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6Chapter Overview
Overview
Structure of Atom explains how scientists moved from the idea of an indivisible atom to the modern quantum mechanical picture. The chapter begins with the discovery of electrons, protons and neutrons through discharge tube, canal ray and neutron experiments. It then compares Thomson’s plum pudding model, Rutherford’s nuclear model and their limitations. Bohr’s model introduces fixed orbits, quantized energy and hydrogen spectrum calculations. The quantum mechanical model replaces definite paths with probability-based orbitals and includes de Broglie waves, Heisenberg uncertainty and Schrödinger’s equation. Quantum numbers describe each electron completely, while Aufbau principle, Pauli exclusion principle and Hund’s rule explain electronic configuration. For NEET, this chapter is highly important because it combines conceptual theory, spectra, formulas and configuration-based MCQs.
- 1The chapter develops from experimental discoveries to mathematical atomic structure.
- 2Bohr model works well only for one-electron systems such as H, He⁺ and Li²⁺.
- 3Quantum numbers define shell, subshell, orbital orientation and spin.
- 4Maximum electrons in a shell = 2n² and in a subshell = 2(2l + 1).
- 5Half-filled and fully-filled subshells are unusually stable due to symmetry and exchange energy.
- 6Atomic spectra provide evidence for quantized energy levels.
- 7NEET frequently asks numerical questions from Bohr radius, energy, wavelength and uncertainty.
Chapter Order
Remember: Particles → Models → Bohr → Quantum → Orbitals → Configuration. First discover what is inside atom, then learn how electrons are arranged.
Most Asked Areas
For NEET, focus on Bohr formulas, quantum numbers, orbital shapes, electronic configuration and exceptions like Cr and Cu.
Big Picture Example
Hydrogen spectrum cannot be explained by Rutherford model because accelerating electrons should radiate continuously. Bohr explained it by saying electrons jump between fixed energy levels and emit photons of definite frequencies.
Mixing Orbit and Orbital
Orbit is Bohr’s fixed circular path; orbital is a three-dimensional probability region from quantum mechanics.
Using Bohr Model for All Atoms
Bohr formulae are valid for hydrogen and hydrogen-like one-electron species only.
Wrong Configuration Order
Filling order follows increasing n + l value, not simply shell number.
Relates wavelength of a moving particle to its momentum.
Variables
λ=de Broglie wavelength
h=Planck constant
m=mass of particle
v=velocity of particle
Energy of electron in nth orbit of a hydrogen-like species.
Variables
E_n=energy of nth orbit
Z=atomic number
n=principal quantum number
Discovery of Subatomic Particles
Overview
The discovery of subatomic particles proved that atoms are divisible. Cathode ray discharge tube experiments showed that negatively charged rays travel from cathode to anode, move in straight lines, produce fluorescence and get deflected by electric and magnetic fields. J. J. Thomson identified these rays as electrons and measured the charge-to-mass ratio, e/m. Millikan’s oil drop experiment later helped determine electron charge, allowing calculation of electron mass. Canal rays, observed in modified discharge tubes, were positively charged and led to the identification of the proton. James Chadwick discovered the neutron by bombarding beryllium with alpha particles and observing neutral radiation. These discoveries formed the basis of atomic structure, nuclear charge, isotopes and mass number.
- 1Cathode ray properties are independent of electrode material and gas, proving electrons are universal particles.
- 2Canal rays depend on gas present because positive ions are formed from gas atoms.
- 3The lightest positive particle is the proton, obtained from hydrogen.
- 4Thomson’s e/m value showed electron has extremely small mass compared with atoms.
- 5Millikan’s charge value plus Thomson’s e/m value gives mass of electron.
- 6Neutron explains isotopes and missing nuclear mass.
- 7Atomic number equals number of protons; mass number equals protons plus neutrons.
Cathode Ray Charge
Cathode rays go toward the positive plate, so they must be negative. Remember: Opposites attract.
Particle Order
Electron first, proton next, neutron last: EPN sounds like 'Experimental Particles Named'.
Canal Rays Depend on Gas
Canal rays are gas ions, so changing gas changes the positive ion.
Electron Mass Calculation
If e = 1.602 × 10⁻¹⁹ C and e/m = 1.76 × 10¹¹ C kg⁻¹, then m = e/(e/m) ≈ 9.1 × 10⁻³¹ kg.
Mass Number Example
For sodium, Z = 11 and A = 23. Number of neutrons = A − Z = 23 − 11 = 12.
Thinking Canal Rays Are Always Protons
Canal rays are positive ions. Only hydrogen gas gives the lightest positive ion related to the proton.
Confusing e/m with m/e
Thomson measured charge-to-mass ratio e/m, not mass-to-charge ratio.
Putting Neutrons Outside Nucleus
Neutrons are nuclear particles along with protons; electrons occupy the extranuclear region.
