Nuclear Chemistry Study Guide

Nucleus: The dense center of the atom containing protons and neutrons.
Isotopes: Atoms of the same element possessing identical proton counts but differing numbers of neutrons, resulting in different mass numbers.
Radioisotope: An unstable isotope that emits ionizing radiation to transition into a more stable nuclear state.
Nuclear Instability: Arises when a nucleus is oversized or maintains an unbalanced proton-to-neutron ratio.
Nuclear Radiation: The emission of particles or high-energy electromagnetic waves from an unstable nucleus striving for stability.
Nuclear Decay Series: A successive sequence of radioactive decays that an unstable nuclide undergoes until reaching a stable end-product isotope.
Electromagnetic Waves: Radiation wavelengths spanning radio waves, microwaves, visible light, and gamma waves.

Alpha Decay ( $\alpha$ ):
- Releases an alpha particle consisting of $2$ protons and $2$ neutrons ( $^4_2\text{He}$ ).
- Alters both the mass number (decreases by $4$ ) and identity/atomic number (decreases by $2$ ) of the radioisotope.
- Lowest penetration capacity; completely blocked by skin or paper.
Beta Decay ( $\beta$ ):
- Involves the conversion of a nuclear nucleon and the release of either an electron or a positron; alters the elemental identity without changing the total mass number.
- Beta Negative Decay ( $\beta^-$ ): A neutron splits into a proton and an emitted electron ( $^0_{-1}e$ ).
- Beta Positive Decay ( $\beta^+$ ): A proton converts into a neutron and an emitted positron ( $^0_{+1}e$ ).
- Moderate penetration capacity; effectively blocked by a thin sheet of metal (such as aluminum).
Gamma Rays ( $\gamma$ ):
- Release of high-energy electromagnetic radiation from an unstable nucleus.
- Does not alter the mass number or the elemental identity of the radioisotope.
- Highest penetration capacity; requires thick lead (several centimeters) or dense concrete to block.
Biological Impact: Alpha, Beta, and Gamma radiation all possess sufficient energy to damage or alter cellular DNA.

Nuclear Fission:
- Process wherein a heavy, unstable nucleus captures a neutron and splits into two smaller nuclei, free neutrons, and significant energy.
- Mechanism utilized to generate commercial nuclear power.
- Example Reaction Pathway: A stray neutron strikes a Uranium-235 ( $^{235}\text{U}$ ) nucleus to create an unstable Uranium-236 ( $^{236}\text{U}$ ) intermediate, splitting into Barium-141 ( $^{141}\text{Ba}$ ), Krypton-92 ( $^{92}\text{Kr}$ ), $3$ free neutrons, and energy.
Nuclear Fusion:
- Process wherein two small, light nuclei collide at high speeds to fuse into a single larger nucleus, releasing a neutron and large quantities of energy.
- Sustaining energy mechanism of the Sun and active stars.
- Example Reaction Pathway: Deuterium ( $^2\text{H}$ ) fuses with Tritium ( $^3\text{H}$ ) to produce Helium-4 ( $^4\text{He}$ ), $1$ free neutron, and energy.

Half-Life ( $t_{1/2}$ ): The fixed duration of time required for exactly half of a radioactive isotope sample to decay.
Fractional Decay Milestones:
- $1$ half-life: $50\%$ remaining ( $\frac{1}{2}$ of original mass)
- $2$ half-lives: $25\%$ remaining ( $\frac{1}{4}$ of original mass)
- $3$ half-lives: $12.5\%$ remaining ( $\frac{1}{8}$ of original mass)
- $4$ half-lives: $6.25\%$ remaining ( $\frac{1}{16}$ of original mass)
Isotope Decay Problems:
- Polonium-207: Half-life is $5.8\,\text{hours}$ . An initial sample of $18.7\,\text{g}$ decaying over $17.4\,\text{hours}$ ( $3$ half-lives) leaves $2.34\,\text{g}$ .
- Potassium-40: Half-life is $1.3\text{ billion years}$ . An initial sample of $67\,\text{g}$ decaying over $5.2\text{ billion years}$ ( $4$ half-lives) leaves $4.19\,\text{g}$ .
- Lawrencium-262: Half-life is $3.61\,\text{hours}$ . Decaying from $360\,\text{g}$ down to $45\,\text{g}$ represents $3$ half-lives, requiring $10.83\,\text{hours}$ .
- Bismuth-214: Half-life is $19.9\,\text{minutes}$ . Decaying from $140\,\text{g}$ down to $8.75\,\text{g}$ represents $4$ half-lives, requiring $79.6\,\text{minutes}$ .