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

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NUCLEAR SCIENCE (NOE046)

Section-wise Solved Answers & Notes

SECTION – A (10 × 2 = 20 Marks)

Short, direct answers (2 marks each)

(a) Properties of nuclear forces

• Very strong • Short range
• Charge independent • Saturation property
• Attractive in nature

(b) Mass defect

Mass defect is the difference between the sum of masses of individual nucleons and the actual mass of the nucleus.

(c) Quadrupole moment

It measures the departure of nuclear charge distribution from spherical symmetry.

(d) Semi-empirical mass formula

It is a formula that gives the binding energy of nucleus by considering volume, surface, Coulomb, asymmetry and pairing energies.

(e) Various nuclear models

• Liquid drop model • Shell model
• Collective model • Fermi gas model

(f) Mean life & relation with half life

Mean life (τ) is the average life of radioactive atoms.
Relation:

τ=T1/20.693\tau = \frac{T_{1/2}}{0.693}τ=0.693T1/2

(g) Principle of Aston Mass Spectrograph

It separates ions based on mass-to-charge ratio using electric and magnetic fields.

(h) Synchrotron

A synchrotron is a particle accelerator where particles move in a circular path and gain energy from alternating electric fields.

(i) Cloud chamber

A cloud chamber is a device used to detect charged particles by observing condensation trails.

(j) Applications of radiotracer technique

• Material science: thickness measurement, crack detection
• Agriculture: fertilizer uptake, soil analysis

SECTION – B (Any 5 × 10 = 50 Marks)

(a) Electron Scattering Method

High-energy electrons are scattered by nuclei. The scattering pattern gives information about nuclear size and charge distribution. It is accurate because electrons interact weakly with nuclei.

(b) Collective Model & Nuclear Fission

Collective model combines liquid drop + shell model concepts.
It explains nuclear vibrations and rotations and helps understand nuclear fission as deformation and splitting of nucleus.

(c) Limitations of Single Particle & Shell Model • Cannot explain nuclear deformation
• Fails for heavy nuclei • Ignores collective motion
• Cannot explain fission completely

(d) Nuclear Reactions & Conservation Laws

Types:
• Elastic • Inelastic
• Fusionn • Fission

Conservation laws: • Energy
• Momentum • Charge
• Nucleon number

(e) Radioactive Decay

It is the spontaneous disintegration of unstable nucleus.

Decay constant (λ): probability of decay per second.
Half life (T½): time for half nuclei to decay.

T1/2=0.693λT_{1/2} = \frac{0.693}{\lambda}T1/2=λ0.693

(f) Gamow Theory of Alpha Decay

Alpha particle tunnels through nuclear potential barrier.
Geiger-Nuttal law relates decay constant with alpha energy.

(g) Van de Graaff Accelerator

Working: High voltage generated using moving belt → accelerates charged particles.

Advantages: • High energy • Simple design

Limitations: • Voltage limitation • Large size

(h) Scintillation Counter

Principle: Radiation produces light flashes in scintillator → converted to electrical signal.

Merits: • High efficiency • Fast response
• Good energy resolution

SECTION – C (Any 2 × 15 = 30 Marks)

Q3. Nuclear Binding Energy & Numerical

Nuclear Binding Energy

Energy required to separate nucleus into nucleons.
Higher binding energy → greater nuclear stability.

Given:

Ni-64 = 63.9280 mu Cu-64 = 63.9298 mu
MN = 1.008665 mu MH = 1.007825 mu

Formula:

Mass defect=ZMH+NMN−Mnucleus\text{Mass defect} = ZM_H + NM_N - M_{nucleus}Mass defect=ZMH+NMN−Mnucleus Binding Energy=Δm×931 MeV\text{Binding Energy} = \Delta m \times 931 \text{ MeV}Binding Energy=Δm×931 MeV

(Steps to be shown clearly in exam)