Atoms & Nuclei – Engineering Services (ESE) Physics Notes
Why this matters for engineers
The behaviour of matter at the atomic and nuclear scale determines material strength, radiation safety, nuclear power, and many cutting‑edge diagnostics. A solid grasp of these concepts will help you interpret data, design safer systems, and innovate in fields ranging from energy to medicine.
1. Simple Explanation
| Concept | What it is | Why it matters |
|---|---|---|
| Atom | Smallest unit of an element that retains its chemical identity. | Forms the building blocks of all materials. |
| Nucleus | Tiny, dense core of an atom, containing protons (positively charged) and neutrons (neutral). | Governs nuclear reactions, radioactivity, and mass. |
| Isotope | Atoms of the same element (same Z) but different neutron numbers → different A. | Determines radioactive stability, half‑life, and chemical behavior. |
| Binding Energy | Energy needed to break a nucleus into individual protons and neutrons. | Indicates nuclear stability and energy that can be released in fusion/fission. |
| Radioactive Decay | Spontaneous change of an unstable nucleus into a more stable one, emitting radiation. | Crucial for nuclear power, radiography, and safety. |
| Semi‑Empirical Mass Formula (SEMF) | Approximate formula to estimate nuclear binding energy and stability. | Helps predict which nuclei are stable or will decay. |
2. Key Points
2.1 Atomic Structure
- Protons (p⁺): +1 e charge, determine element (atomic number Z).
- Neutrons (n⁰): 0 e charge, contribute to mass and stability.
- Electrons (e⁻): -1 e charge, orbit nucleus, determine chemistry.
- Atomic Mass: ( m_{\text{atom}} \approx Z m_p + (A-Z) m_n - \Delta m ) (mass defect accounts for binding energy).
2.2 Nuclear Composition & Mass Number
| Symbol | Meaning | Example |
|---|---|---|
| ( Z ) | Atomic number (proton count) | Hydrogen: ( Z=1 ) |
| ( N ) | Neutron number | ( \text{He‑4} : N=2 ) |
| ( A ) | Mass number = ( Z+N ) | ( \text{U‑235} : A=235 ) |
2.3 Binding Energy & Stability
- Mass defect: ( \Delta m = A(m_p + m_n) - m_{\text{nucleus}} ).
- Binding energy: ( E_B = \Delta m c^2 ).
- Binding energy per nucleon peaks at Fe-56 (~8.8 MeV).
- Stable nuclei lie near this peak; very light (H‑1, He‑4) and very heavy (U‑238) are less tightly bound and can release energy via fusion or fission.
2.4 Radioactive Decay Modes
| Mode | Particle Emitted | Typical Energy | Example |
|---|---|---|---|
| Alpha (( \alpha )) | ( ^4_2\text{He}^{2+} ) | 4–8 MeV | ( ^{238}\text{U} \to ^{234}\text{Th} + \alpha ) |
| Beta‑minus (( \beta^- )) | ( e^- ) + (\bar\nu_e) | 0–10 MeV | ( ^{14}\text{C} \to ^{14}\text{N} + \beta^- + \bar\nu_e ) |
| Beta‑plus / Positron (( \beta^+ )) | ( e^+ ) + ( \nu_e ) | 0–2 MeV | ( ^{22}\text{Na} \to ^{22}\text{Ne} + \beta^+ + \nu_e ) |
| Electron Capture (EC) | Capture of bound ( e^- ) | 0–2 MeV | ( ^{39}\text{K} + e^- \to ^{39}\text{Ar} + \nu_e ) |
| Gamma (( \gamma )) | High‑energy photon | 0.1–10 MeV | De‑excitations in ( ^{60}\text{Co} ) |
- Half‑life ((T_{1/2})): Time for half the nuclei to decay.
- Decay constant ((\lambda)): ( \lambda = \frac{\ln 2}{T_{1/2}} ).
2.5 Nuclear Reactions
- Fusion: Light nuclei combine → heavier nucleus + energy.
- Example: D + T → ( ^4_2\text{He} + n + 17.6)