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: ${}{2}^{4}He$ or ${}{2}^{4}\alpha$
- Beta particle ( $\beta^-$ ):
 - Ordinary electron and is therefore negatively charged.
 - Notation: ${}{-1}^{0}e$ or ${}{-1}^{0}\beta$
- 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: ${}{1}^{1}H$ or ${}{1}^{1}p$
- Positron ( $\beta^+$ ):
 - Positive electron.
 - Notation: ${}{+1}^{0}e$ or ${}{+1}^{0}\beta$
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: ${}{88}^{226}Ra \rightarrow {}{86}^{222}Rn + {}_{2}^{4}He$
Negative beta decay/emission:
- Atomic number increases by 1.
- Mass number remains the same.
- Example: ${}{92}^{239}U \rightarrow {}{93}^{239}Np + {}_{-1}^{0}e$
Gamma emission:
- Both the atomic number and mass number remain the same.
- Example: ${}{92}^{239}U \rightarrow {}{92}^{239}U + {}_{0}^{0}\gamma$
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: ${}{27}^{58}Co \rightarrow {}{26}^{57}Fe + {}_{1}^{1}H$
Positron emission (positive beta emission):
- Atomic number decreases by 1.
- Mass number remains the same.
- Example: ${}{29}^{58}Cu \rightarrow {}{28}^{58}Ni + {}_{+1}^{0}e$
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: ${}{94}^{239}Pu \rightarrow {}{92}^{235}U + {}_{2}^{4}He$
Artificial transmutation:
- Occurs when a stable (nonradioactive) nucleus is bombarded with particles, causing it to become radioactive.
- Example: ${}{4}^{9}Be + {}{2}^{4}He \rightarrow {}{6}^{12}C + {}{0}^{1}n$
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: ${}{1}^{2}H + {}{1}^{3}H \rightarrow {}_{2}^{4}He + energy$
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: ${}{92}^{235}U + {}{0}^{1}n \rightarrow {}{54}^{140}Xe + {}{38}^{94}Sr + 2{}_{0}^{1}n + energy$
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.