27.1 Atomic Nucleus and Isotope

27.1 Atomic Nucleus and Isotope

  • The atom is the building block of matter, consisting of a positively charged nucleus surrounded by a cloud of electrons bound by electrostatic forces.

  • The atomic nucleus is a small, dense region at the center composed of protons and neutrons.

  • Almost all of an atom’s mass resides in the nucleus; the electron cloud contributes very little to mass.

  • Properties of a nucleus are determined by the number of protons (Z) and neutrons (N).

  • A specific combination of protons and neutrons is called a nuclide and represents a unique nucleus.

  • Nuclide notation: AX, where X is the chemical symbol, Z is the atomic number (number of protons), and A is the mass number (A = Z + N).

  • Mass number and atomic number relation: A = Z + N; hence N = A − Z.

  • Example: Aluminum nuclide with A = 27, Z = 13 has N = 27 − 13 = 14 neutrons (nucleons): 13 protons, 14 neutrons.

  • Isotopes are two or more forms of the same element with the same Z but different N, hence different A, and different relative atomic masses but similar chemical properties.

  • Isotopes: two main types

    • Stable isotopes: not radioactive (e.g., 14N, 15N).
    • Radioactive isotopes: unstable and radioactive (e.g., 14C, 40K).

  • Isotopic variations: elements can exist in multiple isotopes with varying numbers of neutrons; distribution of isotopes varies by element.

  • Examples of isotopes and notes:

    • Hydrogen has three isotopes: protium (no neutrons, ^1H), deuterium (^2H) with 1 neutron, tritium (^3H) with 2 neutrons.
    • Oxygen naturally has isotopes including ^16O (dominant), with smaller amounts of ^17O and ^18O.
    • Uranium naturally occurs as ^238U (≈ 99.3%) and ^235U (≈ 0.7%); Uranium has many known isotopes (35 reported).

  • Isotopes share the same chemical properties but differ in mass; this enables separation by techniques like mass spectrometry.

  • Mass spectrograph concept (to be elaborated in 27.1.4): separates isotopes based on mass-to-charge ratio, yielding peaks corresponding to isotopes and peak heights indicating relative abundances.

  • Do you know:

    • Isotopes of hydrogen include protium, deuterium, and tritium with masses 1, 2, and 3 respectively.
    • The most stable uranium isotope is ^238U; ^235U is less abundant but crucial for reactors due to higher fissility.

27.1.4 Mass Spectrograph (Bainbridge Mass Spectrograph)

  • Mass spectrograph purpose: separates isotopes by mass-to-charge ratio (m/q) using a combination of electric and magnetic fields.
  • Bainbridge mass spectrograph (three core components):
    • Ion source: generates positive ions by bombarding a sample with electrons (ionization).
    • Velocity selector: uses perpendicular electric (E) and magnetic (B) fields to allow only ions with a specific velocity to pass without net deflection.
    • Magnetic analyzer: applies a magnetic field to bend ion trajectories; curvature depends on charge-to-mass ratio (e/m).
  • Key relations:
    • When ions are accelerated through a potential difference V, they gain kinetic energy: $$ frac{1}{2} m v^2 = eV \