Structure of the Atom

NEET
Structure of the Atom NEET Notes | Class 11 Chemistry

1. Introduction to Atom

Definition: The atom is the smallest unit of ordinary matter that constitutes a chemical element. The word comes from the Greek "atomos," meaning indivisible.

Historical Perspectives

  • Maharishi Kanad (600 BC): Proposed that matter is made of tiny indestructible particles called 'Parmanu'.
  • Democritus (400 BC): Suggested that if you keep cutting matter, you reach a point where it cannot be cut further (Atomos).
  • Dalton's Theory (1808): Formalized the idea that atoms are indivisible particles (later disproven).

2. Discovery of Sub-Atomic Particles

2.1 Electron (e-)

  • Discoverer: J.J. Thomson (1897).
  • Experiment: Cathode Ray Tube (CRT). At low pressure (0.01 mm Hg) and high voltage (10,000V), rays moved from cathode to anode.
  • Properties: Negatively charged, travel in straight lines, cast shadows, possess kinetic energy.
  • Charge/Mass (e/m): 1.7588 × 1011 C/kg.
[Image of cathode ray tube experiment]Cathode Ray Experiment

2.2 Proton (p+)

Discoverer: Goldstein (1886) observed "Canal Rays" (Anode rays) moving opposite to cathode rays.
Nature: Positively charged gaseous ions. Unlike electrons, their e/m ratio depends on the gas used.

2.3 Neutron (n0)

Discoverer: James Chadwick (1932).
Experiment: Bombarding Beryllium sheets with alpha particles:
4Be9 + 2He4 → 6C12 + 0n1 (Neutron).

ParticleCharge (C)Mass (kg)
Electron-1.6 × 10-199.1 × 10-31
Proton+1.6 × 10-191.672 × 10-27
Neutron01.675 × 10-27

3. Atomic Models

3.1 Thomson's Model ("Plum Pudding")

Atom is a sphere of positive charge with electrons embedded in it like seeds in a watermelon.

Limitation: Could not explain Rutherford's scattering experiment.

3.2 Rutherford's Model (Nuclear Model)

  • Experiment: α-particle scattering on Gold foil.
  • Observation: Most α-particles passed straight; very few bounced back.
  • Conclusion: Positive charge is concentrated in a tiny center called the Nucleus. Electrons revolve around it.
[Image of Rutherford gold foil experiment]Rutherford Experiment

3.3 Bohr's Model

Applicable only for single-electron species (H, He+, Li2+).

  • Electrons revolve in fixed orbits called "stationary states".
  • Angular Momentum: mvr = nh / 2π (Quantized).
  • Energy is absorbed/emitted only when an electron jumps orbits.

4. Dual Nature of Matter

4.1 Photoelectric Effect

Ejection of electrons from a metal surface when light of suitable frequency hits it.

hν = hν0 + K.E.max

(ν0 = Threshold Frequency)

4.2 De-Broglie Wavelength

Matter has both particle and wave nature.

λ = h / mv = h / p

5. Electromagnetic Radiation

Oscillating electric and magnetic fields perpendicular to each other and direction of propagation.

Relation: c = ν × λ
Speed (c): 3 × 108 m/s

Order of Spectrum (Increasing λ):
Cosmic < Gamma < X-rays < UV < Visible < IR < Microwave < Radio

6. Bohr's Theory (Maths)

1. Radius (rn):
rn = 0.529 (n2/Z) Å
2. Energy (En):
En = -13.6 (Z2/n2) eV

(Energy becomes less negative as n increases)

7. Hydrogen Spectrum

Emission spectrum of Hydrogen is a line spectrum.

[Image of hydrogen emission spectrum series]Hydrogen Spectrum
Seriesn1n2Region
Lyman12,3...UV
Balmer23,4...Visible
Paschen34,5...Near IR
Brackett45,6...Mid IR
Pfund56,7...Far IR

8. Quantum Mechanical Model

8.1 Heisenberg Uncertainty

Impossible to determine exact position and momentum simultaneously.

Δx × Δp ≥ h / 4π

8.2 Schrodinger & Wave Function

  • Ψ (Psi): Wave function. Represents the amplitude of electron wave. No physical significance.
  • Ψ2: Probability density. Gives the probability of finding an electron in a region.

9. Orbitals & Quantum Numbers

1. Principal (n):

Describes Size and Energy. Values: 1, 2, 3...

2. Azimuthal (l):

Describes Shape. Values: 0 to n-1.

  • l=0 (s): Spherical
  • l=1 (p): Dumb-bell
  • l=2 (d): Double Dumb-bell
[Image of orbital shapes s p d]Shapes of Orbitals
3. Magnetic (m):

Orientation. Values: -l to +l.

4. Spin (s):

Clockwise (+1/2) or Anti-clockwise (-1/2).

