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Isotopes and Radioisotopes01:28

Isotopes and Radioisotopes

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In the early 1900s, English chemist Frederick Soddy realized that an element could have atoms with different masses that were chemically indistinguishable. These different types are called isotopes — atoms of the same element that differ in mass. Isotopes differ in mass because they have different numbers of neutrons but are chemically identical because they have the same number of protons. Soddy was awarded the Nobel Prize in Chemistry in 1921 for this discovery.
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Mass Spectrometry: Isotope Effect01:13

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Most elements exist in nature as a mixture of isotopes. The isotopes differ in weight due to their respective number of neutrons. The molecular weight of a molecule is different depending on the specific isotope of its elements involved. As a result, the mass spectrum of the molecule exhibits peaks from the same fragment at multiple positions. The positions of these mass signals depend on the mass differences between isotopes. Furthermore, the intensity of these signals is dependent on the...
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Isotopes01:12

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Elements have a set number of protons that determines their atomic number (Z). For example, all atoms with eight protons are oxygen; however, the number of neutrons can vary for atoms of the same element. The sum of the number of protons and the number of neutrons is the mass number (A). Atoms with the same atomic number but different mass numbers are called isotopes. Elements can have multiple isotopes, for example, carbon-12, carbon-13, and carbon-14.
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Atomic Nuclei: Types of Nuclear Relaxation01:28

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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
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Radioactive Decay and Radiometric Dating02:48

Radioactive Decay and Radiometric Dating

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Radioactivity is a spontaneous disintegration of an unstable nuclide and is a random process, as all the nuclei in the sample do not decay simultaneously. The number of disintegrations per unit time is called the activity (A), which is directly proportional to the number of nuclei in the sample. The decay constant (λ) is an average probability of decay per nucleus in unit time.
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BRAIN 2.0: time and memory complexity improvements in the algorithm for calculating the isotope distribution.

Piotr Dittwald1, Dirk Valkenborg

  • 1College of Inter-faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, Warsaw, Poland, piotr.dittwald@mimuw.edu.pl.

Journal of the American Society for Mass Spectrometry
|February 13, 2014
PubMed
Summary

This study enhances the BRAIN algorithm for isotopic distribution calculations. The improved method reduces computational complexity and avoids root calculations for more efficient analysis of molecular isotopes.

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Area of Science:

  • Computational chemistry
  • Mass spectrometry
  • Algorithm development

Background:

  • The BRAIN (Baffling Recursive Algorithm for Isotopic distributioN) algorithm efficiently calculates aggregated isotope distributions using polynomial expansion.
  • The original BRAIN method requires calculations to start from the lightest isotope variant, leading to quadratic complexity with molecular mass.
  • The iterative nature and polynomial expansion present computational challenges for large molecules.

Purpose of the Study:

  • To introduce algorithmic improvements for the BRAIN method to reduce time and memory complexity.
  • To present a generic representation of element isotope distributions to streamline calculations.
  • To avoid the computationally intensive root calculation step in the original BRAIN algorithm.

Main Methods:

  • Implementing two key improvements to the BRAIN algorithm.
  • Developing a generic formulation for element isotope distribution representation.
  • Utilizing algebraic identities and Newton-Girard/Viète's formulae for polynomial expansion.

Main Results:

  • Reduced time and memory complexity for calculating aggregated isotope distributions.
  • Successful illustration of a generic element isotope distribution representation.
  • Avoidance of explicit root calculation for element polynomials, enhancing efficiency.

Conclusions:

  • The proposed modifications significantly enhance the efficiency of the BRAIN algorithm for isotopic distribution calculations.
  • The generic representation offers a more robust and computationally feasible approach, especially for higher-order polynomials.
  • These advancements contribute to more efficient computational analysis in mass spectrometry and related fields.