Thomson determined this ratio for electron using deflection in electric and magnetic fields.
Variables
e=magnitude of electron charge
m=mass of electron
Electron mass is calculated using charge from oil drop experiment and e/m from Thomson experiment.
Variables
m=mass of electron
e=charge of electron
e/m=charge-to-mass ratio
Atomic Models
Overview
Atomic models developed as experimental evidence improved. Thomson proposed the plum pudding model, where negatively charged electrons were embedded in a uniform positively charged sphere, making the atom neutral. Rutherford tested this model using alpha particles directed at a thin gold foil. Most alpha particles passed straight through, some deflected slightly and very few bounced back. This proved that most of the atom is empty space and almost all positive charge and mass are concentrated in a tiny nucleus. Rutherford’s nuclear model placed electrons around the nucleus, but it could not explain atomic stability because revolving electrons should continuously lose energy and fall into the nucleus. It also failed to explain line spectra. Atomic spectra later supported quantized energy levels.
- 1Alpha particles are positively charged helium nuclei.
- 2Large deflection occurs only when alpha particles come close to the positive nucleus.
- 3Nucleus is much smaller than the atom but contains nearly all its mass.
- 4Thomson model could not explain strong back scattering.
- 5Rutherford model was a major step but classical physics made it unstable.
- 6Continuous spectrum contains all wavelengths; line spectrum contains selected wavelengths.
- 7Emission spectrum is produced when excited electrons return to lower energy states.
Rutherford Results
Most pass = mostly empty; few deflect = positive centre; very few return = tiny dense nucleus.
Spectrum Clue
Line spectrum means limited allowed energies; continuous spectrum means all wavelengths.
Scattering Analogy
If you throw marbles at a huge empty stadium with one tiny heavy pillar, most marbles pass through; only those near the pillar deflect. This is like Rutherford scattering.
Spectrum Example
A neon sign glows with specific colours because excited neon atoms emit light at definite wavelengths, forming a line spectrum.
Assuming Rutherford Explained Stability
Rutherford explained the nucleus but failed to explain why orbiting electrons do not fall into it.
Forgetting Alpha Particle Charge
Alpha particles are positively charged, so they are repelled by the positive nucleus.
Confusing Atomic and Nuclear Size
The nucleus is extremely small compared with the atom, but contains almost all mass.
Energy of radiation emitted or absorbed in atomic spectra.
Variables
E=energy of photon
h=Planck constant
ν=frequency of radiation
Connects speed, frequency and wavelength of electromagnetic radiation.
Variables
c=speed of light
ν=frequency
λ=wavelength
Bohr Model of Atom
Overview
Bohr model corrected Rutherford’s instability problem for hydrogen-like atoms by introducing quantization. Bohr proposed that electrons revolve only in certain permitted circular orbits called stationary states without radiating energy. Angular momentum is quantized as mvr = nh/2π. Radiation is emitted or absorbed only when an electron jumps between two energy levels, with energy difference ΔE = hν. For hydrogen-like species, orbit radius increases as n²/Z, velocity varies as Z/n and energy is negative, proportional to −Z²/n². The model successfully explains the line spectrum of hydrogen and spectral series such as Lyman, Balmer and Paschen. However, it fails for multi-electron atoms, fine structure, Zeeman effect and the wave nature of electrons.
- 1Energy levels are negative because electron is bound to the nucleus.
- 2Higher n means larger orbit, higher energy and lower magnitude of negative energy.
- 3Energy gap decreases as n increases, so spectral lines converge.
- 4Emission occurs when electron falls from higher to lower level.
- 5Absorption occurs when electron jumps from lower to higher level.
- 6For hydrogen-like species, replace Z according to nuclear charge.
- 7Bohr model cannot describe exact electron arrangement in multi-electron atoms.
Series Order
Lyman, Balmer, Paschen, Brackett, Pfund have final levels 1, 2, 3, 4, 5. Remember: Little Boys Prefer Bright Places.
Bohr Dependence
Radius goes with n square; energy becomes less negative as n goes higher.
Energy of Second Orbit of Hydrogen
For H, Z = 1 and n = 2. E₂ = −13.6/4 = −3.4 eV.
Radius of First Orbit of He⁺
For He⁺, Z = 2 and n = 1. r₁ = 0.529 × 1²/2 = 0.2645 Å.
Ionisation Energy of Hydrogen
Ground state energy of hydrogen is −13.6 eV, so energy needed to remove the electron to infinity is +13.6 eV.
Wrong Sign of Energy
Bohr energy is negative for bound electrons. Zero energy corresponds to electron at infinity.
Applying to Multi-Electron Atoms
Bohr’s exact formulas work for hydrogen-like species only, not general multi-electron atoms.
