Atomicity and Atomic Structure Comprehensive Study Notes

Course Introduction and Learning Outcomes

• Institution: SEETA UNIVERSITY
• Course: Chemistry
• Programme: Higher Education Certificate (HEC)
• Lecturer: MR. KYEYUNE FRANK
• Topic: ATOMICITY

Learning Outcomes: By the end of this topic, students should be able to:

• Describe the structure of the atom.
• Differentiate between atomic number, mass number, and isotopes.
• Explain radioactivity and its applications.
• Interpret simple mass spectra.
• Write electronic configurations.
• Explain periodic trends.
• Relate periodic trends to chemical bonding.

The Nature of Matter

• Definition of Matter: Matter is anything that has mass and occupies space. It exists in different forms and is made up of tiny particles. These particles can be grouped in different ways to form the substances around us.

Classification of Matter

• Pure Substances: These have a fixed composition and definite properties. They are subdivided into:
  • Elements: Made of only one type of atom. They cannot be broken down into simpler substances by chemical means. Examples include Iron ($Fe$), Copper ($Cu$), and Gold ($Au$).
  • Compounds: Made of two or more different elements chemically combined in a fixed ratio. They can be broken down into simpler substances by chemical means. Examples include Carbon dioxide ($CO_2$) and Water ($H_2O$).
• Mixtures: Made of two or more substances mixed physically in any proportion. Components can be separated by physical means. An example is Sodium chloride (table salt) ($NaCl$) dissolved in water.

Building Blocks

• Atoms: The smallest particles of an element that retain the properties of that element. Atoms are the building blocks of matter (e.g., $He$ atom, $O$ atom).
• Molecules: Two or more atoms chemically bonded together. Molecules may be of the same element (e.g., $O_2$) or of different elements (e.g., $H_2O$).

Summary of Relationship

• Matter forms Pure Substances or Mixtures.
• Pure Substances consist of Elements or Compounds.
• Elements are made of Atoms.
• Atoms form Molecules.
• Molecules of different elements form Compounds.

Atomic Structure and Fundamental Particles

• The Atom: Consists of a central Nucleus containing Protons and Neutrons, with Electrons arranged in shells or energy levels around it.

Table of Fundamental Particles

• Note: These are the fundamental particles of interest to chemistry students, excluding radioactivity.

Atomic Number, Mass Number, and Isotopes

• Atomic Number ($Z$): The number of protons in the nucleus of an atom.
• Atomic Mass (Mass Number, $A$): The sum of the number of protons and neutrons in the nucleus.
• Example (Carbon-12):
  • Protons: $6$
  • Neutrons: $6$
  • Electrons: $6$
  • Atomic Number = $6$
  • Atomic Mass = $12$
• Isotopes: Atoms of the same element that have the same number of protons but different numbers of neutrons.

Radioactivity and Isotope Stability

• Radioactive Isotopes (Radioisotopes): Isotopes with unstable nuclei that spontaneously decay, emitting radiation to become more stable.
• Radioactivity Definition: The spontaneous disintegration of an unstable atomic nucleus to stable nuclei accompanied by the emission of radiation in the form of alpha particles, beta particles, and/or gamma rays.

Factors Determining Isotope Stability

• Neutron : proton ratio ($n/p$ ratio).
• Atomic number.
• Atomic mass / Mass number.
• Binding energy: This is defined as the energy given out when a nucleus is formed from its constituent neutrons and protons, OR the energy required to separate the nucleus into its constituent neutrons and protons.

Properties of Radiations

Balancing Nuclear Equations

• Rule 1: Mass numbers ($A$) must balance. Total $A$ on the left = Total $A$ on the right.
• Rule 2: Atomic numbers ($Z$) must balance. Total $Z$ on the left = Total $Z$ on the right.

Examples of Nuclear Equations

• Alpha decay:
  • $_{92}^{238}U \rightarrow _{90}^{234}Th + _{2}^{4}He$
• Beta decay:
  • $_{7}^{14}N + _{-1}^{0}e \rightarrow _{6}^{14}C$ (Note: In standard beta emission, a neutron becomes a proton, e.g., Carbon-14 decay: $_{6}^{14}C \rightarrow _{7}^{14}N + _{-1}^{0}e$; the slide depicts a capture or reverse process).
• Gamma emission:
  • $_{27}^{60}Co \rightarrow _{27}^{60}Co + _{0}^{0}\gamma$

Practice Questions

1. $_{88}^{226}Ra \rightarrow \dots \dots \dots + _{2}^{4}He$
2. $_{53}^{131}I \rightarrow \dots \dots \dots + _{-1}^{0}e$

Radioactive Decay Law and Half-Life

Radioactive Decay Equations

• $\ln \frac{N_o}{N_t} = \lambda t$
• $2.303 \log \frac{N_o}{N_t} = \lambda t$
• Variables:
  • $N_o$ = initial activity/mass/percentage.
  • $N_t$ = activity/mass/percentage after time, $t$.
  • $\lambda$ = decay constant.
  • $t$ = time for decay.

Half-Life ($T_{1/2}$)

• Definition: The time it takes for half of the radioactive atoms in a sample to decay.
• At half-life, $N_t = \frac{N_o}{2}$.
• Calculation:
  • $\ln \left(\frac{N_o}{N_o/2}\right) = \lambda T_{1/2}$
  • $T_{1/2} = \frac{0.693}{\lambda}$

Worked Examples

1. Decay constant to Half-life: A radioactive isotope has a decay constant of $0.035\,day^{-1}$. Calculate its half-life.
2. Calculating Decay Constant: A radioactive sample initially contains $120\,g$. After $10\,days$, only $45\,g$ remains. Calculate the decay constant.
3. Calculating Remaining Mass: A radioactive sample has a decay constant of $0.046\,day^{-1}$. If the initial mass is $200\,g$, calculate the mass remaining after $15\,days$.

Further Practice Questions

1. A radioactive isotope has a decay constant of $0.025\,day^{-1}$. Calculate its half-life.
2. A sample decreases from $80\,g$ to $20\,g$ in $12\,hours$. Calculate the decay constant.
3. A radionuclide has a decay constant of $0.12\,year^{-1}$. Calculate the mass remaining from an initial $50\,g$ after $5\,years$.
4. A sample has a half-life of $8\,hours$. Calculate its decay constant.
5. A $150\,g$ radioactive sample is reduced to $75\,g$ in $6\,days$. Verify the half-life using both methods.

Applications of Radioisotopes

• Across a Period: Becomes more negative (stronger attraction for incoming electrons).
• Down a Group: Becomes less negative (weaker attraction due to large radius and shielding).

Electronegativity

• Definition: The tendency of an atom to attract the shared pair of electrons toward itself in a chemical bond.
• Across a Period: Increases.
• Down a Group: Decreases.

Questions & Discussion

Conceptual Question

• Question: Why is gamma radiation preferred for treating cancers deep inside the body, whereas alpha radiation is not?
• Context: Based on the properties table, gamma radiation has very high penetrating power (requiring thick lead to stop), allowing it to reach internal tumors. Alpha radiation has low penetrating power and is stopped by skin, meaning it cannot reach internal targets from outside the body.

Individual Assignment

1. Using Aufbau’s rule, Pauli’s exclusion principle, and Hund’s rule of maximum multiplicity, write the electronic configurations of Group II and Period 3 elements.
2. Explain the following trends in the periodic table across Period 3 and down Group II:
   • i) Ionisation energy
   • ii) Electron affinity
   • iii) Electronegativity
   • iv) Atomic radius