Nuclear Chemistry Lecture
NUCLEAR CHEMISTRY: AN OVERVIEW
Pertains to the study of atomic structure and interactions, how atoms bind together, and the forces within atomic nuclei.
This field encompasses the study of radioactivity, nuclear processes like fission and fusion, and the applications of nuclear phenomena in various scientific and technological fields, including medicine, energy production, and dating.
FLOURINE ATOM MASS CALCULATIONS
Isotope of Fluorine: ^{19}F
Atomic Mass: 18.9984 AMU (Atomic Mass Units)
Calculating individual particle masses:
Mass of Proton: 1.007825 AMU (1.6726 imes 10^{-27} kg)
Mass of Neutron: 1.008665 AMU (1.6749 imes 10^{-27} kg)
Mass of Electron: 0.00054858 AMU (9.109 imes 10^{-31} kg)
Query: Why doesn’t the mass add up? The sum of the masses of individual protons, neutrons, and electrons in an atom is always greater than the measured atomic mass of the atom. This difference is known as the mass defect, and it is accounted for by the energy released when the nucleus forms.
MASS DEFECT
Explanation: Mass defect refers to the difference between the sum of the masses of the constituent nucleons (protons and neutrons) and electrons, and the actual measured mass of the atom. It is the mass equivalent of the nuclear binding energy.
Einstein's consideration was that energy loss occurs when forming a nucleus, due to the strong nuclear force, leading to a mass defect. This lost mass is converted into the binding energy that holds the nucleus together.
Concept of mass-energy equivalence: all atoms experience some level of mass defect due to energy release during their formation, meaning their actual mass is slightly less than the sum of their parts.
E = mc²
Einstein’s formula describes the relationship between mass (m, in kilograms) and energy (E, in Joules), where 'c' is the speed of light in a vacuum (2.9979 imes 10^8 m/s).
This equation demonstrates that mass and energy are interchangeable; a small amount of mass can be converted into a tremendous amount of energy, and vice versa.
How to implement:
Insert the change in mass (mass defect) in KG into the equation E=\Delta mc^2.
Energy (E) measured in Joules (J), with Joules defined as rac{(kg imes m^2)}{s^2}. For nuclear reactions, the energy released is typically enormous.
ENERGY IN THE UNIVERSE
Query: How much energy encapsulates the subatomic particles in an atom of Fluorine (F)? This refers to the binding energy associated with its mass defect.
Given: 1.00 KG = 6.022 imes 10^{26} AMU (This is the definition of the atomic mass unit in relation to kilograms for general conversion).
Comparative Analysis: How many Joules are in a mole of Fluorine? This involves calculating the mass defect for a mole of fluorine and then converting that mass into energy using E=mc^2.
Comparison with energy in gasoline: 1.3 x 10^8 Joules per gallon (approximately). Nuclear reactions typically release orders of magnitude more energy than chemical reactions like burning gasoline. For example, the binding energy of a mole of Carbon-12 is about 8.6 imes 10^{12} Joules, which is thousands of times greater than the energy from gasoline.
CALCULATING MOLE ENERGY
Energy holding a mole of ^{12}C:
Molar Mass (MM): 12.000 g/mol (by definition of Carbon-12 scale).
Mass of Protons: 6 protons * 1.007276 g/mol = 6.043656 g/mol.
Mass of Neutrons: 6 neutrons * 1.008665 g/mol = 6.05199 g/mol.
Mass of Electrons: 6 electrons * 0.00054858 g/mol = 0.00329148 g/mol.
Total calculated mass of constituents = 6.043656 + 6.05199 + 0.00329148 = 12.09893748 g/mol.
Steps:
Calculate mass defect: ext{Mass Defect} = ( ext{mass of protons} + ext{mass of neutrons} + ext{mass of electrons}) - ext{actual molar mass}
= 12.09893748 \text{ g/mol} - 12.000 \text{ g/mol} = 0.09893748 \text{ g/mol}.Convert mass defect to kg: 0.09893748 \text{ g/mol} imes (1 \text{ kg} / 1000 \text{ g}) = 9.893748 imes 10^{-5} \text{ kg/mol}.
