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Chemistry · NDA

CN02 — Atomic Structure

📖 Chapter CN02 · NDA Class 11–12 Level 🎯 NDA Level : High Priority

Atomic Structure is one of the most consistently tested topics in NDA Chemistry. Questions appear on atomic models (especially Rutherford and Bohr), subatomic particles, isotopes/isobars/isotones, and electronic configuration. Average students who can write configurations, identify isotopes from Z and A, and recall Bohr's postulates can score reliably from this chapter.

📌 What to expect in NDA (based on 2022–2025 pattern):
(1) Comparison of atomic models — Rutherford's nuclear model & its failure; Bohr's postulates;
(2) Subatomic particles — charge, mass, location of e⁻, p⁺, n⁰;
(3) Atomic number (Z), mass number (A), neutrons = A − Z;
(4) Isotopes, isobars, isotones — definition with examples (¹H/²H/³H; ⁴⁰Ar/⁴⁰Ca; ¹⁴C/¹⁴N);
(5) Electronic configuration using shells (K, L, M, N) and 2n² rule;
(6) Valence electrons and valency; Quantum numbers at basic MCQ level.

Topics at a Glance

① Atomic Models

Dalton → Thomson → Rutherford → Bohr

② Subatomic Particles

e⁻, p⁺, n⁰ — charge, mass, location

③ Z, A, Isotopes

Atomic no., mass no., isotopes, isobars, isotones

④ Electronic Configuration

Shell filling, Aufbau, Pauli, Hund's rule

⑤ Quantum Numbers

n, l, m, s — basic MCQ concepts

1. Atomic Models — Historical Development

1.1

The Four Models — Dalton to Bohr

Each model corrected the previous one's failures

Our understanding of the atom evolved through a series of experiments over 100 years. NDA tests the key features and failures of each model — particularly Rutherford's gold foil experiment and Bohr's postulates.

1808

Dalton

Solid Sphere Model

Atom is the smallest indivisible particle
Atoms of same element are identical
Atoms combine in fixed whole number ratios
Atoms cannot be created or destroyed

⚠ Flaw: No subatomic particles; couldn't explain electricity through matter

1897

Thomson

"Plum Pudding" Model

Atom = sphere of positive charge
Electrons embedded like plums in pudding
First to propose subatomic particles (e⁻)
Overall atom is electrically neutral

⚠ Flaw: Could not explain Rutherford's scattering results

1911

Rutherford

Nuclear Model

Tiny, dense, positive nucleus at centre
Electrons orbit around nucleus
Most of atom is empty space
Based on α-particle (gold foil) experiment

⚠ Flaw: Orbiting e⁻ should radiate energy → spiral into nucleus (unstable)

1913

Bohr

Planetary / Shell Model

Electrons move in fixed circular orbits (shells)
Each orbit has fixed energy — no radiation while in orbit
Energy emitted/absorbed only when e⁻ jumps shells
Explained hydrogen spectrum successfully

⚠ Flaw: Could not explain multi-electron atoms or Zeeman effect

1.2

Rutherford's Gold Foil Experiment

The experiment that revealed the nucleus — most important for NDA

Rutherford bombarded a thin gold foil with a stream of high-energy alpha (α) particles (He²⁺ ions) and observed where they landed on a surrounding fluorescent screen. The results were shocking and overturned Thomson's model completely.

Fig. 1 — Rutherford's Gold Foil (α-scattering) Experiment: most α-particles pass straight through; very few bounce back — proving the nucleus is tiny, dense, and positively charged.

📋 Observations & Conclusions

Most α pass straight through → most of atom is empty space
Few deflected at small angles → positive charge concentrated in tiny region
Very few bounce back (1 in 20,000) → nucleus is extremely dense and small
Nucleus diameter ≈ 10⁻¹⁵ m; atom ≈ 10⁻¹⁰ m (100,000× larger)

📌 Bohr's Postulates (NDA must-know)

Electrons revolve in fixed circular orbits (stationary states) — no radiation
Each orbit has a fixed energy — orbit closest to nucleus has lowest energy
Electron jumps to higher orbit by absorbing energy (photon in)
Electron falls to lower orbit by emitting energy (photon out) → spectral line
Angular momentum quantised: mvr = nh/2π (n = 1, 2, 3…)

