Physics 132: Atomic and Nuclear Physics Notes

Historical context: The concept of the atom originated with Greek philosophers who suggested it as the smallest component of matter.
Early theories: Initially proposed four elements: earth, air, fire, water (not scientifically accurate).
19th Century Advancements: Chemists like Dalton, Avogadro, and Mendeleev established the atomic theory, leading to acceptance of atomic existence.
Atom size: Atoms are approximately $10^{-10}$ m in diameter.

Electrons: Discovered through cathode-ray tube experiments by William Crookes and later by J.J. Thomson.
- Cathode Ray Tubes: Electrons flow from the negative electrode (cathode) to the positive electrode (anode).
- Thomson's findings: Proved cathode rays were negatively charged particles by showing deflection in electric fields.
- Key formula: $a = rac{F}{m} = rac{qE}{m}$ (acceleration related to force and mass).
- Charge-to-mass ratio: $rac{q}{m} = -1.76 imes 10^{11} ext{C/kg}$ , implies all electrons are identical.
- Mass of electron: $m_e = 9.11 imes 10^{-31} ext{kg}$ .
The Nucleus: Hypothesis that electrons are embedded in a positively charged sphere (Thomson’s "plum pudding model").
- Rutherford's Experiment: Used alpha particles to determine the nucleus's size and mass (discovered a small dense nucleus).
- Nuclear Model: Electrons orbit around a massive nucleus similar to planets around the sun.
- Nucleus size: Approximately $10^{-15}$ m, very dense compared to matter.

Introduction of neutrons as a required component due to discrepancies in mass versus atomic number.
- Neutrons: Neutral particles similar in mass to protons, necessary for nuclear stability.
- Mass Number (A): Total number of protons (Z) and neutrons (N) in the nucleus, defined as $A = Z + N$ .

Natural isotopes of an element exist with varying abundances affecting the atomic mass listed on the periodic table.
- Example: Chlorine has two stable isotopes contributing to an average atomic mass.

Nuclear Forces: Strong nuclear force counteracts the electrostatic force between protons.
- Binding Energy: The energy needed to separate nucleons, related to mass difference of nucleus and its components.
- Formula: $E_b = rac{ riangle m c^2}$ , where $c = 3 imes 10^8 ext{m/s}$ .
Types of Decay:
- Alpha Decay: Nucleus emits a helium nucleus, reducing mass number by 4 and atomic number by 2.
- Beta Decay: Nucleus converts a neutron into a proton and emits an electron, increasing atomic number by 1.
- Gamma Decay: Excited nucleus transitions to lower energy state by emitting gamma photons.

Half-life ( $t<em>{1/2}$ ): Time for half of radioactive nuclei to decay. Defined as: $N(t) = N</em>0 imes rac{1}{2}^{(t/t_{1/2})}$ .
- Exponential decay graph represents this decay process.
Activity (R): Rate of decay, given by $R(t) = N(t) imes rac{ ext{ln } 2}{t_{1/2}}$ .
- Unit of activity: Becquerel (Bq) denoting decay per second.

Radiation in Medicine: Used for diagnostic and therapeutic purposes (e.g., imaging and cancer treatments).
- Radiation dose: Measured in grays (Gy), taking into consideration the biological effects of different radiation types.
- Relative Biological Effectiveness (RBE): Quantifies varying biological damage depending on radiation type.

Atoms are structured forms of neg. charged electrons orbiting a pos. charged nucleus.
Electrons are fundamental particles with a charge-to-mass ratio established through experimentation.
Neutrons and protons form the atomic nucleus, and isotopes of elements exhibit variances in nuclear properties.
Radioactive decay processes govern stability and energy release within isotopes, affecting applications in technology and medicine.
Nuclear forces, radioactivity, and early experiments laid the foundation for atomic and nuclear physics as crucial areas of study.