Calculate energy: E = \Delta mc^2 = (9.893748 imes 10^{-5} \text{ kg/mol}) imes (2.9979 imes 10^8 \text{ m/s})^2 \approx 8.90 imes 10^{12} \text{ J/mol}.
BINDING ENERGY
Definition: Binding energy is the energy released when a mole of nuclei is formed from its constituent protons and neutrons, or the energy required to break a mole of nuclei apart. For Carbon-12, this equals approximately 8.90 imes 10^{12} Joules.
Binding energy reflects stability: A higher binding energy per nucleon indicates a more stable nucleus, as more energy is required to break it apart.
CALCULATING BINDING ENERGY IN CARBON
For isotope ^{13}C with a molar mass of 13.00335g:
Number of protons: 6 (Mass of 6 protons: 6 imes 1.007276 \text{ g/mol} = 6.043656 \text{ g/mol})
Number of neutrons: 7 (Mass of 7 neutrons: 7 imes 1.008665 \text{ g/mol} = 7.060655 \text{ g/mol})
Number of electrons: 6 (Mass of 6 electrons: 6 imes 0.00054858 \text{ g/mol} = 0.00329148 \text{ g/mol})
Total calculated constituent mass = 6.043656 + 7.060655 + 0.00329148 = 13.10760248 g/mol.
Steps to calculate:
Calculate mass defect: ext{Mass Defect} = 13.10760248 \text{ g/mol} - 13.00335 \text{ g/mol} = 0.10425248 \text{ g/mol}. (Convert to kg: 1.0425248 imes 10^{-4} \text{ kg/mol}. )
Calculate binding energy: E = \Delta mc^2 = (1.0425248 imes 10^{-4} \text{ kg/mol}) imes (2.9979 imes 10^8 \text{ m/s})^2 \approx 9.37 imes 10^{12} \text{ J/mol}.
Compare values for stability between ^{13}C and ^{12}C: To compare stability, we need to calculate binding energy per nucleon for each isotope.
NUCLEON BINDING ENERGY
Definition: Binding energy in nuclear terms holds a nucleus together. It is the energy required to disassemble an atom's nucleus into its constituent protons and neutrons.
Nucleons = protons + neutrons reside in the nucleus (12 nucleons in ^{12}C, 13 nucleons in ^{13}C).
Determine binding energy per nucleon: Divide the total binding energy by the number of nucleons (mass number, A).
For ^{12}C: (8.90 imes 10^{12} \text{ J/mol}) / 12 \text{ mol nucleons} \approx 7.42 imes 10^{11} \text{ J/nucleon mol}. This value provides a more accurate measure of nuclear stability as it normalizes the binding energy across different sized nuclei.
NUCLEUS STABILITY
Stability is primarily a resultant of binding energy per nucleon. The higher this value, the more stable the nucleus.
Large energy implications are required to break a nucleus apart, demonstrating the immense strength of the strong nuclear force.
Nuclei with mass numbers around 56 (like iron-56) have the highest binding energy per nucleon, indicating they are the most stable nuclei.
CHEMICAL REACTIONS
Atoms remain unchanged during chemical reactions; only their electron configurations and bonding arrangements are altered. The nuclei are not affected.
Energy changes in these reactions are generally much smaller (in thousands of KJ/mol) compared to nuclear reactions (billions of KJ/mol). This highlights the fundamental difference in the forces and particles involved.
Example: Alchemical claim of changing lead into gold has zero possibility based on stability, as it would require nuclear transformation, not just chemical alteration.
NUCLEUS INTEGRITY
Query: Despite an immense scale of energy, why doesn’t the nucleus dismantle? This is due to the strong nuclear force.
Force of interest: The strong force (or strong nuclear interaction) is the most powerful of the four fundamental forces. It is responsible for holding the nucleus together by binding protons and neutrons.
Condition: The strong force must be strong enough to overcome the repulsive electrostatic forces (Coulomb repulsion) between positively charged protons within the confined space of the nucleus. It is a very short-range force, effective only over distances ~10^{-15} m.
NEUTRON ROLE IN STABILITY
Neutrons add to overall mass and contribute to the strong nuclear force without adding any electrostatic repulsion, thus buffering against proton-proton repulsion.
They act as a