⚛ Bohr's Model — Key Formulae

Energy of nth orbit (Hydrogen atom): Eₙ = −13.6/n² eV (n = 1, 2, 3 … = principal quantum number) E₁ = −13.6 eV (ground state); E₂ = −3.4 eV; E₃ = −1.51 eV Radius of nth orbit: rₙ = 0.529 × n² Å (for hydrogen) r₁ = 0.529 Å (Bohr radius); r₂ = 2.116 Å Energy of emitted photon when electron jumps from n₂ to n₁ (n₂ > n₁): ΔE = E_n₂ − E_n₁ = 13.6 (1/n₁² − 1/n₂²) eV Frequency: ΔE = hν (h = 6.626 × 10⁻³⁴ J·s; Planck's constant) Wavelength: c = νλ (c = 3 × 10⁸ m/s; speed of light)

NDA shortcut: The Lyman series (UV) ends at n=1, Balmer series (visible) ends at n=2, Paschen series (IR) ends at n=3. The Balmer series is the only one in the visible region.

📝 TOPIC-WISE PYQ

Atomic Models — NDA Pattern Questions

Q1. In Rutherford's α-scattering experiment, most of the α-particles passed through the gold foil without deflection. This shows that:

(a) Gold atoms are very heavy (b) Most of the atom is empty space (c) Nucleus is negatively charged (d) α-particles have high energy

Answer: (b) Most of the atom is empty space
Since the vast majority of α-particles pass through undeflected, they do not encounter any significant obstruction — meaning the atom is mostly empty. Only the rare α-particle that passes very close to the tiny, dense, positive nucleus gets deflected or bounced back. This is the central conclusion of the gold foil experiment.

Q2. According to Bohr's model, when an electron jumps from a higher energy orbit to a lower energy orbit, it:

(a) Absorbs a photon (b) Emits a photon (c) Neither absorbs nor emits (d) Increases its potential energy

Answer: (b) Emits a photon
Higher orbit = higher energy. Falling to lower orbit means the electron loses energy — this energy is released as a photon (a quantum of light): ΔE = hν. This is how spectral emission lines are produced. Conversely, going from lower to higher orbit requires absorbing a photon (absorption spectrum).

Q3. Which model of the atom described it as a "plum pudding" or "raisin cake"?

(a) Dalton's (b) Thomson's (c) Rutherford's (d) Bohr's

Answer: (b) Thomson's model
J.J. Thomson (1897) proposed that the atom is a uniform sphere of positive charge with electrons embedded in it — like plums (raisins) in a pudding (cake). He was the first to discover the electron through cathode ray experiments. This model was disproved by Rutherford's 1911 scattering experiment.

2. Subatomic Particles

2.1

Electron, Proton, and Neutron — Properties

Location, charge, and mass — the three facts NDA tests directly

Particle	Symbol	Discovered by	Location	Charge	Mass (amu)	Relative Mass
Electron	e⁻	J.J. Thomson (1897)	Orbiting nucleus (shells)	−1 (−1.6 × 10⁻¹⁹ C)	0.000549	1/1836 of proton
Proton	p⁺	E. Rutherford (1919)	Inside nucleus	+1 (+1.6 × 10⁻¹⁹ C)	1.0073	≈ 1
Neutron	n⁰	James Chadwick (1932)	Inside nucleus	0 (neutral)	1.0087	≈ 1

🔑 Memory Shortcut: PEN — Proton is Positive, Electron is (n)Egative, Neutron is Neutral. Proton and Neutron are in the Nucleus; Electrons are Outside (in shells).

