🔙 Prerequisite Revision:
👉 Chapter 12: Atoms (Bohr's Model & Spectrum)Chapter 13: Nuclei
Vol 1: Nuclear Structure & Mass-Energy
Composition: The nucleus contains Protons (positive) and Neutrons (neutral), collectively known as Nucleons.
Representation: $_Z^A X$
• $Z$ = Atomic Number (No. of Protons)
• $A$ = Mass Number (Total Nucleons = $p + n$)
Mass is a form of energy. 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 ($\Delta m$)
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 Curve & Stability
Binding Energy ($E_b$): The energy released when nucleons bind to form a nucleus (or energy required to separate them). $E_b = \Delta m \times c^2$.
Binding Energy per Nucleon ($E_{bn}$): $E_{bn} = E_b / A$. This determines the stability of a nucleus. Higher $E_{bn}$ means more stability.
- The curve is practically constant ($E_{bn} \approx 8$ MeV) for nuclei with mass number $30 < A < 170$.
- Maximum Stability: Iron ($^{56}\text{Fe}$) has the highest $E_{bn}$ of about 8.75 MeV.
- Nuclear Fission: Heavy nuclei ($A > 170$) have lower $E_{bn}$. They split to gain stability.
- Nuclear Fusion: Light nuclei ($A < 30$) have lower $E_{bn}$. They fuse to gain stability.
Vol 3: Radioactivity & Decay Laws
Radioactivity: Spontaneous emission of radiations ($\alpha, \beta, \gamma$) from an unstable nucleus to achieve stability.
Law of Radioactive Decay
The rate of decay ($dN/dt$) is directly proportional to the number of undecayed nuclei ($N$) present at that instant.
$$N = N_0 e^{-\lambda t}$$
($\lambda$ is the Decay Constant)
Half Life & Mean Life
| Parameter | Formula | Relation |
|---|---|---|
| Half Life ($T_{1/2}$) | $$T_{1/2} = \frac{0.693}{\lambda}$$ | Time for $N$ to become $N_0/2$. |
| Mean Life ($\tau$) | $$\tau = \frac{1}{\lambda}$$ | $\tau = 1.44 \times T_{1/2}$ |
Vol 4: Nuclear Energy
[attachment_0](attachment)Nuclear Fission
Process of splitting a heavy nucleus into two lighter nuclei.
Reaction: $^{235}\text{U} + n \rightarrow \text{Ba} + \text{Kr} + 3n + Q$
Application: Nuclear Reactors, Atom Bomb.
Nuclear Fusion
Process of combining two light nuclei to form a heavier nucleus.
Reaction: $^2\text{H} + {}^2\text{H} \rightarrow {}^3\text{He} + n + 3.27 \text{ MeV}$
Application: Energy source of Sun & Stars.
Vol 5: Mission 100 Question Bank
Section A: MCQs
Q1. Which of the following has the highest binding energy per nucleon?
(a) Uranium (b) Helium (c) Iron (d) Hydrogen
Ans: (c) Iron ($^{56}\text{Fe}$).
Q2. The SI unit of radioactivity is:
(a) Curie (b) Rutherford (c) Becquerel (d) Roentgen
Ans: (c) Becquerel (Bq).
Section B: Numericals (High Weightage)
Q3. The half-life of a radioactive sample is 10 hours. What fraction of the original sample will remain undecayed after 40 hours?
Solution:
Given: $T_{1/2} = 10$ hrs, $t = 40$ hrs.
Number of half-lives $n = t / T_{1/2} = 40/10 = 4$.
Remaining fraction $N/N_0 = (1/2)^n = (1/2)^4 = 1/16$.
Ans: 1/16th of original sample.
Q4. Calculate the energy released (in MeV) when 1g of matter is converted into energy.
Solution:
Given: $m = 1 \text{ g} = 10^{-3}$ kg, $c = 3 \times 10^8$ m/s.
$E = mc^2 = 10^{-3} \times (3 \times 10^8)^2 = 9 \times 10^{13}$ Joules.
In MeV: $\frac{9 \times 10^{13}}{1.6 \times 10^{-13}} \approx 5.6 \times 10^{26}$ MeV.
Ans: $9 \times 10^{13}$ J.
Mission 100 Physics Series
Next Chapter: Semiconductor Electronics (The Final Chapter!)
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