11. Electronic Configuration

  • Aufbau Principle: Fill lower energy first. Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d...
  • Pauli Exclusion: No two electrons can have same 4 quantum numbers.
  • Hund's Rule: Pairing happens only after subshell is half-filled.

12. Stability of Orbitals

Half-filled (d5) and Fully-filled (d10) orbitals are extra stable.

Reasons:
1. Symmetry: More symmetrical distribution of electrons.
2. Exchange Energy: Electrons with parallel spins exchange positions, releasing energy. Max exchanges = Max stability.
Example (Chromium Z=24):
Expected: [Ar] 4s2 3d4
Actual: [Ar] 4s1 3d5 (Due to stability of half-filled d-orbital)

Numericals & HOTS

Q1. Calculation of Photons

A 100-watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second.

Solution:
Power = Energy per second = 100 J/s.
Energy of 1 photon (E) = hc / λ

h = 6.626 × 10-34 Js
c = 3 × 108 m/s
λ = 400 nm = 400 × 10-9 m

E = (6.626 × 10-34 × 3 × 108) / (400 × 10-9)
E = 4.969 × 10-19 J

Number of photons (n) = Total Energy / Energy of 1 photon
n = 100 / (4.969 × 10-19)
n = 2.012 × 1020 photons/sec
Q2. Bohr Radius (HOTS)

Calculate the ratio of the radius of the 2nd orbit of He+ ion to the radius of the 3rd orbit of Li2+ ion.

Solution:
Formula: r ∝ n2 / Z

For He+ (2nd orbit):
n1 = 2, Z1 = 2
r1 ∝ 22 / 2 = 4/2 = 2

For Li2+ (3rd orbit):
n2 = 3, Z2 = 3
r2 ∝ 32 / 3 = 9/3 = 3

Ratio r1 / r2 = 2 / 3
Answer: 2:3
Q3. Photoelectric Effect

The threshold frequency for a metal is 7.0 × 1014 s-1. Calculate the kinetic energy of an electron emitted when radiation of frequency 1.0 × 1015 s-1 hits the metal.

Solution:
Formula: K.E. = h(ν - ν0)

ν = 10 × 1014 s-1
ν0 = 7 × 1014 s-1

K.E. = 6.626 × 10-34 × (10 - 7) × 1014
K.E. = 6.626 × 10-34 × 3 × 1014
K.E. = 1.988 × 10-19 J
Q4. Ionization Energy

The ionization energy of H-atom is 13.6 eV. What is the ionization energy of He+ ion?

Solution:
Ionization Energy (IE) ∝ Z2
IEspecies = IEH × Z2

For He+, Z = 2.
IE = 13.6 × (2)2
IE = 13.6 × 4
IE = 54.4 eV
Q5. Rydberg Calculation

Calculate the wavelength of the spectral line in the hydrogen spectrum corresponding to the transition from n=4 to n=2. (RH = 109677 cm-1)

Solution:
1/λ = RH [1/n12 - 1/n22]
n1 = 2, n2 = 4

1/λ = 109677 [1/4 - 1/16]
1/λ = 109677 [3/16]
1/λ = 20564.4 cm-1

λ = 1 / 20564.4 = 4.86 × 10-5 cm
λ = 486 nm (Blue-Green line)
Q6. de Broglie Wavelength

A ball of mass 0.1 kg is moving with a velocity of 10 m/s. Calculate its de Broglie wavelength.

Solution:
Formula: λ = h / mv

λ = 6.626 × 10-34 / (0.1 × 10)
λ = 6.626 × 10-34 / 1
λ = 6.626 × 10-34 m
(Note: This is incredibly small, proving wave nature is negligible for macroscopic objects.)
Q7. Uncertainty Principle

An electron is located within a distance of 0.1 Å. What is the uncertainty in its velocity? (Mass of e- = 9.1 × 10-31 kg)

Solution:
Δx = 0.1 Å = 10-11 m
Formula: Δv = h / (4π m Δx)

Δv = 6.626 × 10-34 / (4 × 3.14 × 9.1 × 10-31 × 10-11)
Δv = 6.626 × 10-34 / (114.3 × 10-42)
Δv = 5.79 × 106 m/s
Q8. Angular Momentum

Calculate the orbital angular momentum of a 4d electron.

Solution:
For d-orbital, azimuthal quantum number l = 2.
Formula: L = √(l(l+1)) × (h/2π)

L = √(2(2+1)) × (h/2π)
L = √6 × (h/2π)
Answer: √6 h/2π
Q9. Magnetic Moment (HOTS)

Calculate the spin-only magnetic moment of Mn2+ ion (Z=25).

Solution:
Step 1: Write configuration.
Mn (Z=25): [Ar] 4s2 3d5
Mn2+ (Remove 2 e- from 4s): [Ar] 3d5

Step 2: Count unpaired electrons (n).
d5 has 5 unpaired electrons. n = 5.

