensional region around the nucleus where the probability of finding an electron is maximum.

Quantum numbers

A set of four numbers used to describe the shell, subshell, orbital orientation and spin of an electron.

Degenerate orbitals

Orbitals having the same energy, such as the three 2p orbitals in an isolated atom.

Node

A region where the probability of finding an electron is zero. Total nodes in an orbital = n - 1.

Atomic models: what each model explains and misses

The story of atomic structure moves from experimental evidence to better models. Thomson model treated the atom as a positively charged sphere with electrons embedded in it, so it explained overall neutrality but could not explain alpha-particle scattering. Rutherford model showed that the atom has a small, heavy, positive nucleus because most alpha particles passed straight through gold foil while a few were deflected strongly. However, according to classical physics, a revolving electron should continuously lose energy and fall into the nucleus; this made Rutherford atom unstable. It also could not explain line spectra. Bohr model fixed these problems for hydrogen by proposing fixed circular orbits with quantised angular momentum. Electrons do not radiate energy in allowed orbits, but emit or absorb energy only during transitions. Modern quantum mechanics replaces fixed orbits with orbitals, because electron behaviour is probabilistic, wave-like and restricted by uncertainty.

Quick comparison of atomic models

Formula sheet: radiation, Bohr model and matter waves

Electromagnetic radiation: speed of light c = νλ, where c = 3.0 × 10^8 m s^-1. Photon energy: E = hν = hc/λ, where h = 6.626 × 10^-34 J s. For one mole of photons, multiply by Avogadro constant NA = 6.022 × 10^23 mol^-1. Bohr radius: r_n = 52.9 pm × n^2/Z for hydrogen-like species. Bohr energy: E_n = -2.18 × 10^-18 × Z^2/n^2 J per atom. The negative sign means the electron is bound to the nucleus; energy becomes less negative as n increases. Transition energy: ΔE = E_final - E_initial; emission occurs when electron falls to lower n and energy is released. Rydberg equation: wave number = RH Z^2(1/n1^2 - 1/n2^2), n2 > n1. de Broglie wavelength: λ = h/mv = h/p. Uncertainty: ΔxΔp >= h/4π.

How to write electronic configuration fast

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Quantum numbers and orbitals in one view

An electron in an atom is identified using four quantum numbers. The principal quantum number n tells the shell, size and energy level; possible values are 1, 2, 3 and so on. The azimuthal quantum number l tells the subshell and shape; l = 0, 1, 2, 3 correspond to s, p, d, f. For a given n, l ranges from 0 to n - 1. The magnetic quantum number m_l tells the orientation of the orbital; it ranges from -l to +l, so the number of orbitals in a subshell is 2l + 1. The spin quantum number m_s is +1/2 or -1/2. Maximum electrons in a shell = 2n^2. Maximum electrons in s, p, d, f subshells are 2, 6, 10, 14 respectively. For orbitals, total nodes = n - 1, angular nodes = l and radial nodes = n - l - 1.

Quantum number revision table

Hydrogen spectrum: series memory map

The hydrogen spectrum is produced when an electron jumps between energy levels. If the electron falls to a lower level, the atom emits radiation; if it jumps to a higher level, it absorbs radiation. The spectral series is named by the final lower level: Lyman series ends at n1 = 1 and lies in ultraviolet region. Balmer series ends at n1 = 2 and lies partly in visible region. Paschen series ends at n1 = 3, Brackett series at n1 = 4 and Pfund series at n1 = 5; these are in infrared region. Memory tip: L B P B P = Lyman, Balmer, Paschen, Brackett, Pfund for n1 = 1, 2, 3, 4, 5. In Rydberg formula, always keep n2 > n1; otherwise the sign and physical meaning become confusing.

Short worked examples

• {"problem":"Find the maximum number of electrons in the M shell.","solution":"M shell means n = 3. Maximum electrons = 2n^2 = 2 × 3^2 = 18."}
• {"problem":"What is the de Broglie wavelength of an electron moving with momentum 3.31 × 10^-24 kg m s^-1?","solution":"λ = h/p = 6.626 × 10^-34 / 3.31 × 10^-24 = 2.00 × 10^-10 m."}
• {"problem":"Write the electronic configuration of Cr, atomic number 24.","solution":"Expected filling gives [Ar] 3d4 4s2, but actual Cr = [Ar] 3d5 4s1 due to extra stability of half-filled 3d subshell."}

Board exam traps and marking cues

Do not write Bohr formulas for every atom; they apply only to hydrogen and hydrogen-like species. In energy questions, keep units consistent: wavelength in metre for SI calculations and remember E = hc/λ gives energy per photon. The negative sign in Bohr energy shows a bound electron, not negative emitted energy. For electronic configuration, many students remove 3d electrons before 4s in transition metal cations; correct rule is to remove ns electrons first. In quantum number questions, check allowed values carefully: if n = 3, l can be 0, 1, 2 only, not 3. For Hund rule diagrams, show single electrons with parallel spins before pairing.

Quick revision checks

• Which experiment proved the presence of a small positive nucleus? Rutherford alpha-particle scattering experiment.
• What is the maximum number of orbitals in a d subshell? For d, l = 2, so orbitals = 2l + 1 = 5.
• Why is Bohr energy negative? Because the electron is bound to the nucleus and energy must be supplied to remove it completely.
• State the relationship between wavelength and momentum in matter waves. de Broglie relation: λ = h/p = h/mv.

Frequently Asked Questions