Atoms & Nuclei – Physics Study Notes
(For the INI CET exam – Physics section)
1. Simple Explanation
- Atoms are the basic units of matter.
- An atom consists of a nucleus (protons + neutrons) surrounded by electrons.
- The nucleus is the heavy, positively charged core.
- Nuclear properties (mass, stability, reactions) are governed by the strong nuclear force, not by the electromagnetic force that keeps electrons in orbit.
2. Key Points
| Concept | What It Means | Why It Matters |
|---|---|---|
| Atomic Number (Z) | Number of protons | Determines element identity |
| Mass Number (A) | Total number of protons + neutrons | Gives atomic mass |
| Neutrons (N) | (N = A - Z) | Influence stability, isotope variations |
| Binding Energy (BE) | Energy that holds nucleus together | Determines nuclear stability |
| Binding Energy per Nucleon | (BE/A) | Peak at Fe‑56; explains why light nuclei fission and heavy nuclei fuse |
| Radioactive Decay | Spontaneous change of nucleus | Types: α, β, γ, spontaneous fission |
| Decay Constants & Half‑Life | (\lambda) and (t_{1/2}) | Predict activity over time |
| Nuclear Reactions | Fusion (light → heavy), Fission (heavy → light), Capture | Power generation, medical isotopes |
| Conservation Laws | Energy, mass‑energy, charge, baryon number | Guide reaction equations |
3. Worked Example
Problem
A nucleus of (^{12}!C) (6 p, 6 n) has a mass of 12.0000 u. The mass of a proton is 1.00728 u and a neutron is 1.00866 u.
Calculate the binding energy of the (^{12}!C) nucleus and the binding energy per nucleon.
Solution
-
Compute the mass defect
[ \begin{aligned} m_{\text{calc}} &= 6,m_p + 6,m_n \ &= 6(1.00728) + 6(1.00866) \ &= 6.04368 + 6.05196 = 12.09564\ \text{u} \end{aligned} ][ \Delta m = m_{\text{calc}} - m_{\text{obs}} = 12.09564 - 12.0000 = 0.09564\ \text{u} ]
-
Convert mass defect to energy
(1\ \text{u} = 931.5\ \text{MeV})[ BE = \Delta m \times 931.5 = 0.09564 \times 931.5 \approx 89.2\ \text{MeV} ]
-
Binding energy per nucleon
[ \frac{BE}{A} = \frac{89.2}{12} \approx 7.43\ \text{MeV/nucleon} ]
Answer
- Binding Energy: ≈ 89 MeV
- Binding Energy per Nucleon: ≈ 7.4 MeV/nucleon
(Typical value for (^{12}!C) is 7.68 MeV/nucleon; the difference is due to rounding.)
4. Quick Revision Summary
- Atomic structure: nucleus (Z protons, N neutrons) + electrons.
- Mass number (A = Z + N).
- Binding energy is the energy released when a nucleus forms from individual nucleons.
- Binding energy per nucleon peaks at Fe‑56 (~8.8 MeV).
- Radioactive decay types:
- α‑decay: emits (^{4}!He).
- β‑decay: (n \rightarrow p + e^- + \bar\nu_e) (β⁻) or (p \rightarrow n + e^+ + \nu_e) (β⁺).
- γ‑decay: emits high‑energy photons.
- Half‑life (t_{1/2} = \frac{\ln 2}{\lambda}).
- Fusion (light → heavy) releases energy if (A) is < 56.
- Fission (heavy → light) releases energy if (A) is > 56.
- Conservation laws (energy, charge, baryon number) must hold in every nuclear reaction.
Use these points as a quick cheat‑sheet before the exam. Good luck!