🔙 Prerequisite Revision:
👉 Chapter 12: Atoms (Bohr Model & Spectrum)Chapter 13: Nuclei
Vol 1: Nuclear Structure & Mass Defect
Composition: The nucleus consists of Protons (positive) and Neutrons (neutral), collectively called Nucleons.
Mass can be converted into energy and vice-versa.
$$E = mc^2$$
Important Conversion:
1 Atomic Mass Unit (1 u) $\approx 931.5$ MeV.
Mass Defect ($\Delta m$)
It is observed that the mass of a stable nucleus is always less than the sum of the masses of its constituent nucleons. This difference is called Mass Defect.
Vol 2: Binding Energy & Stability
Binding Energy ($E_b$): The energy equivalent to the mass defect. It is the energy required to break the nucleus into its constituent nucleons.
Binding Energy per Nucleon ($E_{bn}$): $E_{bn} = E_b / A$. This determines the stability of a nucleus.
The Binding Energy Curve (Most Important)
A graph plotted between Binding Energy per Nucleon ($E_{bn}$) and Mass Number ($A$).
[attachment_0](attachment)- $E_{bn}$ is practically constant (approx 8 MeV) for nuclei with $30 < A < 170$. This shows saturation of nuclear forces.
- Maximum Stability: For Iron ($^{56}\text{Fe}$), $E_{bn}$ is max ($\approx 8.75$ MeV).
- Nuclear Fission: Heavy nuclei ($A > 170$) have lower $E_{bn}$. They tend to split into lighter, more stable nuclei.
- Nuclear Fusion: Very light nuclei ($A < 30$) have lower $E_{bn}$. They tend to fuse to form heavier, stable nuclei.
Vol 3: Radioactivity & Decay Laws
Radioactivity: The phenomenon of spontaneous emission of radiation ($\alpha, \beta, \gamma$) from an unstable nucleus.
Law of Radioactive Decay
The rate of disintegration of radioactive atoms is directly proportional to the number of atoms present at that instant.
$$N = N_0 e^{-\lambda t}$$
(Where $\lambda$ is the Decay Constant)
Half Life & Mean Life
| Parameter | Definition | Formula |
|---|---|---|
| Half Life ($T_{1/2}$) | Time in which number of nuclei reduces to half. | $$T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$$ |
| Mean Life ($\tau$) | Average life of all nuclei. | $$\tau = \frac{1}{\lambda} = 1.44 T_{1/2}$$ |
Vol 4: Nuclear Fission & Fusion
[attachment_1](attachment)Nuclear Fission
Splitting of a heavy nucleus into two lighter nuclei.
Ex: $^{235}\text{U} + n \rightarrow \text{Ba} + \text{Kr} + 3n + Q$
Principle of Atom Bomb & Nuclear Reactor.
Nuclear Fusion
Combining of two light nuclei to form a heavier nucleus.
Ex: $^1\text{H} + {}^1\text{H} \rightarrow {}^2\text{H} + \dots$
Source of Energy in Sun & Stars.
Vol 5: Mission 100 Question Bank
Section A: MCQs
Q1. The energy equivalent of 1 amu mass is:
(a) 931.5 eV (b) 931.5 MeV (c) 1 J (d) 9.31 MeV
Ans: (b) 931.5 MeV.
Q2. Which quantity remains conserved during nuclear decay?
(a) Kinetic Energy (b) Mass (c) Total Energy & Momentum (d) Only Mass
Ans: (c) Total Energy & Momentum.
Section B: Numericals (Important)
Q3. The half-life of a radioactive substance is 30 days. Calculate (a) Decay constant (b) Mean life.
Solution:
Given: $T_{1/2} = 30$ days.
(a) $\lambda = \frac{0.693}{T_{1/2}} = \frac{0.693}{30} = 0.0231 \text{ days}^{-1}$.
(b) $\tau = 1.44 \times T_{1/2} = 1.44 \times 30 = 43.2$ days.
Ans: 0.0231 day⁻¹, 43.2 days.
Section C: Conceptual
Q4. Why is the density of a nucleus independent of its Mass Number ($A$)?
Ans: Nuclear Mass $\propto A$ and Nuclear Volume $\propto A$ (since $R \propto A^{1/3} \Rightarrow V \propto A$). Therefore, the ratio (Density = Mass/Volume) becomes constant ($\approx 2.3 \times 10^{17}$ kg/m³).
Mission 100 Physics Series
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