Modern Physics - Nuclear Reactions

Modern Physics – Nuclear Reactions

Introduction

  • Part 3 focuses on nuclear reactions.
  • Key topics:
    • Quarks and nuclei stability.
    • Mass-energy equivalence and binding energy.
    • Calculating binding energy.
    • Why binding energy is negative.
    • Conservation laws in nuclear reactions.
    • Binding energy per nucleon and nuclei stability.
    • Average mass per nucleon and nuclei stability.
    • Fission and fusion reactions related to nuclei stability.
    • Energy release during fission and fusion.

Discovery of Radioactivity

  • In 1896, Henri Becquerel discovered radioactivity with uranium ore.
  • Marie Curie named the energy radioactivity and isolated radium and polonium.
  • Radioactivity originates within the nucleus, unaffected by physical or chemical changes.

Chemical vs. Nuclear Reactions

  • Chemical Reactions:
    • Reactivity determined by outermost electrons.
  • Nuclear Reactions:
    • Reactivity determined by nucleons (protons and neutrons) within the nucleus.

Atomic Notation

  • XZAX_Z^A
    • A: Nucleon number or Mass number (neutrons + protons).
    • Z: Charge number or Atomic number (number of protons).
    • X: Symbol of the element.

Isotopes

  • Atoms with the same number of protons but different numbers of neutrons.
  • Same Z, different A.
Examples of Hydrogen Isotopes
  • Hydrogen (H11H_1^1): 1 proton, 0 neutrons.
  • Deuterium (H12H_1^2): 1 proton, 1 neutron.
  • Tritium (H13H_1^3): 1 proton, 2 neutrons.
Examples of Carbon Isotopes
  • Carbon-12 (C612C_6^{12}): 6 protons, 6 neutrons (most common).
  • Carbon-14 (C614C_6^{14}): 6 protons, 8 neutrons (radioactive).

Nuclear Reactions: Types

  • Radioactive Decay: spontaneous decay of unstable nuclei.
  • Fusion: Combining smaller nuclei into larger ones.
  • Fission: Breaking down large nuclei into smaller ones. It can be:
    • Spontaneous: Occurring because of unstable nuclei.
    • Artificial: Induced by bombarding nuclei with high-speed particles.

Nuclide Symbols and Representation

  • Alpha particle: He24He_2^4 or α\alpha (Helium nuclei: 2 protons, 2 neutrons).
  • Beta particle: e−10e_{-1}^0 or β\beta (High-energy electrons).
  • Positron: e+10e_{+1}^0 or β+\beta^{+} (Same mass as electron, +1 charge).
  • Proton: H11H_1^1 or p (Hydrogen nuclei).
  • Neutron: n01n_0^1 (Mass ≈ proton, no charge).
  • Gamma ray: γ\gamma (High-energy electromagnetic radiation).

Principles of Nuclear Reactions

  • Conservation of Mass Number (Nucleon Number).
  • Conservation of Charge Number (Atomic Number).
  • Example:
    • Th<em>90230→Ra</em>88226+α24Th<em>{90}^{230} \rightarrow Ra</em>{88}^{226} + \alpha_2^4
    • A: 230=226+4230 = 226 + 4
    • Z: 90=88+290 = 88 + 2

First Artificial Nuclear Reaction

  • Ernest Rutherford bombarded nitrogen gas with alpha particles.
  • Nitrogen transformed into oxygen and hydrogen (artificial transmutation).
  • N<em>714+α</em>24→O<em>817+H</em>11N<em>7^{14} + \alpha</em>2^4 \rightarrow O<em>8^{17} + H</em>1^1
    • A: 14+4=17+114 + 4 = 17 + 1
    • Z: 7+2=8+17 + 2 = 8 + 1

Difference Between Radioactive Decay and Artificial Transmutation

  • Artificial transmutation involves converting an element into another by bombarding it with a fundamental particle.

Energy Release

  • Energy is released in nuclear reactions.
  • Energy cannot be created or destroyed (Law of Conservation of Energy)

Four Fundamental Forces

  • Gravitational Force.
  • Electromagnetic Force.
  • Weak Nuclear Force.
  • Strong Nuclear Force (strongest, shortest distance).

Questions to Consider

  1. What keeps protons and neutrons intact within the nucleus?
  2. Is there a mass difference between reactants and products in a nuclear reaction?
  • Example:
    • U<em>92235+n</em>01→Ba<em>56138+Kr</em>3695+3n01+EnergyU<em>{92}^{235} + n</em>0^1 \rightarrow Ba<em>{56}^{138} + Kr</em>{36}^{95} + 3n_0^1 + Energy

Nuclear Force

  • The nucleus contains positive protons and neutral neutrons.
  • Protons should repel each other (Coulombic repulsion).
  • Nuclear force keeps the nucleus together.

Strong Nuclear Force

  • Attractive forces between subnucleonic particles (quarks).
  • Quarks are inside protons and neutrons.
  • Strong interaction: attractive force between quarks.
  • Acts between all nucleons.

Mass Defect and Energy Release

  • There is a mass difference between reactants and products in nuclear reactions.
  • Mass is not conserved; mass-energy is conserved.

Mass-Energy Equivalence

  • Mass may be lost and converted into energy.
  • E=mc2E = mc^2
    • c = speed of light (3.00×108m/s3.00 \times 10^8 m/s).
  • Mass is a concentrated form of energy.
  • Einstein's special relativity: energy and mass are essentially the same.

Conservation Laws for Nuclear Reactions

  • Mass number (Nucleon number).
  • Atomic number (Charge).
  • Momentum.
  • Mass-energy.

Examples

Question 1 (a)
  • Conservation of charge number: H<em>11+Li</em>37=2×He24H<em>1^1 + Li</em>3^7 = 2 \times He_2^4
    • A: 1+3=41 + 3 = 4
  • Conservation of mass number: H<em>11+Li</em>37=2×He24H<em>1^1 + Li</em>3^7 = 2 \times He_2^4
    • Z: 1+7=81 + 7 = 8
Question 1 (b)
  • Net energy = Energy after – Energy before
  • =2×(1.481×10−12)–(0.178×10−12)=2.784×10−12J= 2 \times (1.481 \times 10^{-12}) – (0.178 \times 10^{-12}) = 2.784 \times 10^{-12} J
  • E=mc2→m=Ec2→m=2.784×10−12(3×108)2=3.093×10−29kgE = mc^2 \rightarrow m = \frac{E}{c^2} \rightarrow m = \frac{2.784 \times 10^{-12}}{(3 \times 10^8)^2} = 3.093 \times 10^{-29} kg
Question 1 (c)
  • Mass of reactants = Mass of products + energy mass equivalent
  • (1.673×10−27)+Mass of nucleus=2×(6.645×10−27)+3.093×10−29(1.673 \times 10^{-27}) + \text{Mass of nucleus} = 2 \times (6.645 \times 10^{-27}) + 3.093 \times 10^{-29}
  • Mass of nucleus =11.65×10−27kg= 11.65 \times 10^{-27} kg
Question 1 (d)
  • Momentum.
  • Charge number.
  • Nucleon number (mass number).