Fig. 2 — Bohr's atomic model showing nucleus (protons + neutrons) and electron shells K, L, M with their maximum electron capacities

⚛ Subatomic Particle Formulae

Atomic Number (Z): Z = number of protons in nucleus = number of electrons (in neutral atom) Mass Number (A): A = number of protons + number of neutrons A = Z + N → N (neutrons) = A − Z Standard notation: ᴬ_Z X (A on top, Z on bottom, X = element symbol) Example: ²³_₁₁ Na → Z=11 (protons=11), A=23, N=23−11=12 neutrons Max electrons per shell (2n² rule): K shell (n=1): 2×1² = 2 L shell (n=2): 2×2² = 8 M shell (n=3): 2×3² = 18 N shell (n=4): 2×4² = 32 (Note: outermost shell can hold maximum 8; second from last max 18)

The 2n² rule gives the maximum capacity of each shell. In practice, the outermost shell (valence shell) never holds more than 8 electrons (octet rule), and the penultimate shell is limited to 18.

3. Atomic Number, Mass Number & Key Terms

3.1

Isotopes, Isobars, and Isotones

The most commonly confused trio — NDA tests with specific examples

🔬 Isotopes

Same Z, different A (same element, different mass)
Same number of protons & electrons
Different number of neutrons
Same chemical properties, different physical properties
Examples:
¹H, ²H (deuterium), ³H (tritium) — hydrogen isotopes
¹²C and ¹⁴C (carbon-14 used in dating)
²³⁵U and ²³⁸U (uranium isotopes — nuclear fuel)

🔮 Isobars

Same A, different Z (same mass number, different element)
Different protons, different electrons
Different neutrons
Different chemical properties
Examples:
⁴⁰₁₈Ar and ⁴⁰₂₀Ca (A=40; Ar has 18p, Ca has 20p)
¹⁴₆C and ¹⁴₇N (A=14)
³H and ³He (A=3)

⚛ Isotones

Same number of neutrons, different Z and A
N = A − Z is same for all isotones
Different elements, different masses
Examples:
¹⁴₆C (N=8) and ¹⁵₇N (N=8)
³H (N=2) and ⁴He (N=2)
³⁹K (N=20) and ⁴⁰Ca (N=20)

Term	Same	Different	Example pair	NDA Memory Trick
Isotopes	Z (protons)	A and N (neutrons)	¹²C and ¹⁴C	ISOtopes → same topic (same element)
Isobars	A (mass no.)	Z and N	⁴⁰Ar and ⁴⁰Ca	ISObars → same bar (weight)
Isotones	N (neutrons)	Z and A	¹⁴C and ¹⁵N	ISOtones → same neutrone count

📌 NDA Special Case — Isoelectronic Species: Atoms or ions with the same number of electrons are called isoelectronic. Example: Na⁺, Mg²⁺, Al³⁺, Ne, F⁻, O²⁻ all have 10 electrons. This appears in NDA as a statement match or identification question.

📝 TOPIC-WISE PYQ

Atomic Number, Isotopes, Isobars, Isotones — NDA Pattern Questions

Q1. An element ²⁷₁₃Al has how many neutrons in its nucleus?

(a) 13 (b) 27 (c) 14 (d) 40

Answer: (c) 14
Neutrons = A − Z = 27 − 13 = 14 neutrons. Z = 13 = protons = electrons (neutral atom). A = 27 = total nucleons.

Q2. Which of the following pairs represents isobars?

(a) ¹H and ²H (b) ¹⁴₆C and ¹⁴₇N (c) ¹⁴₆C and ¹²₆C (d) ³⁹₁₉K and ⁴⁰₂₀Ca

Answer: (b) ¹⁴₆C and ¹⁴₇N
Isobars have the same mass number (A) but different atomic numbers (Z). Both ¹⁴C and ¹⁴N have A = 14 but different Z (6 and 7). Option (a) is isotopes (same Z=1, different A). Option (c) is also isotopes (same Z=6). Option (d) has different A (39 vs 40) — they are isotones (same N=20).

Q3. ²³⁵U and ²³⁸U are both used in nuclear technology. What is their relationship?

(a) Isobars (b) Isotopes (c) Isotones (d) Isoelectronic

Answer: (b) Isotopes
Both are Uranium (same Z = 92) but have different mass numbers (235 and 238) and therefore different numbers of neutrons (143 and 146). ²³⁵U is fissile (used in reactors and bombs); ²³⁸U is more abundant but not directly fissile. Same element, different mass = Isotopes.

