Grade 10 Chemistry EOS2 Practice Sheet: Nuclear Chemistry and Radioactive Decay

Fundamentals of Nuclear Decay and Radioactivity

Nuclear decay is defined as the spontaneous change of an unstable nucleus. During this process, unstable atomic nuclei emit radiation in order to attain more stable atomic configurations. Radioactive decay is characterized as a random process for individual nuclei, meaning it is impossible to predict exactly when a specific nucleus will decay.

Classification and Properties of Radioactive Particles

There are three primary types of radiation emitted during nuclear decay, distinct in their composition, charge, and physical properties:

Alpha Particles ( $\alpha$ ) An alpha particle consists of $2$ protons and $2$ neutrons. It is represented by the symbol $\alpha$ . Among the common types of radiation, alpha particles possess the strongest ionizing ability but have the lowest penetrating power. They can be stopped by simple materials, such as a single sheet of paper.
Beta Particles ( $\beta$ ) A beta particle is an electron emitted from the nucleus. It is represented by the symbol $\beta$ . The mass of a beta particle, which is equal to the mass of an electron, is much smaller than the mass of the atomic nucleus. Because of this extremely small mass, the mass of beta particles is typically ignored in nuclear reaction balance calculations.
Gamma Radiation ( $\gamma$ ) Gamma radiation is a form of electromagnetic radiation and is represented by the symbol $\gamma$ . Unlike alpha and beta particles, gamma radiation has no mass and no charge. Consequently, it has the greatest penetrating power of all types of radiation. To reduce exposure to gamma radiation, dense materials such as lead are commonly used as shielding.

Mechanics of Nuclear Decay Processes

Specific nuclear decay processes result in predictable changes to the atomic number ( $Z$ ) and mass number ( $A$ ) of the parent isotope:

Alpha Decay: During alpha decay, the atomic number of the nucleus decreases by $2$ , and the mass number decreases by $4$ . An example of this is the decay of Uranium-238 to Thorium-234 ( $\text{Uranium-238} \rightarrow \text{Thorium-234} + \alpha$ ).

Beta-Minus Decay: In beta-minus decay, a neutron is converted into a proton while an electron (the beta particle) is emitted. This results in the atomic number increasing by $1$ . For example, an atom undergoing beta emission will have its atomic number increased by $1$ .

Positron Emission: This process occurs when a proton within the nucleus is converted into a neutron and a positron ( $\beta^+$ ). The positron is then emitted. During positron emission, the atomic number of the atom decreases by $1$ .

Gamma Emission: Gamma radiation is often emitted alongside other types of decay or to release excess energy. During gamma emission, the mass number and the atomic number of the isotope remain unchanged ( $\text{Cobalt-60} \rightarrow \text{Cobalt-60} + \gamma$ ).

Neutron-to-Proton Ratio: Radioactive decay processes serve to adjust the neutron-to-proton ratio of a nucleus to move it toward a more stable state. Different processes will either increase or decrease this ratio depending on the starting instability of the nucleus.

Isotopes and Half-Life Calculations

Isotopes are defined as atoms of the same element that have the same number of protons but different masses due to a different number of neutrons.

Radioactivity is measured over time using the concept of half-life, which is the time required for half of a radioactive sample to decay. According to the practice data:

Initial amount: $100\,g$
Amount remaining after one half-life: $50\,g$
Amount remaining after two half-lives (as recorded): $12.5\,g$

Nuclear Equations and Balancing

Nuclear equations must be balanced to account for both mass number and atomic number. Based on the practice sheets, the following balanced nuclear equations are evaluated for correctness:

Beta Decay of Potassium-38: $^{38}_{19}K \rightarrow ^{38}_{20}Ca + ^{0}_{-1}\beta$ In this reaction, the mass number stays at $38$ , while the atomic number increases from $19$ to $20$ .

Electron Capture of Promethium-142: $^{142}_{61}Pm + ^{0}_{-1}e \rightarrow ^{142}_{60}Nd$ In this reaction, an electron is captured, resulting in the atomic number decreasing from $61$ to $60$ .

Alpha Decay Radioisotopes: The sheet provides the following isotopes as subjects for balanced alpha decay equations:

Polonium-210 ( $^{210}_{84}Po$ )
Radon-222 ( $^{222}_{86}Rn$ )
Uranium-234 ( $^{234}_{92}U$ )
Thorium-230 ( $^{230}_{90}Th$ )

Periodic Table References

The practice sheet references various elements and their chemical properties as found in the periodic table:

Group 1A to 8A elements, including Boron ( $B$ , $10.811$ ), Carbon ( $C$ , $12.0107$ ), Nitrogen ( $N$ , $14.0067$ ), Oxygen ( $O$ , $15.9994$ ), Aluminum ( $Al$ , $26.9815$ ), Silicon ( $Si$ , $28.0855$ ), Phosphorus ( $P$ , $30.9737$ ), and Sulfur ( $S$ , $32.065$ ).
Transition metals such as Manganese ( $Mn$ , $54.938$ ), Iron ( $Fe$ , $55.845$ ), Cobalt ( $Co$ , $58.933$ ), Silver ( $Ag$ , $107.8682$ ), and Gold ( $Au$ , $196.966$ ).
Lanthanides and Actinides involved in decay chains, including Neodymium ( $Nd$ , $144.242$ ), Promethium ( $Pm$ , $145$ ), Thorium ( $Th$ , $232.038$ ), and Uranium ( $U$ , $238.02891$ ).