Guide to Nuclear Chemistry: Structure, Transmutation, and Applications

Foundations of Nuclear Chemistry and Atomic Structure

• Core Focus: Unlike traditional chemistry, which focuses on how the electrons of atoms and ions are shared, transferred, and involved in bonding, Nuclear Chemistry specifically focuses on the NUCLEUS.

• The Nature of Nuclear Chemistry: Nuclear chemistry is described as "weird" because it involves changes within the nucleus rather than electron movement.

Essential Atomic Components and Measurements

• Nucleus Construction: Atoms contain protons and neutrons within the nucleus, with electrons orbiting the outside.

• Electrical Neutrality: In every neutral atom, the number of positive protons equals the number of negative electrons ($p^+ = e^-$).

• Atomic Number: The Atomic Number is defined as the number of protons in an atom.

• Atomic Mass in High School Chemistry:

  • Defined as the sum of the number of protons ($p$) plus the number of neutrons ($n$).

  • Measured in Atomic Mass Units (AMUs).

  • Weight of individual particles: Each proton = $1\,AMU$; Each neutron = $1\,AMU$.

  • Molar Mass Correlation: Atomic mass (in amu) correlates to molar mass (in g/mole).

  • Helium ($He$): $4\,amu$ ($2p + 2n$ ) = $4\,g/mole$.

  • Mercury ($Hg$): $201\,amu$ ($80p + 121n$) = $201\,g/mole$.

  • Copper ($Cu$): $64\,amu$ ($29p + 35n$) = $64\,g/mole$.

• Calculating Neutrons and Electrons:

  • Example: Uranium (element 92) with an atomic mass of 238.

  • Calculation: $238\,(\text{protons + neutrons}) - 92\,(\text{protons}) = 126\,\text{neutrons}$.

  • Electron identification: Since there are 92 positive protons, there must be 92 negative electrons for the atom to remain neutral.

Element Identity and Isotopes

• Proton Identity: Every atom has a unique number of protons that determines its identity.

  • 12 protons = Magnesium ($Mg$).

  • 29 protons = Copper ($Cu$).

  • 90 protons = Thorium ($Th$).

• Isotopes: Atoms of the same element that possess a DIFFERENT number of neutrons but the SAME number of protons and electrons.

• Radium Example (The most common isotope):

  • Atomic symbol: $^{226}_{88}Ra$

  • Atomic Number: 88, which means 88 protons and 88 electrons.

  • Atomic Mass: $226\,AMU$.

  • Neutrons: $226 - 88 = 138\,\text{neutrons}$.

Isotopes and Nuclear Stability

• Stability and the Neutron-to-Proton Ratio:

  • Carbon-12 (C-12):

  • Mass: $12\,AMU$.

  • Numbers: 6 protons, 6 neutrons.

  • Ratio: $6:6$ or $1:1$. This ratio is stable; therefore, C-12 is not radioactive.

  • Carbon-14 (C-14):

  • Mass: $14\,AMU$.

  • Numbers: 6 protons, 8 neutrons.

  • Ratio: $8:6$ or $1.33:1$. This ratio is unstable; therefore, C-14 is radioactive.

  • Phosphorous-31 (Stable P):

  • Mass: $31\,AMU$.

  • Numbers: 15 protons, 16 neutrons.

  • Ratio: $16:15$, which is stable.

  • Phosphorous-32 (Radioactive P):

  • Mass: $32\,AMU$.

  • Numbers: 15 protons, 17 neutrons.

  • Ratio: $17:15$, which is unstable.

• The Zone of Stability:

  • Of the 118 known elements, there are approximately 1500 known isotopes.

  • Most isotopes are stable. Only about 150 are unstable (radioactive).

  • Stable Ratios by Atom Size:

  • Smaller atoms (up to Calcium, $Ca$): approximately $1\,n^0/p^+$.

  • Medium atoms (up to Zirconium, $Zr$): approximately $1.25\,n^0/p^+$.

  • Larger atoms (the rest): approximately $1.5\,n^0/p^+$.

  • Ratios outside this "band of stability" are unstable and must fix the ratio to become stable.

Radioactive Particles and Radiation Properties

• Emission Mechanism: Unstable isotopes emit radiation (nuclear particles and/or energy) to fix a "funky" neutron-to-proton ratio and achieve stability.

• Reference Table O: Lists official symbols, masses, and charges for radioactive particles.

• Types of Radiation:

  • Alpha ($\alpha$):

  • Symbol: $^4_2He$

  • Mass: $4\,AMU$

  • Charge: $+2$

  • Penetrating Power: WEAKEST (stopped by paper).

  • Beta (Beta-minus, $\beta^-$):

  • Symbol: $^0_{-1}e$

  • Mass: Zero (as defined in High School)

  • Charge: $-1$

  • Penetrating Power: STRONG (stopped by aluminum/metal).