Confusing Emission and Absorption
Higher to lower level emits energy; lower to higher level absorbs energy.
Only those orbits are allowed for which electron angular momentum is an integral multiple of h/2π.
Variables
m=mass of electron
v=velocity of electron
r=radius of orbit
n=orbit number
h=Planck constant
Radius of nth Bohr orbit for hydrogen-like species.
Variables
r_n=radius of nth orbit
n=principal quantum number
Z=atomic number
Speed of electron in nth Bohr orbit of hydrogen-like atom.
Variables
v_n=velocity in nth orbit
Z=atomic number
n=orbit number
Quantum Mechanical Model
Overview
The quantum mechanical model replaces Bohr’s fixed circular orbits with orbitals, which are regions of high probability of finding electrons. It is based on the dual nature of matter, de Broglie’s hypothesis and Heisenberg’s uncertainty principle. de Broglie proposed that moving particles have wavelength λ = h/mv, explaining why electrons show wave character. Heisenberg stated that position and momentum of a microscopic particle cannot both be measured exactly at the same time. Schrödinger developed a wave equation whose solutions are wave functions, ψ. The square of the wave function, ψ², gives probability density of finding an electron. Thus, modern atomic structure does not describe exact paths but predicts allowed energies, orbitals and electron distribution around the nucleus.
- 1Wave nature is significant for microscopic particles like electrons, not ordinary macroscopic objects.
- 2Greater certainty in position causes greater uncertainty in momentum.
- 3Exact electron trajectory is not meaningful in quantum mechanics.
- 4Orbitals are obtained from acceptable solutions of Schrödinger equation.
- 5Probability of finding electron is high where electron cloud density is high.
- 6Nodes are regions where probability of finding electron is zero.
- 7Quantum model explains multi-electron atoms better than Bohr model.
ψ and ψ²
Psi is a mathematical wave function; psi square is the physical probability. Remember: Square makes it real.
Uncertainty
Pin down position tightly, momentum becomes fuzzy. Quantum particles do not allow perfect tracking.
de Broglie
More momentum means shorter wavelength: fast heavy objects have negligible matter waves.
de Broglie Concept Example
An electron accelerated to high velocity has measurable wavelength, so it can show diffraction. A cricket ball also has wavelength but it is immeasurably small due to large mass.
Uncertainty Example
If the position of an electron is known very accurately inside a tiny region, its velocity becomes highly uncertain, so a fixed Bohr-like path is impossible.
Thinking Uncertainty Is Instrument Error
Heisenberg uncertainty is not due to poor instruments; it is a fundamental limitation for microscopic particles.
Treating Orbitals as Fixed Paths
Orbitals are probability regions, not circular tracks followed by electrons.
Using de Broglie Significantly for Large Objects
All matter has wavelength, but for macroscopic objects it is too small to observe.
Every moving particle has an associated wavelength.
Variables
λ=wavelength associated with particle
h=Planck constant
m=mass of particle
v=velocity of particle
p=momentum of particle
There is a fundamental limit to simultaneous precision of position and momentum.
Variables
Δx=uncertainty in position
Δp=uncertainty in momentum
h=Planck constant
Atomic Orbitals & Quantum Numbers
Overview
Atomic orbitals are three-dimensional regions around the nucleus where the probability of finding an electron is high. Each electron in an atom is described by four quantum numbers. The principal quantum number, n, gives shell, size and energy level. The azimuthal quantum number, l, gives subshell and orbital shape; l = 0, 1, 2, 3 correspond to s, p, d and f. The magnetic quantum number, m, describes orbital orientation and has values from −l to +l. The spin quantum number, s, describes electron spin as +1/2 or −1/2. Orbital shapes include spherical s orbitals, dumbbell-shaped p orbitals, cloverleaf d orbitals and complex f orbitals. Nodes are zero-probability regions and are important for orbital structure.
- 1No two electrons in an atom can have the same set of four quantum numbers.
- 2An orbital can hold maximum two electrons with opposite spins.
- 3For n = 3, possible subshells are 3s, 3p and 3d.
- 4p subshell has three orbitals: p_x, p_y and p_z.
- 5d subshell has five orbitals and f subshell has seven orbitals.
- 6s orbitals are spherical and non-directional.
- 7Number of orbitals in a shell = n²; maximum electrons in shell = 2n².
- 8Nodes increase with shell number and affect orbital energy and size.
Quantum Numbers
n = Nest, l = Look or shape, m = Magnetic orientation, s = Spin.
Subshell Order
s p d f corresponds to l = 0, 1, 2, 3. Remember: Some People Do Forget.
Nodes
Total nodes are one less than n. Angular nodes equal l. Whatever remains is radial nodes.
Allowed Quantum Numbers Example
For a 3p electron: n = 3, l = 1, m can be −1, 0 or +1, and s can be +1/2 or −1/2.
