THEORY EXAMINATION (SEM–IV) 2016-17 NUCLEAR SCIENCE

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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=τln⁡2T_{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:

log⁡10T1/2=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