Nuclear Chemistry Notes

Table O: Symbols Used in Nuclear Chemistry

Overview

• Radioactive elements emit particles and/or energy from their nuclei.
• These nuclear particles or energy have different effects on the nuclei of these elements.
• Radioactive decay process is represented by nuclear equations, showing the identity of the reactants, products, and the radiation released.
• In these equations, both charge and mass must be conserved.
• To balance a nuclear equation:
  • The sum of the atomic charge numbers on each side must be equal.
  • The sum of the mass numbers on each side must be equal.

Table of Symbols

• The table provides the Name, Notation (used in writing nuclear equations), and Symbol of common types of radiation.
• Going down the chart in order:
  • Alpha particle ($\alpha$):
    • Helium nucleus and is therefore positively charged.
    • Notation: ${}<em>{2}^{4}He$ or ${}</em>{2}^{4}\alpha$
  • Beta particle ($\beta^-$):
    • Ordinary electron and is therefore negatively charged.
    • Notation: ${}<em>{-1}^{0}e$ or ${}</em>{-1}^{0}\beta$
  • Gamma radiation ($\gamma$):
    • Emission of pure energy from the nucleus.
    • Carries no charge or mass.
    • Notation: ${}_{0}^{0}\gamma$
  • Neutron (n):
    • Neutral particle of unit mass found in the nucleus of atoms.
    • Notation: ${}_{0}^{1}n$
  • Proton (p):
    • Hydrogen nucleus, a positive particle of unit mass found in the nucleus of atoms.
    • Notation: ${}<em>{1}^{1}H$ or ${}</em>{1}^{1}p$
  • Positron ($\beta^+$):
    • Positive electron.
    • Notation: ${}<em>{+1}^{0}e$ or ${}</em>{+1}^{0}\beta$
• Mass number:
  • The number at the upper left of the notation.
• Atomic number:
  • The number at the lower left of the notation.
• When a particle is emitted, conservation of these numbers must take place with the reactants and products.
• If the emission of the particle affects the atomic number, the identity of the element changes.

Additional Information on Radioactive Decay:

• Alpha decay/emission:
  • Atomic number decreases by 2.
  • Mass number decreases by 4.
  • Example: ${}<em>{88}^{226}Ra \rightarrow {}</em>{86}^{222}Rn + {}_{2}^{4}He$
• Negative beta decay/emission:
  • Atomic number increases by 1.
  • Mass number remains the same.
  • Example: ${}<em>{92}^{239}U \rightarrow {}</em>{93}^{239}Np + {}_{-1}^{0}e$
• Gamma emission:
  • Both the atomic number and mass number remain the same.
  • Example: ${}<em>{92}^{239}U \rightarrow {}</em>{92}^{239}U + {}_{0}^{0}\gamma$
• Neutron emission:
  • Atomic number remains the same.
  • Mass number decreases by 1.
• Proton emission:
  • Both the atomic number and mass number decrease by 1.
  • Example: ${}<em>{27}^{58}Co \rightarrow {}</em>{26}^{57}Fe + {}_{1}^{1}H$
• Positron emission (positive beta emission):
  • Atomic number decreases by 1.
  • Mass number remains the same.
  • Example: ${}<em>{29}^{58}Cu \rightarrow {}</em>{28}^{58}Ni + {}_{+1}^{0}e$
• Natural transmutation:
  • The identity of a nucleus or element changes due to a change in the number of protons (atomic number) in the nucleus.
  • Example: ${}<em>{94}^{239}Pu \rightarrow {}</em>{92}^{235}U + {}_{2}^{4}He$
• Artificial transmutation:
  • Occurs when a stable (nonradioactive) nucleus is bombarded with particles, causing it to become radioactive.
  • Example: ${}<em>{4}^{9}Be + {}</em>{2}^{4}He \rightarrow {}<em>{6}^{12}C + {}</em>{0}^{1}n$
• Nuclear fusion:
  • Combining of lightweight nuclei to produce a heavier nucleus.
  • Usually involves hydrogen nuclei combining to produce a helium nucleus.
  • This is the source of solar energy.
  • Example: ${}<em>{1}^{2}H + {}</em>{1}^{3}H \rightarrow {}_{2}^{4}He + energy$
• Nuclear fission:
  • Splitting of a heavier nucleus into lighter weight nuclei.
  • U-235 and Pu-239 are the most common elements to undergo fission.
  • This is the source of the energy produced in nuclear reactors.
  • Example: ${}<em>{92}^{235}U + {}</em>{0}^{1}n \rightarrow {}<em>{54}^{140}Xe + {}</em>{38}^{94}Sr + 2{}_{0}^{1}n + energy$
• Nuclear reactions release large amounts of energy due to the conversion of some mass into energy according to Einstein's equation: $E=mc^2$
• Penetrating power of radiation:
  • Alpha radiation: Weakest penetrating power due to being the largest particle.
  • Gamma radiation: Greatest penetrating power due to being massless and neutral.