Nodes Example
For 3p orbital, n = 3 and l = 1. Total nodes = 2, angular nodes = 1 and radial nodes = 1.
Using l = n
For a given n, l values go only from 0 to n − 1. If n = 3, l cannot be 3.
Wrong m Range
For l = 2, m values are −2, −1, 0, +1, +2, giving five d orbitals.
Ignoring Opposite Spins
Two electrons in the same orbital must have opposite spins, not the same spin.
Azimuthal quantum number values available for a given principal quantum number.
Variables
l=azimuthal quantum number
n=principal quantum number
Magnetic quantum number values representing orientations of orbitals.
Variables
m=magnetic quantum number
l=azimuthal quantum number
Calculates the number of orientations in a subshell.
Variables
l=azimuthal quantum number
Electronic Configuration
Overview
Electronic configuration describes the distribution of electrons among orbitals of an atom or ion. Aufbau principle states that electrons fill lower-energy orbitals before higher-energy orbitals, generally guided by the n + l rule. Pauli exclusion principle states that an orbital can contain maximum two electrons and they must have opposite spins. Hund’s rule states that electrons occupy degenerate orbitals singly with parallel spins before pairing. The filling order explains configurations such as 1s² 2s² 2p⁶. Some atoms, especially chromium and copper, show exceptions because half-filled and fully-filled subshells are extra stable due to symmetry and exchange energy. Ions are formed by adding or removing electrons; for transition metal cations, electrons are removed from ns before (n − 1)d.
- 1Electronic configuration must conserve total number of electrons.
- 2Orbital filling order is not simply 1, 2, 3, 4 shells; 4s fills before 3d.
- 3Degenerate orbitals are orbitals of the same subshell with equal energy.
- 4Half-filled and fully-filled configurations have greater stability.
- 5For cations, remove electrons from the outermost shell first, not necessarily the last filled subshell.
- 6Noble gas shorthand saves time and reduces mistakes.
- 7Hund’s rule maximizes unpaired electrons before pairing begins.
Aufbau Order
Use the diagonal rule or remember: 1s 2s 2p 3s 3p 4s 3d 4p 5s.
Pauli Principle
One orbital is like a two-seat bench: only two electrons, and they must sit with opposite spins.
Hund's Rule
Empty bus seats first: electrons occupy separate equal-energy orbitals before pairing.
Cr and Cu
Chromium wants d⁵, copper wants d¹⁰. Half-filled and fully-filled d subshells are extra stable.
Configuration of Calcium
Calcium has Z = 20. Configuration = 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² or [Ar] 4s².
Configuration of Fe²⁺
Fe is [Ar] 3d⁶ 4s². For Fe²⁺, remove two 4s electrons first, so Fe²⁺ = [Ar] 3d⁶.
Configuration of Copper
Copper, Z = 29, has actual configuration [Ar] 3d¹⁰ 4s¹ because a completely filled d subshell is more stable.
Removing 3d Before 4s in Ions
Although 4s fills before 3d, transition metal cations lose 4s electrons before 3d electrons.
Pairing Too Early
In p, d and f subshells, electrons remain unpaired with parallel spins as far as possible before pairing.
Ignoring Exceptions
Cr and Cu do not follow the simple expected configuration because d⁵ and d¹⁰ are more stable.
Wrong Electron Count in Ions
Always adjust electron count first: cation loses electrons, anion gains electrons.
Predicts relative order of orbital filling in Aufbau principle.
Variables
n=principal quantum number
l=azimuthal quantum number
Gives the maximum number of electrons in a subshell.
Variables
l=azimuthal quantum number
Formula Sheet
10Relates wavelength of a moving particle to its momentum.
Variables
λ=de Broglie wavelength
h=Planck constant
m=mass of particle
v=velocity of particle
Energy of electron in nth orbit of a hydrogen-like species.
Variables
E_n=energy of nth orbit
Z=atomic number
n=principal quantum number
Gives maximum number of electrons in a shell with principal quantum number n.
Variables
n=principal quantum number or shell number
Thomson determined this ratio for electron using deflection in electric and magnetic fields.
Variables
e=magnitude of electron charge
m=mass of electron
Electron mass is calculated using charge from oil drop experiment and e/m from Thomson experiment.
Variables
m=mass of electron
e=charge of electron
e/m=charge-to-mass ratio
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NEET PYQs — Structure of Atom
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Match List I with List II: Choose the correct answer from the options given below.
The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes n = 2 → n = 3 and n = 4 → n = 6 transitions, respectively, is
The energy of an electron in the ground state $(n=1)$ for $\mathrm{He^+}$ ion is $-x\,J$, then that for an electron in $n=2$ state for $\mathrm{Be^{3+}}$ ion in J is:
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