Chapter 4: Subatomic Particles and Atomic Structure

Atomic Models and Subatomic Particles

Atomic Models

• Physical Model: A scaled representation of something that is either too large or too small to study effectively at its actual size. Examples include architectural buildings or microscopic bacteria.

• Conceptual Model: A model used to describe a system that does not possess a regular or defined shape, such as atoms or weather patterns. A weather map, for instance, is a type of conceptual model.

Discovery of the Electron

• The electron was the first subatomic particle to be discovered.

• Cathode Ray Tube Experiment: This involved applying a voltage across a sealed tube of gas, which resulted in the production of a particle beam. This technology was foundational for early televisions.

  • Since these particles were observed to be drawn towards a positively charged plate, it was concluded that they must carry a negative charge.

  • Electrons are assigned a charge of $-1$.

  • Electrons are exceptionally light, with a mass approximately $1/2000$th that of a hydrogen atom.

Early Atomic Models

J. J. Thompson's Plum Pudding Model

• Proposed to address two key questions in atomic theory:

  • What neutralizes the negative charge of the electrons within an atom?

  • How are both positive and negative charges distributed and combined within the atom?

Rutherford's Gold Foil Experiment and Nuclear Model

• Objective: Ernest Rutherford designed an experiment in $1909$ to test the validity of Thompson's Plum Pudding Model.

• Experimental Design:

  • Used positively charged $\alpha$-particles (which are essentially Helium nuclei) accelerated to high speeds.

  • These $\alpha$-particles were directed towards an ultra-thin sheet of gold foil to minimize absorption.

  • Expected Result: According to the Plum Pudding Model, the $\alpha$-particles, being positively charged, should have passed through the uniformly distributed charge of the gold atoms with minimal or no deflection.

• Experimental Results:

  • The overwhelming majority of $\alpha$-particles passed straight through the gold foil without any deflection.

  • A small fraction of particles exhibited deflection.

  • Remarkably, about $1$ in $20,000$ $\alpha$-particles bounced back directly.

• Conclusion: Based on these unexpected results, Rutherford concluded that atoms must consist mostly of empty space, with a tiny, dense, positively charged central region which he termed the nucleus.

Subatomic Particles: Components of the Atom

The Nucleus

• Contains nucleons, which are protons and neutrons.

  • Protons: Carry a positive charge of $+1$.

  • Neutrons: Carry no electrical charge (neutral), meaning their charge is $0$.

• Mass: Both protons and neutrons have approximately the same mass, which is about $2000$ times greater than that of an electron, roughly equivalent to the mass of a hydrogen atom.

Properties of Subatomic Particles

• Note: The actual masses are calculated from experimental data and are not directly measured. The masses $9.11 \times 10^{-31} \text{ kg}$ is equivalent to $0.000000000000000000000000000000911 \text{ kg}$.

Atomic Number, Mass Number, and Isotopes

• Atomic Number: This is defined solely by the number of protons in an atom's nucleus. It determines the identity of an element.

• Mass Number: Represents the total number of nucleons (protons + neutrons) in an atom's nucleus.

  • Atoms of the same element always have the same atomic number (number of protons), but their mass numbers may differ.

• Isotopes: These are atoms of the same element (meaning they have the identical number of protons) but possess different mass numbers due to variations in their number of neutrons.

  • If the identity of an element is determined by the number of protons, then the atomic particle that must vary in isotopes is the neutron.

Examples of Isotopes

• Hydrogen Isotopes:

  • Hydrogen-1 (Protium): $1$ proton, $0$ neutrons.

  • Hydrogen-2 (Deuterium): $1$ proton, $1$ neutron.

  • Hydrogen-3 (Tritium): $1$ proton, $2$ neutrons.

• Iron Isotopes:

  • Iron-56: $26$ protons, $30$ neutrons.

  • Iron-55: $26$ protons, $29$ neutrons.

Practice Examples (Determination of p, n, e for neutral atoms/isotopes)

• For K-39 (Potassium-39):

  • Potassium (K) is Atomic Number $19$, so $19$ protons.

  • Neutrons: $39 \text{ (mass number)} - 19 \text{ (protons)} = 20$ neutrons.

  • Electrons: For a neutral atom, electrons = protons, so $19$ electrons.

• For $^{66}_{30}\text{Zn}$ (Zinc-66):

  • Zinc (Zn) is Atomic Number $30$, so $30$ protons.

  • Neutrons: $66 \text{ (mass number)} - 30 \text{ (protons)} = 36$ neutrons.

  • Electrons: For a neutral atom, electrons = protons, so $30$ electrons.

Atomic Mass: A Weighted Average

• Atomic Mass: Refers to the actual mass of an atom.

• Atomic Mass Unit (amu):

  • The standard unit for atomic mass.

  • Defined as exactly $1/12$ the mass of one atom of carbon-$-12$ ($^{12}\text{C}$).

  • $1 \text{ amu} = 1.66054 \times 10^{-24} \text{ g}$ (or $1.99265 \times 10^{-23} \text{ g}$ for a $^{12}\text{C}$ atom which has $12 \text{ amu}$).

