Atomic Number, Mass Number & Isotopes

Key Definitions

• Atomic Number (Z) signifies the number of protons in an atom.
• Mass Number (A) represents the sum of protons and neutrons in an atom.
• Isotopes/Nuclides are atoms sharing the same atomic number but differing in mass numbers and neutron counts.
• Nucleons are particles constituting the nucleus, which includes protons and neutrons; their total number equals the mass number.

Nuclear Facts

• The nucleus is very small and dense.
• The nucleus is held together by the nuclear strong force.
• Protons and neutrons are located within the nucleus.
• Most of an atom's mass is concentrated in the nucleus.

Mass Defect

• The mass of an atom is not equivalent to the sum of its constituent particles' masses, which include protons, neutrons and electrons.
• Protons have a mass of 1.007276 amu.
• Neutrons have a mass of 1.008665 amu.
• Electrons have a mass of 0.0005486 amu.
• Mass defect refers to the variance between an atom's calculated and actual mass.
• According to Albert Einstein, the lost mass during nucleus formation is converted into energy.

Nuclear Binding Energy

• Nuclear binding energy is the energy released during the formation of a nucleus from nucleons, which can be calculated using E=mc².
• The variable "m" represents mass in kilograms in Einstein's equation.
• The constant "c" stands for the speed of light squared, equaling 3.00 x 108 m/s.

Binding Energy per Nucleon

• Binding energy per nucleon is used in comparing stabilities among different nuclides.
• It's determined by dividing the nucleus's binding energy by its total number of nucleons.
• Higher binding energy per nucleon indicates a more stable nuclide because it is tightly packed together.
• Elements possessing intermediate atomic masses exhibit the highest binding energies per nucleon, making them exceptionally stable; iron stands out as the most stable isotope.

Nuclear Stability

• The nuclear strong force balances the electrostatic forces between protons to keep the nucleus intact.
• The nuclear strong force enables proton attraction at short distances.
• More neutrons are needed to enhance the nuclear force and stabilize the nucleus.
• Nuclides with an atomic number greater than 83 do not have stable isotopes.

Band of Stability

• Stable nuclides have a specific neutron-to-proton ratio.
• Plotting the number of neutrons against the number of protons reveals a pattern.
• The neutron-proton ratio for stable isotopes clusters around a "band of stability."
• For atoms with low atomic numbers, the stable neutron-to-proton ratio is about 1:1.
• As the atomic number increases, this ratio increases to approximately 1.5:1.

Magic Numbers

• Stable nuclides often have even numbers of nucleons.
• 256 stable nuclides have been identified.
• 159 stable nuclides have even numbers of both protons and neutrons.
• Only 4 stable nuclides have odd numbers of both protons and neutrons.
• 2, 8, 20, 28, 50, 82, and 126 are considered magic numbers.

Nuclear Shell Model

• Nucleons exist in distinct energy levels within the nucleus, analogous to electron shells in atoms.
• Nucleon numbers such as 2, 8, 20, 28, 50, 82, and 126 correspond to completed nuclear energy levels, known as magic numbers.

Nuclear Reactions

• Unstable nuclei spontaneously change, thus altering the counts of protons and/or neutrons.
• These reactions release substantial energy through radioactive decay.
• Unstable radioisotopes transform into stable isotopes of other elements.
• Both mass number and atomic number must be conserved on both sides of the reaction equation
• A transformation (transmutation) in nuclear identity arises from a change in proton count.

Types of Radiation

• Nuclear reactions can result in the emission of radiation.
• Alpha Radiation consists of heavy, short-range particles equivalent to helium nuclei without electrons.
• Alpha radiation is composed of 2 protons and 2 neutrons, carrying a +2 charge after shedding both electrons with a large mass of 4 amu.
• Alpha radiation is easily shielded by paper or clothing and has low penetration power.
• Alpha radiation reduces the mass number by 4 amu and the atomic number by 2.
• Beta Radiation involves fast-moving electrons formed in nuclei with excess neutrons.
• When beta radiation occurs, a neutron converts into a proton and emits a beta particle.
• Beta particles are electrons not belonging in the nucleus that are thrown out.
• Beta radiation has a charge of -1 and a mass of 1/1840 or 0.0005486 amu, with moderate penetration powers.
• Metal foil can shield beta radiation.
• Beta radiation emitted causes the mass number to remain unchanged, while the atomic number increases by 1.
• Positron emission consists of a positive electron with a charge of +1 and the same mass as an electron (1/1840 or 0.0005486 amu).
• Positron emission converts a proton into a neutron, which decreases the atomic number by 1.
• Electron Capture happens in unstable nuclei with too many protons like positron emission.
• In electron capture, an inner orbiting electron is absorbed using a proton converted to neutrons.
• The mass number remains the same but the atomic number decreases by 1.
• Gamma radiation comprises high-energy electromagnetic radiation.
• Gamma radiation has no mass and no charge, with no effect on the nucleus.
• Lead or concrete is used as a shield and is always released with another form of radiation.

Half-Life

• Each radioisotope has its unique decay rate.
• t1/2 symbolizes the duration it takes for half of the atoms in a radioactive nuclide to decay.
• Longer half-lives indicate greater nuclide stability.
• The half-life variable descriptions: Ao = original amount, A = final amount, T = total time elapsed, t1/2 = half-life, and n = number of half-lives.

Decay series

• A decay series is a series of radioactive nuclides produces by successive radio active decay until a stable nuclide is reached.
• In decay series, the initial nuclide is the heaviest, which is called the parent nuclide and its product nuclides are called daughter nuclides.

Artificial Transmutation

• Artificial radioactive nuclides are those not found naturally on Earth and are made by artificial transmutations through nucleus bombardment via charged/uncharged particles.
• Neutrons, lacking charge and mass, easily penetrate an atom's nucleus unlike positively charged particles repelled by it.
• Supplying sufficient energy is vital when bombarding nuclei with these particles, potentially achieved through particle accelerators using magnetic or electric fields.
• Technetium and Promethium are artificially produced elements that fill periodic table gaps.
• Transuranium elements contain over 92 protons inside of their nucleus.

Nuclear Radiation

• Nuclear radiation transfers energy from nuclear decay to atom electrons/molecules, which causes ionization.
• A roentgen (R) measures nuclear radiation exposure.
• A rem measures ionizing radiation dose accounting for effects on human tissue.
• Long-term radiation exposure can lead to genetic defects like cancer because of DNA mutations.
• The average annual background radiation exposure in the US is roughly 0.1 rem.

Radiation Detection Methods:

• Film badges quantify radiation exposure of individuals working directly with radioactive material.
• Geiger-Muller counters quantify radiation via pulses created as gas ionizes.
• Scintillation counters use emitted-light conversion into electric signals for quantifying radiation levels.