CHEM 2090 Comprehensive Study Notes: The Atom, Nuclear Chemistry, and Atomic Structure
The Atom and Nuclear Chemistry
The Atom: Fundamental Concepts
Definition of Atom: The smallest component of an element.
Definition of Element: A substance that cannot be separated into simpler substances by chemical means.
Definition of Compound: Consists of two or more different elements chemically bonded together (e.g., XxYy).
Atom as Basic Unit: The basic unit of an element that can enter into a chemical combination.
Atomic Structure
Nucleus:
Positively charged, extremely dense, contains most of the atom's mass.
Radius: approximately 10^{-14} to 10^{-13} cm.
Composed of protons (p) and neutrons (n).
Protons (p): Positively charged. Charge unit: +1. Charge in Coulombs: +1.6022 \times 10^{-19} C. Mass: 1.672622 \times 10^{-24} g.
Neutrons (n): No charge (neutral). Charge unit: 0. Mass: 1.674928 \times 10^{-24} g.
Electrons (e-): Negatively charged, much less massive than protons or neutrons.
Located approximately 10^{-8} cm away from the nucleus.
Charge unit: -1. Charge in Coulombs: -1.6022 \times 10^{-19} C. Mass: 9.1094 \times 10^{-28} g.
Ions
Neutral Atom: Occurs when number of protons (np) = number of electrons (ne).
Positive Ion (Cation): Occurs when np > ne. Overall positive charge.
Negative Ion (Anion): Occurs when np < ne. Overall negative charge.
Atomic Notation
Atomic Mass Unit (amu): Defined as 1/12 the mass of a carbon-12 atom. Approximately equal to the mass of a proton or neutron (1 \text{ amu} \approx 1.6605 \times 10^{-24} \text{ g}).
Elemental Symbol: Represents the element.
Mass Number (A): Written as a superscript before the symbol (^AZ\text{Elem}). It is the total number of protons and neutrons in the nucleus (A = np + n_n).
Isotopes: Atoms of the same element (same number of protons, Z) but with different numbers of neutrons (different mass numbers, A). For example, Carbon-12 (^{12}6\text{C}) and Carbon-14 (^{14}6\text{C}).
Atomic Number (Z): Written as a subscript before the symbol (^A_Z\text{Elem}). It is the number of protons, which defines the element. The number of electrons in a neutral atom is also Z.
Example: ^{35}_{17}\text{Cl} means Chlorine with mass number 35 and atomic number 17. It has 17 protons and 35 - 17 = 18 neutrons.
Scale Analogy: If the average nucleus were a golf ball, the average electron would be about 2000 meters away.
Discovery of the Electron
J. J. Thompson's Experiment (1897)
Objective: To determine the charge-to-mass ratio (e/m) of an electron.
Method: Used a cathode ray tube (CRT). He observed that cathode rays (streams of electrons) were deflected by electric and magnetic fields. By balancing the electric and magnetic forces, he could determine the e/m ratio.
Conclusion: The cathode rays were composed of negatively charged particles (electrons) much smaller than atoms. This led to the "plum pudding" model of the atom.
Discovery of the Nucleus
Ernest Rutherford's Gold Foil Experiment (1911)
Objective: To test the "plum pudding" model of the atom and determine the internal structure of the atom.
Method: Directed a beam of positively charged alpha particles at a very thin sheet of gold foil. A detector screen was placed around the foil to observe the scattering of alpha particles.
Observations:
Most alpha particles passed straight through the foil with little or no deflection.
A small percentage of alpha particles were deflected at very large angles, some even bouncing straight back.
Conclusion:
The atom is mostly empty space (explaining why most alpha particles passed through).
There is a small, dense, positively charged center within the atom, which he called the nucleus (explaining the large-angle deflections and reflections). This experiment disproved the "plum pudding" model and led to the nuclear model of the atom.
Nuclear Chemistry: Radioactivity and Decay
Radioactivity
Definition: The spontaneous emission of radiation by an unstable atomic nucleus.
Unstable Isotopes (Radionuclides): Isotopes with an unstable nucleus that undergo radioactive decay to achieve a more stable configuration.
Nuclear Force: The strong attractive force between nucleons (protons and neutrons) in the atomic nucleus, much stronger than the electrostatic repulsion between protons.
Belt of Stability: A region on a plot of neutron number versus proton number where stable nuclei are found. Nuclei outside this belt tend to be radioactive.
Types of Radioactive Decay
Alpha (\alpha) Decay:
Emission of an alpha particle (a helium nucleus, ^4_2\text{He}) from the nucleus.
Occurs mainly in very heavy nuclei (Z > 83) to reduce both mass number and atomic number.
The parent nucleus's atomic number decreases by 2 and its mass number decreases by 4.