  • For example, $^{12}\text{C}$ has an atomic mass of $12 \text{ amu}$. $^{13}\text{C}$ has an atomic mass of $13.00335 \text{ amu}$.

• Weighted Average Atomic Mass: The value typically listed on the periodic table. It is calculated by taking into account the mass of each naturally occurring isotope of an element and its relative natural abundance.

  • Formula: $\text{Weighted average atomic mass} = (\text{Mass of isotope 1} \times \text{Abundance of isotope 1}) + (\text{Mass of isotope 2} \times \text{Abundance of isotope 2}) + \ldots$

• Example (Carbon):

  • Carbon-12: Mass $12 \text{ amu}$, Abundance $98.89\%$

  • Carbon-13: Mass $13.00335 \text{ amu}$, Abundance $1.11\%$

  • $\text{Weighted average atomic mass of carbon}$:

  • $(12 \text{ amu} \times 0.9889) + (13.00335 \text{ amu} \times 0.0111)$

  • $= 11.8668 + 0.144337185 = 12.01113719 \approx 12.011 \text{ amu}$

• Practice Problem (Bromine):

  • Bromine has two isotopes: Br-$-79$ ($55\%$ abundance) and Br-$-81$ ($45\%$ abundance).

  • $\text{Weighted mass} = (79 \text{ amu} \times 0.55) + (81 \text{ amu} \times 0.45) = 43.45 + 36.45 = 79.90 \text{ amu}$

• Conceptual Practice: If element X has isotopes X-$-77$ ($80\%$ abundance), X-$-79$ ($10\%$ abundance), and X-$-75$ ($10\%$ abundance), its atomic mass would be closest to $77$ because X-$-77$ has the highest abundance. Calculated average is $(77 \times 0.80) + (79 \times 0.10) + (75 \times 0.10) = 61.6 + 7.9 + 7.5 = 77.0 \text{ amu}$. Thus, its atomic mass would be $77$.

Neutral Atoms and Ions

Neutral Atoms

• For an atom to be electrically neutral, the number of negatively charged electrons must exactly equal the number of positively charged protons.

  • $\text{Number of electrons} = \text{Number of protons}$

Summary of Subatomic Particle Roles

• Number of Protons ($\text{p}$):

  • Always determines the element's identity. If the number of protons changes, the element changes.

  • $=$ Number of electrons in a neutral atom.

• Number of Neutrons ($\text{n}$):

  • Can vary within an element, leading to isotopes.

  • Affects the atom's mass number.

• Number of Electrons ($\text{e}$):

  • Can vary, leading to charged atoms (ions).

  • Affects the atom's overall charge.

Ionic Charges (Ions)

• Elements can gain or lose electrons, resulting in a net electrical charge.

• This charge is indicated by a $+\text{ or } -$ sign in the upper right-hand corner of the chemical symbol.

  • Cations: Positively charged ions, formed when an atom loses electrons (e.g., $Ca^{2+}$, $Na^+$, $Fe^{3+}$).

  • Anions: Negatively charged ions, formed when an atom gains electrons (e.g., $N^{3-}$, $Cl^-$).

Practice Examples (Calculating p, n, e for neutral atoms)

• Cu-65 has $29$p, $36$n, $29$e (Cu is element $29$, $65-29=36$ neutrons, and for neutral atom, $29$ electrons).

• Rb-80 has $37$p, $43$n, $37$e (Rb is element $37$, for neutral atom, $37$ electrons, $80-37=43$ neutrons).

• Br-$80$ has $35$p, $45$n, $35$e (Br is element $35$, for neutral atom, $35$ electrons, $35+45=80$ mass number).

• F-19 has $9$p, $10$n, $9$e (F is element $9$, $19-9=10$ neutrons, and for neutral atom, $9$ electrons).

• S-$-32$ has $16$p, $16$n, $16$e (Atom with $16$ protons is Sulfur (S), $16+16=32$ mass number, and for neutral atom, $16$ electrons).

Light and Electromagnetic Radiation

• Light: A form of energy known as electromagnetic radiation.

• Electromagnetic Spectrum: Encompasses a wide range of wavelengths and frequencies, from high-energy gamma rays to low-energy radio waves. Visible light occupies a small portion of this spectrum.

  • Wavelength ($\lambda$): The distance between two consecutive crests or troughs of an electromagnetic wave.

    • Shorter wavelength implies higher energy.

    • Longer wavelength implies lower energy.

  • Wave Frequency ($\nu$): The number of wave oscillations (cycles) that pass a point per unit of time, typically measured in Hertz ($\text{Hz}$).

    • Higher frequency implies higher energy.

    • Higher frequency corresponds to a shorter wavelength (inverse relationship).

Atomic Spectra and Quantization of Light

• Splitting Light: White light is a composite of all visible light waves. Each color (or wavelength) has its own distinct frequency.

  • When white light passes through a prism or diffraction grating, it splits into its component colors, forming a continuous spectrum.

• Spectroscope: An instrument used to observe the color components of light. For white light, it shows a continuous band of all colors blending seamlessly.

• Light from Atoms: When atoms are excited by electricity or heat, they emit light that is not a continuous band. Instead, they emit discrete bands of color, forming a unique line emission spectrum.

  • This unique pattern of colors acts like a