Table N: Selected Radioisotopes

Overview

• The nucleus of many elements is unstable and gives off particles and/or energy when going to a more stable state.
• These elements are called radioactive elements.
• This process is referred to as radioactive decay, and the emitted particles or energy is referred to as radiation.
• The term radioisotope is a contraction of the words radioactive isotope.

Table Information

• Table N lists the Nuclide, Half-Life, Decay Mode, and the Nuclide Name of selected radioisotopes.
• Nuclide:
  • The symbol and mass number are given for each nuclide.
  • Atomic number can be obtained from the Periodic Table.
  • Nuclide refers to any nucleus.
  • Decay of the radioisotopes occurs in the nucleus.
• Half-life:
  • The time in which one-half the nuclei of a sample of that radioisotope decays.
• Decay mode:
  • Indicates what particle is emitted as the nucleus undergoes decay.
  • Decay modes listed on the table:
    • $\beta^-$: Negative beta decay, which is the emission of an ordinary electron.
    • $\beta^+$: Positive beta decay, which is the emission of a positive electron or a positron.
    • $\alpha$: Alpha decay, which is the emission of a particle identical to a helium nucleus.
  • See Table O for Symbol and Notation.

Radioactive Decay

• During radioactive decay, a radioactive element gradually changes into another element.
• The time in which one-half of the nuclei of the original element decays is called the half-life.
• Table N gives the half-lives of selected radioisotopes.
• Each radioactive isotope has its own half-life that is unaffected by pressure, temperature, or any other external factors.
• When a substance undergoes radioactive decay, the radiation decreases, but the half-life remains constant.
• At the conclusion of each half-life, the mass of the radioactive sample is one-half of the mass it had at the beginning of that half-life.

Half-Life Example 1

• What amount remains of a 20-gram sample of radium-226 after 4,797 years?
• From Table N, the half-life of radium-226 is 1,599 years.
• Since the half-life is constant, 4,797 years equals 3 half-lives:
  • $\frac{4797 \text{ years}}{1599 \text{ years}} = 3$
• After each half-life, the amount of radioactive isotope remaining would be half of the original amount, or:
  • After the 1st half-life, 10 grams remain.
  • After the 2nd half-life, 5 grams remain.
  • After the 3rd half-life, 2.5 grams remain.
• Answer: 2.5 g

Half-Life Example 2

• What fraction remains of a 20-gram sample of radium-226 after 4,797 years?
• Using the same procedure as Example 1 and including the fractional amounts:
  • After the 1st half-life, 10 grams remain, which is 1/2 of the original amount.
  • After the 2nd half-life, 5 grams remain, which is 1/4 of the original amount.
  • After the 3rd half-life, 2.5 grams remain, which is 1/8 of the original amount.
• Answer: 1/8

Half-Life Example 3

• How much time must elapse before 16 grams of potassium-42 decays, leaving 2 grams of potassium-42 radioactive?
• Table N shows that potassium-42 (${}^{42}K$) has a half-life of 12.36 hours.
• This is the time it takes for half of the radioactive substance to decay.
• Since the half-life is a constant, the time for the first half-life would be 1 x 12.36 h or 12.36 hours, and the amount remaining would be half of the original, or 8 grams.
• The time for two half-lives would be 2 x 12.36 h or 24.72 hours, and 4 grams would remain.
• The time for three half-lives would be 3 x 12.36 h or 37.08 hours, and 2 grams of the original sample would remain radioactive.
• Answer: 37.08 h

Additional Information

• In most cases, the identity (name) of the nuclide changes during radioactive decay.
• Another decay mode not shown on the table is gamma emission ($\gamma$), which is the emission of pure energy from the nucleus.
• Radioisotopes are used in dating geologic and archeological finds.
  • C-14, found in all plant and animal matter, is used to date such finds.
  • U-238 is used to date minerals.
• Radioisotopes with short half-lives, which will be quickly eliminated from the body, are used medicinally.
  • An example is the use of I-131, with a half-life of 8.021 days, to treat thyroid disorders.
• Other medical uses of radioisotopes:
  • Ra-226 and Co-60 are used in cancer therapy.
  • Tc-99 is used to pinpoint brain tumors.
• Radiation can be used to kill insect eggs, molds, bacteria, and yeasts in foods, increasing the shelf-life of certain food items.