🧠 TRICKY QUESTIONS

Isotopes, Isobars & Isotones — Conceptual Traps

Q. ³⁹₁₉K and ⁴⁰₂₀Ca — What is the relationship between these two?

Answer: Isotones (same number of neutrons)
K: neutrons = 39 − 19 = 20
Ca: neutrons = 40 − 20 = 20
Same neutron count (N=20), but different Z and different A → they are Isotones.
Common trap: students see the A values are close (39, 40) and assume isobars (A must be exactly same for isobars — not close).

Q. Do isotopes of an element have the same chemical properties? Why?

Answer: Yes — because they have the same electronic configuration.
Chemical properties depend on the number and arrangement of electrons (especially valence electrons), NOT on neutrons. Isotopes have the same Z → same electron count → same electronic configuration → same chemical behaviour.
Physical properties (mass, density, melting point) differ because A differs. ¹H₂O, ²H₂O (heavy water), ³H₂O all undergo the same chemical reactions but have different densities and boiling points.

4. Electronic Configuration

4.1

Shell Filling — Rules and Configuration

Three rules govern how electrons fill orbitals — all three are NDA-tested

① Aufbau Principle

Electrons fill orbitals in increasing order of energy
Lower energy orbitals fill first before higher ones
Energy order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p …
Remember: 4s fills before 3d (counter-intuitive!)
Aufbau = "building up" in German

② Pauli Exclusion Principle

No two electrons in an atom can have the same set of all four quantum numbers
An orbital can hold maximum 2 electrons, with opposite spins (↑↓)
s subshell: 1 orbital → 2 electrons max
p subshell: 3 orbitals → 6 electrons max
d subshell: 5 orbitals → 10 electrons max

③ Hund's Rule of Maximum Multiplicity

Within the same subshell, electrons occupy orbitals singly first before pairing
All singly occupied orbitals have the same spin direction (↑↑↑)
Pairing only after all orbitals of that subshell are half-filled
Maximises total spin → greater stability
Explains paramagnetism of partially filled orbitals

🔮 Orbital Filling Order — Memory Aid

Orbital capacity: s=2, p=6, d=10, f=14 Filling order (Aufbau): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ … Arrow diagonal trick (n + l rule): Fill orbitals in increasing order of (n + l); if equal, lower n fills first. 3d: n+l = 3+2 = 5 | 4s: n+l = 4+0 = 4 → 4s fills before 3d ✓ 4p: n+l = 4+1 = 5 | 3d: n+l = 3+2 = 5 → 3d fills before 4p (lower n) ✓

For NDA (shell notation): use K(2) L(8) M(18) N(32) with outer shell max 8. The orbital notation (1s² 2s² 2p⁶ …) is for higher-level questions.

Hydrogen

H (Z=1)

K: 1 | Config: 1s¹

Valence e⁻: 1

Carbon

C (Z=6)

K:2, L:4 | 1s²2s²2p²

Valence e⁻: 4

Nitrogen

N (Z=7)

K:2, L:5 | 1s²2s²2p³

Valence e⁻: 5

Oxygen

O (Z=8)

K:2, L:6 | 1s²2s²2p⁴

Valence e⁻: 6

Sodium

Na (Z=11)

K:2, L:8, M:1 | [Ne]3s¹

Valence e⁻: 1

Chlorine

Cl (Z=17)

K:2, L:8, M:7 | [Ne]3s²3p⁵

Valence e⁻: 7

Calcium

Ca (Z=20)

K:2, L:8, M:8, N:2

Valence e⁻: 2

Argon

Ar (Z=18)

K:2, L:8, M:8

Noble gas (0)

📋 Valence Electrons and Valency:
Valence electrons = electrons in the outermost shell. They determine chemical reactivity and bonding.
Valency = number of electrons an atom gains, loses, or shares to achieve the nearest noble gas configuration (stable octet or duplet for H, Li).
Rule: If valence electrons ≤ 4 → valency = valence electrons (tends to lose/share). If valence electrons ≥ 5 → valency = 8 − valence electrons (tends to gain).
Na (1 valence e⁻) → valency = 1 (loses 1e⁻). Cl (7 valence e⁻) → valency = 8−7 = 1 (gains 1e⁻).

