Nuclear Physics Core Concepts

In Rutherford's scattering experiment, alpha particles that directly collide with the nucleus of a gold atom experience a strong repulsive force due to the positive charge of the nucleus. This interaction causes the alpha particles to be deflected back along their original path rather than passing through or being absorbed. The unexpected reflection of some alpha particles indicated that the nucleus is small, dense, and positively charged, leading to the conclusion that most of the atom's mass is concentrated in the nucleus.

Isotopes are variants of a chemical element that share the same number of protons and electrons, which defines their identity and chemical behavior. However, they differ in their atomic mass due to variations in the number of neutrons in their nuclei. This difference in neutron count leads to different isotopes having distinct physical properties, such as stability and radioactivity, while still retaining the same chemical properties since they have the same electron configuration.

During alpha decay, an atomic nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. This emission results in a decrease of 2 in the atomic number, as the loss of 2 protons reduces the element's identity. Additionally, since an alpha particle contains 4 nucleons (2 protons and 2 neutrons), the total nucleon number decreases by 4. Therefore, the process leads to a change where the atomic number decreases by 2 and the nucleon number decreases by 4.

Alpha particles have the highest ionization power due to their large mass and charge, allowing them to interact strongly with matter. Beta particles, being lighter and carrying a single charge, have a lower ionization power than alpha particles but are still more ionizing than gamma rays. Gamma rays are electromagnetic radiation with no mass or charge, resulting in the least ionization power. Therefore, the correct ranking from highest to lowest ionization power is Alpha, Beta, Gamma.

Alpha rays are positively charged and deflect upward in a magnetic field due to the Lorentz force acting on them. Beta particles, being negatively charged electrons, would deflect downward. Gamma rays are uncharged and thus travel in a straight line, unaffected by magnetic fields. In an electric field, alpha rays, as positively charged particles, will also deflect downward. These behaviors are consistent with the principles of electromagnetism, which dictate how charged particles interact with magnetic and electric fields.

Carbon-14 dating is a reliable method for determining the age of archaeological finds because it is based on the radioactive decay of carbon-14, which is present in all living organisms. When an organism dies, it ceases to take in carbon-14, and the amount of this isotope in its remains begins to decrease over time at a known rate. By measuring the remaining carbon-14, scientists can calculate how long it has been since the organism's death, providing an estimate of the object's age.

After 60 years, which is three half-lives (20 years each), the count rate of the radioactive sample will decrease by half three times. Starting with an initial count rate of 800 counts per minute, the calculations are as follows: after the first half-life (20 years), the count rate becomes 400 counts per minute; after the second half-life (40 years), it reduces to 200 counts per minute; and after the third half-life (60 years), it drops to 100 counts per minute.