About this previous year paper
Course: B.Tech (Common Elective)
Subject Code: EOE046
Subject Title: Nuclear Science
Exam Type: Theory
Duration: 3 Hours
Maximum Marks: 100
SECTION – A (10 × 2 = 20 Marks)
Short conceptual questions testing definitions, laws, and physical principles
| No. | Question | Concept Summary |
|---|---|---|
| (a) | Properties of Nuclear Forces | Short-range, charge independent, saturating, strong attractive force acting between nucleons; spin-dependent. |
| (b) | Mass Defect | Difference between actual nuclear mass and sum of constituent nucleons’ masses — due to binding energy. |
| (c) | Quadrupole Moment | Measure of non-spherical charge distribution in a nucleus (indicates nuclear deformation). |
| (d) | Semi-Empirical Mass Formula (Weizsäcker Formula) | Expresses nuclear binding energy considering volume, surface, Coulomb, asymmetry, and pairing terms. |
| (e) | Nuclear Models | Liquid Drop Model, Shell Model, Collective Model, Optical Model. |
| (f) | Mean Life (τ) | Average lifetime of an unstable nucleus. Relation: T1/2=τln2T_{1/2} = \tau \ln 2T1/2=τln2. |
| (g) | Aston Mass Spectrograph Principle | Measures isotopic masses by deflecting ions through electric and magnetic fields to detect charge-to-mass ratio. |
| (h) | Synchrotron | A cyclic particle accelerator that maintains constant orbital radius by synchronizing magnetic field with particle energy. |
| (i) | Cloud Chamber | Visualization chamber showing ionizing particle tracks as condensed vapor droplets. |
| (j) | Radiotracer Applications | Used in agriculture (nutrient absorption), medicine (diagnostics), and material science (diffusion and corrosion studies). |
⚙️ SECTION – B (5 × 10 = 50 Marks)
Analytical and descriptive questions covering nuclear structure, decay, and detection
(a) Electron Scattering Method
Determines nuclear radius by analyzing electron diffraction patterns.
Formula: R=R0A1/3R = R_0 A^{1/3}R=R0A1/3, with R0≈1.2×10−15 mR_0 ≈ 1.2 \times 10^{-15} \, \text{m}R0≈1.2×10−15m.
Based on the scattering angle and intensity distribution of electrons.
(b) Collective Model of Nucleus
Combines features of shell and liquid drop models.
Considers collective motion of nucleons → explains nuclear deformation and energy levels.
Helps explain fission, where deformation energy overcomes surface tension.
(c) Limitations of Single Particle and Shell Model
| Model | Limitation |
|---|---|
| Single Particle | Ignores nucleon interaction, oversimplifies binding. |
| Shell Model | Fails for deformed nuclei; cannot explain all excited states. |
(d) Nuclear Reactions & Conservation Laws
Types: Elastic, inelastic, fission, fusion, spallation.
Conservation: Charge, baryon number, linear & angular momentum, energy, and parity.
(e) Radioactive Decay
N=N0e−λtN = N_0 e^{-\lambda t}N=N0e−λt; T1/2=0.693λT_{1/2} = \frac{0.693}{\lambda}T1/2=λ0.693.
Decay constant (λ): Probability of decay per unit time.
Exponential law governs alpha, beta, and gamma decay.
(f) Gamow’s Theory of Alpha Decay
Based on quantum tunneling of alpha particle through nuclear potential barrier.
Derives Geiger–Nuttall Law:
- log10T1/2=aZEα+b\log_{10} T_{1/2} = a \frac{Z}{\sqrt{E_\alpha}} + blog10T1/2=aEαZ+b
showing correlation between decay energy and half-life.
(g) Van de Graaff Accelerator
Principle: Electrostatic potential accelerates charged particles.
Construction: Conveyor belt transports charge to high-voltage dome.
Advantages: Simple, stable beam; Limitations: Voltage breakdown limits energy (~10 MeV).
(h) Scintillation Counter
Working: Converts radiation energy into light flashes detected by photomultiplier tubes.
Merits: High sensitivity, fast response, can detect low-intensity radiation.
SECTION – C (2 × 15 = 30 Marks)
Long, numerical and theoretical questions
Q3. Nuclear Binding Energy
Concept: Energy required to break nucleus into protons and neutrons.
Formula:
- B.E.=[ZMH+(A−Z)Mn−Matom]×931.5 MeVB.E. = [Z M_H + (A - Z) M_n - M_{atom}] \times 931.5 \text{ MeV}B.E.=[ZMH+(A−Z)Mn−Matom]×931.5 MeV
Used to explain nuclear stability — higher binding energy per nucleon → more stable nucleus.
Example problem:
Calculate B.E. for Ni⁶⁴ and Cu⁶⁴ using atomic masses (given in the question).
Q4. Nuclear Reactor – Components and Working
Components:
Fuel: U-235 or Pu-239 (fissionable material).
Moderator: Graphite, heavy water — slows neutrons.
Control Rods: Cd/B control reaction rate.
Coolant: Removes heat (water, CO₂, sodium).
Shielding: Prevents radiation leakage.
Working Principle:
Chain reaction controlled to maintain steady energy release, converted into thermal and then electrical power.
Q5. Interaction of Radiation with Matter
Charged Particles: Lose energy via ionization and excitation.
Gamma Rays: Interact by photoelectric effect, Compton scattering, and pair production.
Neutrons: Interact through elastic scattering and nuclear capture.
Leads to secondary radiation and material activation.
Summary
The Nuclear Science (EOE046) paper comprehensively tests:
| Core Topic | Concepts Covered |
|---|---|
| Nuclear Structure | Mass defect, binding energy, nuclear models |
| Nuclear Decay | Alpha, beta, gamma, decay constants |
| Nuclear Reactions | Types, conservation laws, fission/fusion |
| Detection & Measurement | Scintillation counter, cloud chamber, spectrograph |
| Applications | Radiotracers, reactors, accelerators |