Atomic Structure

Topics covered: Discovery of subatomic particles, atomic models, electromagnetic radiation, Bohr model, hydrogen spectrum, de Broglie waves, Heisenberg uncertainty principle.

1) Subatomic Particles

• Electron: Discovered by J.J. Thomson
• Proton: Discovered by Goldstein
• Neutron: Discovered by Chadwick

Charge of electron = −1.6 × 10⁻¹⁹ C
Mass of electron = 9.1 × 10⁻³¹ kg
Charge of proton = +1.6 × 10⁻¹⁹ C
Mass of proton ≈ 1.67 × 10⁻²⁷ kg
  

2) Atomic Models

Thomson’s Atomic Model

• Atom is a positively charged sphere with electrons embedded in it.
• Failed to explain α-particle scattering experiment.

Rutherford’s Atomic Model

• Most of the atom is empty space.
• Positive charge and mass concentrated in the nucleus.
• Failed to explain stability of atom.

3) Electromagnetic Radiation

Speed of light:
c = λν

Energy of radiation:
E = hν

h = 6.626 × 10⁻³⁴ Js
  

Electromagnetic spectrum (increasing energy):

• Radio waves → Microwaves → Infrared → Visible → UV → X-rays → Gamma rays

4) Bohr’s Model of Hydrogen Atom

Postulates

• Electrons revolve in fixed circular orbits.
• Angular momentum is quantised.
• Energy is emitted or absorbed during transitions.

Angular momentum:
mvr = n(h/2π)

Radius of nth orbit:
rₙ = 0.529 × n² Å

Energy of nth orbit:
Eₙ = −13.6 / n² eV
  

Energy of photon emitted or absorbed:

ΔE = hν = E₂ − E₁
  

5) Hydrogen Emission Spectrum

1/λ = R (1/n₁² − 1/n₂²)

R = 1.097 × 10⁷ m⁻¹
  

• Lyman series: n₁ = 1 (UV region)
• Balmer series: n₁ = 2 (Visible region)
• Paschen series: n₁ = 3 (IR region)

6) de Broglie Wave Equation

λ = h / p = h / mv
  

For electrons accelerated through potential V:

λ (Å) = 12.27 / √V
  

7) Heisenberg Uncertainty Principle

Δx · Δp ≥ h / 4π
  

• Exact position and momentum cannot be determined simultaneously.
• More significant for microscopic particles.

8) Limitations of Bohr’s Model

• Applicable only to hydrogen-like species.
• Fails to explain fine structure and Zeeman effect.
• Does not account for wave nature of electrons.