Nuclei Decomposition and Radioactivity Study Notes LEC14

Nuclei Decomposition Causes

  • Strong force holds nucleus particles together.

  • Neutrons stabilize the nucleus by adding to the strong force without repelling each other.

N/Z Ratio

  • Ratio of neutrons to protons indicates nucleus stability.

  • High N/Z ratio: neutrons convert to protons via beta decay.

  • Low N/Z ratio: protons convert to neutrons via positron emission/electron capture, or alpha decay.

Valley of Stability

  • Stable N/Z ratios:

    • Z = 1-20: N/Z ≈ 1

    • Z = 20-40: N/Z approaches 1.25

    • Z = 40-80: N/Z approaches 1.5

    • Z > 83: no stable nuclei.

Radioactive Decay Example

  • Mg-22 (Z = 12, N = 10, N/Z = 0.83): undergoes positron emission or electron capture due to low N/Z.

Magic Numbers

  • Stability is affected by even numbers of protons/neutrons.

  • Stable nuclei favor magic numbers: N or Z = 2, 8, 20, 28, 50, 82, 126.

Decay Series

  • A chain of radioactive nuclides until reaching a stable nuclide.

  • Determine stable nuclide by counting alpha and beta decays.

Detecting Radioactivity

  • Radioactive rays can expose film (film badge dosimeters).

  • Ionization detection by electroscope and Geiger-Müller counter.

  • Scintillation counters detect radiation via flashes of light.

Kinetics of Radioactive Decay

  • First-order kinetics: Rate = \frac{\Delta N}{\Delta t} = kN.

  • Each radionuclide has a specific half-life; shorter half-lives indicate faster decay.

  • Half-life formula: t_{\frac{1}{2}} = \frac{\ln 2}{k}.

Half-Lives of Various Nuclides

  • Th-232: 1.4 x 10^{10} yr (alpha decay)

  • U-238: 4.5 x 10^{9} yr (alpha decay)

  • C-14: 5730 yr (beta decay)

  • Rn-220: 55.6 sec (alpha decay).

Radiometric Dating

  • Measure parent radioactive isotopes versus stable daughter isotopes to determine age.

  • Example: U-238 to Pb-206 dating Earth’s age (4.0-4.5 billion yrs).

Radiocarbon Dating

  • C-14 decays with a half-life of 5730 yrs; produced at a steady rate.

  • Ratios of C-14/C-12 decrease post-mortem, allowing age estimation.

  • Effective for objects up to 50,000 years old.

Nonradioactive Nuclear Changes

  • Nuclear fission: large nucleus splits into smaller ones when hit by a neutron.

  • Nuclear fusion: small nuclei combine to form larger ones.

  • Both fission and fusion release significant energy, with fusion being more energy-efficient.