📝 TOPIC-WISE PYQ

Electronic Configuration — NDA Pattern Questions

Q1. The electronic configuration of phosphorus (Z=15) is:

(a) 2, 8, 5 (b) 2, 8, 4, 1 (c) 2, 5, 8 (d) 2, 8, 3, 2

Answer: (a) 2, 8, 5
Z=15 electrons fill shells: K=2, L=8 (full), remaining = 15−10 = 5 → M=5.
Configuration: K:2, L:8, M:5 → written as 2,8,5. Valence electrons = 5; Valency = 8−5 = 3.

Q2. An element with electronic configuration 2,8,2 belongs to which period and group?

(a) Period 2, Group II (b) Period 3, Group II (c) Period 2, Group 12 (d) Period 4, Group 2

Answer: (b) Period 3, Group II
Total electrons = 2+8+2 = 12, so Z=12 = Magnesium (Mg). Number of shells = 3 → Period 3. Valence electrons = 2 → Group II (Group 2). Mg configuration: K:2, L:8, M:2.

Q3. According to Hund's rule, the three 2p electrons in nitrogen (Z=7) are arranged as:

(a) ↑↓ in one orbital, ↑ in second, empty third (b) ↑ in each of three separate orbitals (c) ↑↓ in each orbital (d) All in one orbital

Answer: (b) ↑ in each of three separate orbitals
Nitrogen has 3 electrons in the 2p subshell (which has 3 orbitals: 2p_x, 2p_y, 2p_z). By Hund's rule, electrons occupy each orbital singly with parallel spin before any pairing occurs: ↑ | ↑ | ↑. This gives maximum spin multiplicity and greater stability. Pairing would occur only with the 4th electron onwards (e.g., in O, Z=8: ↑↓ | ↑ | ↑).

🧠 TRICKY QUESTIONS

Electronic Configuration — Exceptions and Traps

Q. Copper (Z=29) has configuration [Ar] 3d¹⁰ 4s¹ instead of expected [Ar] 3d⁹ 4s². Why?

Answer: Extra stability of completely filled d-subshell
The expected configuration by Aufbau would be [Ar] 3d⁹ 4s². However, a fully filled d subshell (3d¹⁰) is extra stable — it has symmetrical charge distribution and exchange energy. So one electron from 4s migrates to 3d, giving [Ar] 3d¹⁰ 4s¹.
Similarly, Chromium (Z=24): expected [Ar] 3d⁴ 4s² but actual is [Ar] 3d⁵ 4s¹ (half-filled d is also extra stable). These are classic NDA exceptions — Cu and Cr.

Q. Calcium (Z=20) has configuration 2,8,8,2 — but the M shell can hold 18 electrons. Why is it not 2,8,10?

Answer: The outermost shell follows the octet rule (max 8) during shell-by-shell filling
The 2n² rule gives the maximum possible capacity, but electrons do not simply fill shells to maximum before starting the next. After M shell has 8 electrons (filling 3s and 3p), the next 2 electrons (for Ca) go into the N shell (4s²) because 4s has lower energy than 3d. The 3d orbitals of M shell fill only after 4s is occupied. This is why Ca is 2,8,8,2 and not 2,8,10. The M shell's full 18 is achieved only by elements Z=28 onwards (when 3d is fully filled).

5. Quantum Numbers — Basic MCQ Concepts

5.1

The Four Quantum Numbers

Each electron is uniquely described by four quantum numbers — Pauli's basis

Quantum numbers are like an electron's "address" within an atom — they specify which shell, subshell, orbital, and spin orientation the electron occupies. NDA tests these at the identification and definition level, not calculation level.