  • Origin: A neutron emits a negative charge of no mass and becomes a proton ($n^0 \rightarrow p^+ + \beta^-$).

  • Gamma ($\gamma$):

  • Symbol: $^0_0\gamma$

  • Mass: Zero

  • Charge: Neutral

  • Penetrating Power: STRONGEST (stopped by lead; nothing stops it completely).

  • Neutron ($n$):

  • Symbol: $^1_0n$

  • Mass: $1\,AMU$

  • Charge: Neutral

  • Penetrating Power: MEDIUM (stopped by water/concrete/lead).

  • Proton ($p$):

  • Symbol: $^1_1H$

  • Mass: $1\,AMU$

  • Charge: $+1$

  • Positron (Beta-plus, $\beta^+$):

  • Symbol: $^0_{+1}e$

  • Mass: Zero (as defined in High School)

  • Charge: $+1$

  • Penetrating Power: Similar to Beta particles.

  • Origin: A proton emits a positive charge of no mass and becomes a neutron ($p^+ \rightarrow n^0 + \beta^+$).

Transmutation: Natural and Artificial

• Transmutation Definition: The process of a nucleus changing into a different kind of atom (changing the neutron-to-proton ratio).

• Natural Transmutation (Radioactive Decay):

  • Occurs spontaneously on its own.

  • Nothing can speed up or slow down this process.

  • Examples from Table N:

  • Alpha Decay of U-238: $^{238}_{92}U \rightarrow ^4_2He + ^{234}_{90}Th$. U-238 transforms into Thorium-234.

  • Beta Decay of C-14: $^{14}_6C \rightarrow ^0_{-1}e + ^{14}_7N$. Carbon transmutes into Nitrogen-14 as a neutron becomes a proton.

  • Positron Decay of Ca-37: $^{37}_{20}Ca \rightarrow ^0_{+1}e + ^{37}_{19}K$. Calcium transmutes into Potassium-37.

  • Alpha Decay of Ra-226: $^{226}_{88}Ra \rightarrow ^4_2He + ^{222}_{86}Rn$. Radium transmutes into Radon-222.

  • Beta Decay of Cs-137: $^{137}_{55}Cs \rightarrow ^0_{-1}e + ^{137}_{56}Ba$. Cesium transmutes into Barium-137.

  • Positron Decay of Fe-53: $^{53}_{26}Fe \rightarrow ^0_{+1}e + ^{53}_{25}Mn$. Iron transmutes into Manganese-53.

  • Beta Decay of Au-198: $^{198}_{79}Au \rightarrow ^0_{-1}e + ^{198}_{80}Hg$. Gold transmutes into Mercury-198.

  • Positron Decay of Ne-19: $^{19}_{10}Ne \rightarrow ^0_{+1}e + ^{19}_9F$. Neon transmutes into Fluorine-19.

  • Alpha Decay of Fr-220: $^{220}_{87}Fr \rightarrow ^4_2He + ^{216}_{85}At$. Francium transmutes into Astatine-216.

• Artificial Transmutation:

  • Caused by humans; done by scientists through bombardment.

  • Historical Examples:

  • Ernest Rutherford (1919): Bombarded Nitrogen with alpha particles. Reaction: $^{14}_7N + ^4_2He \rightarrow ^{17}_8O + ^1_1p$.

  • James Chadwick (1932): Bombarded Beryllium with alpha particles (led to the discovery of the neutron). Reaction: $^9_4Be + ^4_2He \rightarrow ^{12}_6C + ^1_0n$.

  • Marie Curie (1934): Created the first artificial radioisotope by bombarding Aluminum. Reaction: $^{27}_{13}Al + ^4_2He \rightarrow ^{30}_{15}P + ^1_0n$.

Half-Life and Radioactive Decay Problems

• Half-Life Definition: The amount of time required for one half of a given radioisotope to transmute.

• Values from Table N:

  • Gold-198 ($Au-198$): $2.695\,days$

  • Carbon-14 ($C-14$): $5715\,years$

  • Calcium-37 ($Ca-37$): $182\,ms$

  • Uranium-238 ($U-238$): $4.47 \times 10^9\,years$

  • Plutonium-239 ($Pu-239$): $2.410 \times 10^4\,years$

  • Radium-226 ($Ra-226$): $1599\,years$

  • Radon-222 ($Rn-222$): $3.823\,days$

  • Strontium-90 ($Sr-90$): $29.1\,years$ (derived from calculation)

• Half-Life T-Chart Rules:

  • Always make a T-chart.

  • Used to solve for: % left/transmuted, grams left/transmuted, fractions, or time elapsed.