Step 3: Calculate μ.
μ = √(n(n+2)) = √(5(7)) = √35
μ = 5.92 B.M.
Q10. Radial Nodes

How many radial and angular nodes are present in a 4f orbital?

Solution:
For 4f orbital: n = 4, l = 3.

1. Angular Nodes = l = 3
2. Radial Nodes = n - l - 1
Radial Nodes = 4 - 3 - 1 = 0

Answer: 3 angular nodes, 0 radial nodes.

Important Formulae

1. Planck's Quantum Theory

Energy of a photon:

E = hν = hc / λ

h = 6.626 × 10-34 J s (Planck's Const)
c = 3 × 108 m/s (Speed of light)

2. Photoelectric Effect
hν = hν0 + K.E.max

ν0 = Threshold frequency
hν0 = Work Function (Φ)

3. Bohr's Model (H-like species)

Radius (rn):

rn = 0.529 × (n2 / Z) Å

Energy (En):

En = -13.6 × (Z2 / n2) eV/atom

Velocity (vn):

vn = 2.18 × 106 × (Z / n) m/s

Angular Momentum:

mvr = nh / 2π
4. Rydberg Formula

For transition from n2 to n1:

1/λ = ν̄ = RH Z2 [ 1/n12 - 1/n22 ]

RH ≈ 109677 cm-1

Hydrogen Series Diagram
5. Quantum Mechanics

de Broglie Wavelength:

λ = h / mv = h / √(2m(K.E.))

Heisenberg Uncertainty:

Δx × Δp ≥ h / 4π
6. Nodes & Angular Momentum
  • Radial Nodes: n - l - 1
  • Angular Nodes: l
  • Total Nodes: n - 1
  • Orbital Angular Momentum: √(l(l+1)) × (h/2π)
  • Spin Magnetic Moment: μ = √(n(n+2)) B.M. (n = unpaired e-)

20 Golden Facts (NEET)

  • 1. e/m Ratio: The charge-to-mass ratio of cathode rays (electrons) is universal and independent of the gas in the tube. For anode rays (protons), it depends on the gas.
  • 2. Heaviest Particle: Neutron is slightly heavier than proton. Order: n > p > e. (Mass of neutron ≈ Mass of proton ≈ 1837 × Mass of electron).
  • 3. Isotopes: Same atomic number (Z), different mass number (A). Chemical properties are same (depend on Z), physical properties differ (depend on mass).
  • 4. Isobars: Different Z, same A (e.g., 40Ar and 40Ca). They have different chemical properties.
  • 5. Isotones: Species having same number of neutrons. Formula: A - Z is constant. (e.g., 14C6 and 16O8; both have 8 neutrons).
  • 6. Distance of Closest Approach: Used to estimate nucleus size. At this distance, Kinetic Energy of α-particle = Potential Energy of repulsion.
  • 7. Bohr's Limit: Bohr theory fails for multi-electron atoms and cannot explain the Zeeman effect (splitting in magnetic field) or Stark effect (electric field).
  • 8. Negative Energy: The total energy of an electron is negative, indicating it is bound to the nucleus. At n=∞, energy is zero (free electron).
  • 9. Line Spectrum: Known as the "fingerprint" of atoms. No two elements have the same line spectrum.
  • 10. Lyman Series: The only series in the Hydrogen spectrum found in the Ultraviolet (UV) region. All transitions jump to n=1.
  • 11. Limiting Line: The spectral line corresponding to the transition from n=∞ to a specific shell. It represents the shortest wavelength (highest energy) in that series.
  • 12. Max Spectral Lines: When an electron jumps from n to 1 in a sample of atoms, max lines = n(n-1)/2.
  • 13. Macroscopic Objects: de Broglie wavelength is negligible for heavy objects (like a cricket ball) because mass is in the denominator (λ ∝ 1/m).
  • 14. Nodal Plane: A plane passing through the nucleus where the probability of finding an electron is zero. s-orbital has 0 nodal planes; p-orbital has 1.
  • 15. Spin Quantum Number: It does not arise from the solution of the Schrodinger Wave Equation. It was introduced later to account for electron spin.
  • 16. 4s vs 3d Energy: Even though 4s is filled before 3d (Aufbau), 4s electrons are removed before 3d electrons during ionization (because 4s is the outermost shell).
  • 17. Copper Exception: Cu (Z=29) is [Ar] 3d10 4s1, not 3d9 4s2. Fully filled d-orbitals are more stable.
  • 18. Violet vs Red: In the visible spectrum, Violet has the shortest wavelength (~400 nm) and highest energy; Red has longest wavelength (~700 nm) and lowest energy.
  • 19. Probability Density: Ψ2 is always positive. Ψ can be positive or negative. At a node, Ψ2 = 0.
  • 20. Magnetic Moment of Fe2+: Config is [Ar] 3d6. It has 4 unpaired electrons. μ = √(4(6)) = √24 ≈ 4.9 B.M.
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