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Modern Physics

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Photoelectric Effect

Key Concepts:

Einstein's Equation: E = hf = hc/λ
Work Function (φ): Minimum energy to emit electron
Kinetic Energy: KE = hf - φ
Stopping Potential: V₀ = (hf - φ)/e

Important Relations:

h = 6.626 × 10⁻³⁴ J⋅s

c = 3 × 10⁸ m/s

e = 1.6 × 10⁻¹⁹ C

1 eV = 1.6 × 10⁻¹⁹ J

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Wave-Particle Duality

De Broglie Wavelength:

λ = h/p = h/mv

Where p = momentum, m = mass, v = velocity

Applications:

• Electron microscopes
• Neutron diffraction
• Davisson-Germer experiment

Uncertainty Principle:

Δx⋅Δp ≥ ℏ/2

ΔE⋅Δt ≥ ℏ/2

ℏ = h/2π

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Atomic Structure

Bohr's Model:

• rₙ = n²a₀ (n = 1,2,3...)
• a₀ = 0.529 Å
• Eₙ = -13.6/n² eV
• vₙ = 2.18×10⁶/n m/s

Energy Levels:

• Ground state: n = 1
• Excited states: n > 1
• Ionization: n = ∞
• ΔE = hf = 13.6(1/n₁² - 1/n₂²)

Spectral Series:

• Lyman: n₁ = 1 (UV)
• Balmer: n₁ = 2 (Visible)
• Paschen: n₁ = 3 (IR)
• Brackett: n₁ = 4 (IR)

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Radioactivity

Decay Law:

N(t) = N₀e^(-λt)

A(t) = A₀e^(-λt)

t₁/₂ = ln(2)/λ = 0.693/λ

Types of Decay:

• α-decay: ₂He⁴ emission
• β⁻-decay: electron emission
• β⁺-decay: positron emission
• γ-decay: electromagnetic radiation

Important Constants:

• Avogadro: 6.022×10²³
• Atomic mass unit: 931.5 MeV
• Electron mass: 0.511 MeV
• Proton mass: 938.3 MeV

Mass-Energy:

E = mc²

Binding Energy = (Δm)c²

Q-value = (m₁ - m₂)c²

Quick Formula Reference

Photoelectric

KE = hf - φ

eV₀ = hf - φ

De Broglie

λ = h/p

λ = h/√(2mE)

Bohr Model

rₙ = n²×0.529Å

Eₙ = -13.6/n² eV

Radioactivity

N = N₀e^(-λt)

t₁/₂ = 0.693/λ

Energy

E = mc²

1 u = 931.5 MeV

Constants

h = 6.626×10⁻³⁴

c = 3×10⁸ m/s

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