Discrete Energy and Radioactivity Notes

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).

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.

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 (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.

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.

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.

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.