• Practice Problem Calculations:

  • C-14 (22.0g to 2.75g): This is 3 half-lives ($22.0 \rightarrow 11.0 \rightarrow 5.50 \rightarrow 2.75$). Calculation: $3 \times 5715 = 17,145\,years$.

  • I-131 (2.00g to 0.125g): This is 4 half-lives ($2.00 \rightarrow 1.00 \rightarrow 0.500 \rightarrow 0.250 \rightarrow 0.125$). Calculation: $4 \times 8.021 = 32.084\,days$.

  • Fe-53 (400.0g to 12.5g): This is 5 half-lives. Calculation: $5 \times 8.51\,minutes = 42.55\,minutes$.

  • Na-25 half-life: If 1.00g remains of 16.00g after 237 seconds: ($16 \rightarrow 8 \rightarrow 4 \rightarrow 2 \rightarrow 1$) = 4 cycles. Calculation: $237 / 4 = 59.3\,seconds$.

Nuclear Energy: Fission and Fusion

• Einstein’s Equation: $E = mc^2$. Energy equals mass times the speed of light squared. Matter and energy are different forms of the same thing.

• Mass Defect: The missing mass in a nuclear reaction that was converted into energy. The Law of Conservation of Mass does not apply in nuclear chemistry.

• Nuclear Fission:

  • The splitting of atoms by artificial transmutation.

  • Triggered by neutron bombardment to start a chain reaction.

  • Example: $^{235}_{92}U + ^1_0n \rightarrow ^{140}_{56}Ba + ^{93}_{36}Kr + 3\,^1_0n + \text{energy}$.

  • Example: $^{235}_{92}U + ^1_0n \rightarrow ^{144}_{54}Xe + ^{90}_{38}Sr + 2\,^1_0n + \text{energy}$.

  • Each cycle releases more neutrons, facilitating exponential growth (3, 9, 27…).

  • Comparing Bomb vs. Power Plant: In a bomb, the chain reaction is an "out of control" release of energy in seconds. In a power plant, it is controlled over months.

• Nuclear Fusion:

  • The "squishing together" of smaller atoms to make larger ones.

  • Loss of mass occurs during the process (mass defect).

  • Fusion is much more powerful than fission.

  • Solar Fusion: The Sun squashes 4 hydrogen atoms into helium: $4\,^1_1H \rightarrow ^4_2He + 2\,^0_{+1}e + \text{energy}$.

  • Laboratory Fusion: Humans use isotopes of hydrogen ($H-2$ and $H-3$) because fusing normal $H-1$ requires temperature/pressure that is too high for containment: $^2H + ^3H \rightarrow ^4_2He + ^1_0n + \text{energy}$.

Nuclear Power Plant Mechanics

• Method of Electricity Generation: Heat from fission $\rightarrow$ Water turns to steam $\rightarrow$ Steam spins turbine blades $\rightarrow$ Spinning rotates magnets around copper wire in a generator $\rightarrow$ Electricity created.

• Core Components:

  • Reactor Vessel: Location of the fission reaction (U-235 bombardment).

  • Control Rods: Made of materials like Cadmium, Silver, or Indium. They absorb neutrons to slow down/moderate the reaction and prevent explosion.

  • Containment Structure: Reinforced dome designed to keep radiation in and external factors out.

• Water Loops:

  • Inner Loop (Pink/Red): Highly radioactive water in close contact with the reactor; stays sealed in the containment dome.

  • Secondary Loop (Blue): Picks up heat from the inner loop via heat exchange; turns into steam to spin turbines.

  • Cooling Loop: Uses water from an outside source (lake/ocean) to condense turbine steam back into water. This releases excess heat via cooling towers.

• Pros and Cons of Nuclear Energy:

  • Pros: Low CO2 emissions, reliable, national energy independence, low operating costs.

  • Cons: Mining impact, potential for disasters, high setup cost, limited uranium supplies, creation of long-term radioactive waste (remains dangerous for 20,000+ years).

Practical and Medical Applications

• Radioactive Carbon Dating:

  • Mechanism: High-energy neutrons hit nitrogen in the atmosphere: $n + ^{14}_7N \rightarrow ^{14}_6C + ^1_1p$.

  • Constant ratio: Living things have a constant ratio of C-14 to C-12 because they replace carbon through eating.

  • After death: The organism stops eating; C-14 begins decaying into nitrogen without replacement.

  • Limit: Accurate up to 50,000 years. Cannot date dinosaurs.

  • Case Study: La Brea Tar Pits (Mastodons preserved in tar used for dating).

• Medical Radioisotopes:

  • Iodine-131: Used for thyroid disorder diagnosis and treatment. The gland picks up radioactive iodine chemically; beta radiation emitted can kill thyroid cancer cells.

  • Cobalt-60: Used for internal cancer treatment. Emits beta radiation beams aimed precisely at tumors to kill cancer cells with minimal healthy cell damage.