Atomic and Nuclear Phenomena

9.1 Photoelectric Effect

Light incident on a metal can eject electrons if its frequency exceeds a threshold. Energy of photons determines whether electrons are emitted and their kinetic energy.

• Key concepts:
  • Electrons emitted from metal by high-frequency light
  • Current depends on number of electrons ejected
  • Intensity vs. frequency: Higher intensity → more photons, but only photons above threshold frequency eject electrons
  • Threshold frequency: Minimum frequency to eject electron (depends on metal)
  • Photon energy: $E = hf$ (h = Planck’s constant, f = frequency)
  • Kinetic energy of ejected electrons: $K_\text{max} = hf - W$ (W = work function)

9.2 Absorption and Emission of Light

Electrons absorb or emit discrete photon energies corresponding to energy level differences. This underpins spectroscopy and fluorescence.

• Absorption: Electron moves from lower → higher energy level
• Emission: Electron falls from higher → lower energy level, photon emitted
• Fluorescence: UV light excites electron, visible light emitted as electron returns to ground state
• Energy/frequency relationship: Photon energy = difference between electron levels

9.3 Nuclear Binding Energy and Mass Defect

Nuclei have less mass than the sum of protons and neutrons; difference is converted to energy via E = mc².

• Mass defect: $\Delta m = (\text{sum of nucleons}) - (\text{nucleus mass})$
• Binding energy: Energy required to break nucleus
• Strong nuclear force: Binds nucleons, counteracts proton-proton repulsion
• Weak nuclear force: Smaller effect, contributes to stability
• Most stable nucleus: Iron (peak binding energy per nucleon)

9.4 Nuclear Reactions

Nuclei undergo fusion, fission, or radioactive decay. Conservation of mass number and atomic number applies.

• Fusion: Small nuclei combine → larger nucleus + energy (e.g., 4H → 1He in stars)
• Fission: Large nucleus splits → smaller nuclei + energy; can induce chain reactions
• Radioactive decay:
  • Alpha (α): $^4_2\text He$ emitted; massive, low penetration $^{A}{Z}X \to ^{A-4}{Z-2}Y + ^4_2\alpha$
  • Beta (β⁻): Electron emitted; more penetrating, neutron → proton $^{A}{Z}X \to ^{A}{Z+1}Y + \beta^-$
  • Positron (β⁺): Positively charged electron emitted (no mass); proton → neutron $^{A}{Z}X \to ^{A}{Z-1}Y + \beta^+$
  • Gamma (γ): High-energy photon emitted; no change in A or Z
  • Electron capture: Inner electron absorbed by nucleus → proton converted to neutron
• Half-life: Time for half of nuclei to decay
  • Exponential decay: $N = N_0 e^{-\lambda t}$
  • Decay constant: $\lambda = \frac{0.693}{t_{1/2}}$
  • Number of nuclei: $N = \text{moles} \times N_A$

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