Quantum Number	Symbol	What it describes	Allowed values	Determines
Principal	n	Shell / energy level (distance from nucleus)	1, 2, 3, 4 … (positive integers)	Size & energy of orbital; n=1 is K shell
Azimuthal (Angular momentum)	l	Subshell / shape of orbital	0 to (n−1); for n=3: l=0,1,2	Shape of orbital (l=0:s, 1:p, 2:d, 3:f)
Magnetic	m or m_l	Orientation of orbital in space	−l to +l (including 0); total (2l+1) values	Number of orbitals in subshell
Spin	s or m_s	Spin of electron	+½ (↑) or −½ (↓) only	Direction of electron spin (clockwise/anticlockwise)

📋 Subshell Names & Orbital Count

s subshell (l=0): 1 orbital → max 2 electrons
p subshell (l=1): 3 orbitals → max 6 electrons
d subshell (l=2): 5 orbitals → max 10 electrons
f subshell (l=3): 7 orbitals → max 14 electrons
Total orbitals in shell n = n² | Total e⁻ = 2n²

📌 Quick Values for n=2 (NDA example)

n=2 → l can be 0 or 1 (two subshells: 2s, 2p)
For l=0 (2s): m=0 only → 1 orbital
For l=1 (2p): m=−1,0,+1 → 3 orbitals
Total orbitals in n=2 shell = 1+3 = 4 = n²
Total electrons = 8 = 2n²

📌 NDA-level Quantum Number Questions — What to Expect:
(1) "What is the value of l for a p electron?" → l = 1
(2) "How many orbitals are in the 3d subshell?" → 2l+1 = 2(2)+1 = 5
(3) "Which quantum number determines the shape of an orbital?" → Azimuthal (l)
(4) "Maximum electrons in n=4 shell?" → 2n² = 2×16 = 32
(5) "What are the possible values of m for l=2?" → −2, −1, 0, +1, +2 (five values)

📝 TOPIC-WISE PYQ

Quantum Numbers — NDA Pattern Questions

Q1. The maximum number of electrons that can be accommodated in the shell with principal quantum number n = 3 is:

(a) 8 (b) 18 (c) 32 (d) 6

Answer: (b) 18
Maximum electrons = 2n² = 2 × (3)² = 2 × 9 = 18. The M shell (n=3) contains subshells 3s (2e⁻) + 3p (6e⁻) + 3d (10e⁻) = 18 electrons total.

Q2. Which quantum number determines the shape of an atomic orbital?

(a) Principal quantum number (n) (b) Azimuthal quantum number (l) (c) Magnetic quantum number (m) (d) Spin quantum number (s)

Answer: (b) Azimuthal quantum number (l)
l=0 → spherical (s orbital); l=1 → dumbbell-shaped (p orbital); l=2 → double dumbbell (d orbital). The principal quantum number n determines the size/energy. The magnetic quantum number m determines the orientation in space. Spin s determines the direction of electron spin only.

Q3. How many electrons can be present in the 3p subshell?

(a) 2 (b) 6 (c) 10 (d) 14

Answer: (b) 6
The p subshell (l=1) has 3 orbitals (m = −1, 0, +1). Each orbital holds 2 electrons (Pauli exclusion). So p subshell max = 3 × 2 = 6 electrons. This applies to 2p, 3p, 4p, etc. — the number is always 6 regardless of the shell.

🧠 TRICKY QUESTIONS

Quantum Numbers — Common NDA Conceptual Traps

Q. Can two electrons in the same atom have quantum numbers n=2, l=1, m=0, s=+½ for both? What principle is violated?

Answer: No — this violates the Pauli Exclusion Principle.
All four quantum numbers (n, l, m, s) are identical for both electrons — which is forbidden. The Pauli Exclusion Principle states no two electrons in the same atom can have the same set of all four quantum numbers. The only way two electrons can share n=2, l=1, m=0 is if one has s=+½ and the other has s=−½ (opposite spins: ↑↓).

Q. An electron has n=3, l=2. In which subshell is it? How many electrons can this subshell hold?

Answer: 3d subshell — holds maximum 10 electrons.
n=3 → third shell (M); l=2 → d subshell. So it's the 3d subshell.
Number of orbitals = 2l+1 = 2(2)+1 = 5 orbitals.
Each orbital holds 2 electrons → 5 × 2 = 10 electrons maximum in 3d.
Remember: 3d fills after 4s (Aufbau) even though it's inside the M shell.