Example: ^{238}{92}\text{U} \rightarrow ^{234}{90}\text{Th} + ^4_2\text{He}
Beta (\beta) Decay:
Beta-minus (\beta^-) Decay: Emission of an electron (^0_{-1}\text{e}) from the nucleus.
Occurs when a neutron converts into a proton and an electron (n \rightarrow p + e^-).
Increases the atomic number by 1, while the mass number remains unchanged.
Example: ^{14}6\text{C} \rightarrow ^{14}7\text{N} + ^0_{-1}\text{e}
Beta-plus (\beta^+ or Positron) Decay: Emission of a positron (a positively charged electron, ^0_{+1}\text{e}) from the nucleus.
Occurs when a proton converts into a neutron and a positron (p \rightarrow n + e^+).
Decreases the atomic number by 1, while the mass number remains unchanged.
Example: ^{22}{11}\text{Na} \rightarrow ^{22}{10}\text{Ne} + ^0_{+1}\text{e}
Electron Capture (EC): A nucleus captures an inner-shell electron.
A proton converts into a neutron (p + e^- \rightarrow n).
Decreases the atomic number by 1, while the mass number remains unchanged.
Example: ^{81}{37}\text{Rb} + ^0{-1}\text{e} \rightarrow ^{81}_{36}\text{Kr}
Gamma (\gamma) Emission:
Emission of high-energy photons (gamma rays) from an excited nucleus.
Often accompanies other decay processes as the nucleus transitions from a higher energy state to a lower one.
Does not change the atomic number or mass number, as it involves energy release, not particle emission.
Example: A nucleus (X^) in an excited state emits a gamma ray to reach a stable state (X): X^ \rightarrow X + \gamma
Neutron Emission:
Emission of a neutron (^1_0\text{n}) from an unstable nucleus.
Converts a neutron into a proton, but mass number decreases by 1 while atomic number remains the same.
Occurs in very neutron-rich nuclei.
Example: ^{87}{35}\text{Br} \rightarrow ^{86}{35}\text{Br} + ^1_0\text{n}
Half-Life and Radioactive Decay Kinetics
Half-Life (t_{1/2})
Definition: The time required for half of the radioactive nuclei in a sample to undergo decay.
First-Order Process: Radioactive decay follows first-order kinetics, meaning the rate of decay is proportional to the number of radioactive nuclei present.
Decay Constant (\lambda): A constant characteristic of each radionuclide, representing the probability of decay per unit time.
Half-life Formula: t_{1/2} = \frac{\text{ln}(2)}{\lambda} = \frac{0.693}{\lambda}
Calculation of Remaining Amount: Nt = N0 \left(\frac{1}{2}\right)^n, where Nt is the amount at time t, N0 is the initial amount, and n is the number of half-lives elapsed (n = t/t_{1/2}).
Nuclear Reactions: Fission and Fusion
Nuclear Fission
Definition: The process by which a heavy atomic nucleus splits into two or more smaller nuclei, often accompanied by the release of a large amount of energy and neutrons.
Induced Fission: Usually initiated by bombarding a heavy nucleus (e.g., Uranium-235, Plutonium-239) with a neutron.
Chain Reaction: The neutrons released during fission can induce further fission in other heavy nuclei, leading to a self-sustaining chain reaction.
Critical Mass: The minimum amount of fissile material needed to sustain a nuclear chain reaction.
Applications: Nuclear power plants (controlled chain reactions) and atomic bombs (uncontrolled chain reactions).
Example: ^{235}{92}\text{U} + ^10\text{n} \rightarrow ^{141}{56}\text{Ba} + ^{92}{36}\text{Kr} + 3^1_0\text{n} + \text{energy}
Nuclear Fusion
Definition: The process by which two light atomic nuclei combine to form a single heavier nucleus, releasing immense amounts of energy.
Conditions: Requires extremely high temperatures (millions of degrees Celsius) and pressures to overcome the electrostatic repulsion between the positively charged nuclei.
Occurrence: The primary energy source of stars, including our Sun.
Potential Applications: Future clean energy source on Earth, if controlled fusion can be achieved (e.g., tokamak reactors).
Example: ^21\text{H} + ^31\text{H} \rightarrow ^42\text{He} + ^10\text{n} + \text{energy} (Deuterium-Tritium fusion)
Applications of Nuclear Chemistry
Medicine:
Diagnosis: Medical imaging (PET scans using eta^+ emitters like Fluorine-18), diagnostic tracers.
Treatment: Radiation therapy for cancer (Cobalt-60, Iodine-131 for thyroid cancer), sterilization of medical equipment.
Energy Generation: Nuclear power plants.
Dating and Archaeology: Radiometric dating (Carbon-14 dating for organic materials, Uranium-Lead dating for geological samples).
Industrial Applications: Smoke detectors (Americium-241), industrial radiography, sterilization of food and agricultural products.
Research: Tracers in