Discrete Energy and Radioactivity Notes

Discrete Energy and Radioactivity

• Microscopic Energy:

  • The energy of particles like electrons in atoms and protons/neutrons in nuclei occurs at a microscopic scale.
  • Discrete Energy: Unlike macroscopic physics where energy is continuous, microscopic energy only exists at specific values.

• Emission Spectra:

  • When a gas at low pressure is exposed to a strong electric field, it emits light which can be analyzed using a prism or diffraction grating.
  • The emitted light shows a series of bands at different wavelengths, creating an emission spectrum unique to each element (like fingerprints).

Exam Tip: All distinct elements have different emission wavelengths.

• Bohr's Model (1913):

  • Niels Bohr provided a model explaining that an atom's energy is not random but discrete, represented in energy level diagrams (e.g., hydrogen's diagram shows energy levels like -13.6 eV, -3.4 eV, etc.).
  • Transitions between these energy levels involve photons being emitted, where the energy difference corresponds to the emitted photon.

• Photon Energy Equation:

  • Current understanding of photon energy involves equations:
  • E = hf (where h is Planck’s constant: 6.63 × 10^−34 J·s)
  • E = hc/λ (where c is the speed of light).

• Energy Transitions:

  • When an electron transitions to a higher energy state by absorbing energy, it can later drop back down, emitting a photon. The energy of the photon corresponds to the energy lost during the transition.

• Ground and Excited States:

  • Ground State: Lowest energy state where electrons reside (e.g., hydrogen at n=1).
  • Excited State: Higher energy levels that electrons can reach after absorbing energy.
  • Relaxation occurs when electrons drop back down to lower energy levels, emitting photons of specific frequencies.

• Nuclear Structure:

  • The nucleus consists of protons and neutrons (collectively termed as nucleons).
  • Atomic Number (Z): Number of protons in a nucleus.
  • Mass Number (A): Total count of nucleons (protons + neutrons).

Isotopes

• Definition: Isotopes are variants of elements with the same number of protons but different neutrons, leading to different mass numbers.
• Isotropic variations of hydrogen: 1H, 2H, 3H; for uranium: 23592U, 23692U.
• Isotopes share chemical properties but may differ physically.

Radioactive Decay

• Discovery: Radioactivity was uncovered primarily due to the work of Henri Becquerel and others in the late 19th to early 20th centuries.

• Decay Process: Unstable nuclei emit particles (energy can be lost) and decay into more stable forms.

  • Types of decays:
    • Alpha particles: Helium nuclei emitted; ex. 23892U → 23490Th + 42α.
    • Beta particles: Neutrons convert to protons, emitting electrons and neutrinos.
    • Gamma decay: Emission of gamma rays without changing the nucleus itself.

• Decay Properties:

  • Alpha particles are the most ionizing but least penetrating.
  • Beta particles have moderate ionizing and penetrating power.
  • Gamma rays are the least ionizing but the most penetrating.

Activity and Half-life

• Activity (A): Measured in becquerels (Bq), indicating decays per second.

• Half-life: The time taken for half the nuclei in a sample to decay, leading to an exponential decline in activity.

• Activity reduces by half in a timeframe equal to the half-life.

• Decay and Stability: Nuclei stability is related to neutron to proton ratios and the underlying fundamental forces like the strong nuclear force maintaining balance.

Fundamental Forces

• Electromagnetic: Acts on charged particles.
• Weak Nuclear: Responsible for decay processes like beta decay.
• Strong Nuclear: Holds protons and neutrons in nucleus; counteracts electromagnetic repulsion among protons.
• Gravitational: Negligible at atomic scales, operates on large mass bodies.

Practical Applications

• Understanding emission spectra aids in element identification.
• Knowledge of isotopes and decay series is essential in fields like medicine (e.g., radiotherapy) and energy (nuclear reactors).

Theory Tip: Energy released in decay events can be predicted based on mass differences before and after reactions, adhering to conservation laws.

Summary

• Energy states are discrete in atomic structures, influencing electron transitions and emission spectra.
• Nuclear reactions (fission and fusion) release energy, verified using mass-energy equivalence.
• The characteristics of atomic nuclei, isotopes, and radioactivity form foundational concepts in atomic physics with wide-ranging applications in technology and medicine.