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Modern Physics

Photoelectric effect, atomic models, nuclear physics

Key Concepts
  • Photoelectric effect: light ejects electrons only above threshold frequency (Einstein)
  • Bohr model: electrons in fixed orbits; energy quantised as E_n = −13.6/n² eV
  • de Broglie: matter has wave nature; λ = h/mv
  • Radioactive decay: first-order process, characterised by half-life
  • Mass defect × c² = binding energy of nucleus
Important Formulae
Photon energy E = hf = hc/λ
Photoelectric effect KE_max = hf − φ (work function φ)
Bohr energy levels E_n = −13.6/n² eV
de Broglie wavelength λ = h/p = h/mv
Radioactive decay law N = N₀ e^(−λt)
Half-life t₁/₂ = 0.693/λ
Quick Tips
  • Threshold frequency f₀ = φ/h; stopping potential V₀ = KE_max/e.
  • Hydrogen spectrum: Lyman (UV, n→1), Balmer (visible, n→2), Paschen (IR, n→3).
  • Nuclear fission: heavy nucleus splits; fusion: light nuclei combine — both release energy.
Sample Practice Questions

  1. Energy of a photon of frequency ν:

    • hν²
    • hν
    • h/ν
    • h²ν
    Show answer

    Answer: hν

  2. The threshold frequency in photoelectric effect is the minimum frequency to:

    • Create photons
    • Eject electrons from the surface
    • Cause nuclear fusion
    • Ionize gas
    Show answer

    Answer: Eject electrons from the surface

  3. de Broglie wavelength: λ = h/p. For electron accelerated through V volts:

    • λ = h/mv
    • λ = h/√(2meV)
    • λ = √(2meV)/h
    • λ = h/(2meV)
    Show answer

    Answer: λ = h/√(2meV)

  4. In hydrogen spectrum, Lyman series is in:

    • Infrared region
    • Visible region
    • Ultraviolet region
    • X-ray region
    Show answer

    Answer: Ultraviolet region

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Practice Questions

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