📄 CN02 Formula & Fact Sheet — Quick Reference

⚛ Atomic Number & Mass

Z = protons = electrons (neutral atom)
A = protons + neutrons = Z + N
Neutrons N = A − Z
Notation: ᴬ_Z X → ²³_₁₁Na: Z=11, A=23, N=12
Max electrons per shell: 2n²

🔬 Isotopes / Isobars / Isotones

Isotopes: same Z, different A (same element, different mass)
Isobars: same A, different Z (¹⁴C and ¹⁴N)
Isotones: same N = A−Z (³⁹K and ⁴⁰Ca, both N=20)
Isoelectronic: same electron count (Na⁺, Mg²⁺, Ne all = 10e⁻)
Isotopes: same chemistry, different physical properties

🔮 Quantum Numbers

n (principal): shell, energy — values 1,2,3,4
l (azimuthal): shape — 0 to (n−1); s=0, p=1, d=2, f=3
m (magnetic): orientation — −l to +l; (2l+1) values
s (spin): +½ or −½ only
Orbitals in subshell = 2l+1 | Electrons = 2(2l+1)

⚡ Three Filling Rules

Aufbau: fill lowest energy first (4s before 3d)
Pauli: max 2e⁻ per orbital, opposite spins
Hund's: fill each orbital singly in subshell before pairing
Exceptions: Cu = [Ar]3d¹⁰4s¹; Cr = [Ar]3d⁵4s¹
Valency: if v.e ≤4 → valency = v.e; if v.e ≥5 → valency = 8−v.e

📌 Bohr's Model Formulae

Eₙ = −13.6/n² eV (H atom energy levels)
rₙ = 0.529 × n² Å (orbit radius)
ΔE = hν = 13.6(1/n₁² − 1/n₂²) eV
Balmer series: visible light, n₁=2
Lyman series: UV, n₁=1

📈 Subatomic Particles

Proton: +1 charge, mass ≈1 amu, inside nucleus
Neutron: 0 charge, mass ≈1 amu, inside nucleus
Electron: −1 charge, mass = 1/1836 amu, outer shells
Discovered: e⁻ by Thomson; p⁺ by Rutherford; n⁰ by Chadwick
Nucleus diameter ≈10⁻¹⁵ m; atom ≈10⁻¹⁰ m

⚡ Quick Revision Booster — CN02 Atomic Structure

🔋 Atomic Models Sequence

Dalton (1808): solid indivisible sphere
Thomson (1897): plum pudding, e⁻ discovered
Rutherford (1911): nuclear model, gold foil
Bohr (1913): fixed orbits, explains H spectrum
Rutherford's flaw: orbiting e⁻ should spiral → collapse

🔮 Particle Shortcut

Z = protons = electrons (neutral atom)
N (neutrons) = A − Z (always compute this first)
Mass ≈ protons + neutrons (electrons negligible)
Chadwick (1932) discovered neutron — last subatomic particle
Electron mass = 1/1836 proton mass ≈ 0 for mass number

🔬 Iso-Triples (learn the examples)

Isotopes: ¹H, ²H, ³H | ¹²C, ¹⁴C | ²³⁵U, ²³⁸U
Isobars: ¹⁴C and ¹⁴N | ⁴⁰Ar and ⁴⁰Ca
Isotones: ³⁹K and ⁴⁰Ca (N=20 for both)
Isoelectronic: Na⁺, Mg²⁺, Al³⁺, Ne, F⁻, O²⁻ (all 10e⁻)
Key: Isotopes → same Z; Isobars → same A; Isotones → same N

📋 Shell Filling Shortcuts

K=2, L=8, M=18, N=32 (2n² rule)
Outer shell max = 8 always (octet)
4s fills before 3d (Aufbau — n+l rule)
Cu [Ar]3d¹⁰4s¹; Cr [Ar]3d⁵4s¹ (exceptions)
Valence e⁻ = electrons in last shell

⚛ Quantum Number Facts

n → shell/size (1=K, 2=L, 3=M, 4=N)
l → shape (0=s, 1=p, 2=d, 3=f)
m → orientation (2l+1 values)
s → spin (+½ or −½)
Pauli: no two e⁻ same all four QN

🚨 Common Traps

Isotopes have same chemical properties (same electrons)
Isobars: same A but different elements (different Z)
39K and 40Ca are isotones, NOT isobars (A is different)
3d fills after 4s — M shell's 18 fills late
1 mole of any atom contains Nₐ = 6.022×10²³ atoms

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