ISABELLE Exam Notes: Nuclear Model, Isotopes, and Early Atomic Theory

Observation (Rutherford experiment): nearly all alpha particles passed straight through the sample; some alpha particles were deflected; a few alpha particles were reflected back.
Interpretation:
- Most of the atom is empty space.
- A massive, positively charged nucleus exists.
- The nucleus is tiny compared to the atom.
Rutherford's Nuclear Model:
- A dense, positively charged nucleus contains most of the atom's mass.
- Electrons orbit the nucleus in mostly empty space.

Subatomic particles (basic properties):
- Proton: charge $+e$ ; relative mass approximately $m_p$ (basic unit for mass).
- Neutron: charge $0$ ; relative mass approximately $mn \approx mp$ .
- Electron: charge $-e$ ; relative mass approximately $me \approx \frac{1}{1838} mp$ .
Note: The transcript lists
- Proton: $+1$
- Neutron: $\sim 1$
- Electron: $\sim \frac{1}{1838}$
  which correspond to the conventional charges and mass ratios above.
Isotopes:
- Isotopes are atoms of the same element with different atomic masses due to different numbers of neutrons.
- Isotopes share the same atomic number (Z) but have different mass numbers (A).
Atomic notation (example):
- Mass number A, atomic number Z, element symbol X.
- For example, $^{A}{Z}\mathrm{X}$ ; a specific instance: $^{23}{11}\mathrm{Na}$
- From the transcript: MASS NUMBER = 23, ATOMIC NUMBER = 11, NET CHARGE = 0.
- Nuclear charge of the nucleus would be $+Z e\,,$ while the neutral atom has a total charge of 0 due to $Z$ electrons of charge $-e$ .
- The notation indicates:
- Mass number A = protons + neutrons.
- Atomic number Z = number of protons.
- Net charge of the atom is zero when neutral.

Atomic weight (average atomic mass) is calculated as a weighted average of isotopic masses based on their natural abundance.
Isotopes (from the transcript):
- Isotope I: Mass = $61.53\ \mathrm{amu}$ , Abundance = $45.5\%$
- Isotope II: Mass = $74.54\ \mathrm{amu}$ , Abundance = $55.5\%$
Formula for average atomic weight:
- If abundances are given as percentages, the average atomic weight is:
 $\bar{A} = \sumi Mi \left(\dfrac{\text{abundance}_i}{100}\right)$
- Using the provided values:
 $\bar{A} = 61.53\left(\dfrac{45.5}{100}\right) + 74.54\left(\dfrac{55.5}{100}\right)$
Numerical result (calculation not shown step-by-step in the transcript):
- $\bar{A} \approx 69.57\ \mathrm{amu}$

Core statements:
- All matter is composed of invisible atoms.
- Atoms of a given element are identical; atoms of different elements are distinct.
Laws associated:
- Law of Conservation of Mass: mass is conserved in chemical reactions.
- Law of Constant Composition (Definite Proportions): a compound contains elements in fixed, whole-number ratios.
- Atoms combine to form compounds in fixed ratios; this relates to the Law of Multiple Proportions, which states that atoms bond in various ways to form different compounds.
Connection to compounds:
- Atoms combine with fixed ratios to form compounds.
- The difference in compounds arises from different ways atoms bond and combine in fixed ratios.

Cathode Ray Tube experiments (1897): J. J. Thomson conducted important experiments using the cathode ray tube.
The ray produced in the tube is composed of beta-like particles that bend away from the negative electrode and toward the positive electrode.
Key findings:
- Beta particles are negatively charged electrons.
- Electrons have mass, about $\dfrac{1}{1838}$ of the mass of a proton:
 $me \approx \dfrac{mp}{1838}$
- Hydrogen was known to be the smallest particle at the time.
Thomson's model (Plum Pudding Model):
- Electrons embedded in a positively charged sphere (a positive "muffin").
- This model depicted a diffuse positive charge with embedded negative electrons to balance charge.

Rutherford tested the plum pudding model by bombarding thin gold foil with alpha particles (helium nuclei).
Observed outcomes (from the earlier notes):
- Most alpha particles passed through the foil with little or no deflection.
- Some alpha particles were deflected at large angles.
- A few alpha particles were reflected back toward the source.
Conclusions:
- The atom is mostly empty space.
- A small, dense, positively charged nucleus exists at the center.
- The nucleus contains most of the atom's mass.
- Electrons orbit the nucleus in the surrounding empty space.

How the discoveries connect: Thomson’s electron discovery (negative charge) combined with Rutherford’s nucleus led to the modern view of a tiny core (nucleus) surrounded by electrons in largely empty space.
Foundational implications:
- Shift from the Plum Pudding model to a nuclear model of the atom.
- Recognition that atoms have substructures (protons, neutrons, electrons) with distinct properties (charge, mass).
Real-world relevance (inferred from the material):
- Understanding atomic structure underpins chemistry, physics, and applications ranging from energy to medicine.
- Isotopes and atomic weights are essential for chemistry calculations, dating methods, and material analysis.

Electron mass ratio to proton:
- $me \approx \dfrac{mp}{1838}$
Proton charge and neutron/electron details:
- Proton: charge $+e$ ; relative mass approximately $m_p$ .
- Neutron: charge $0$ ; relative mass approximately $m_p$ .
- Electron: charge $-e$ ; relative mass approximately $\dfrac{m_p}{1838}$ .
Nuclear notation example (isotopes):
- $^{A}_{Z}\mathrm{X}$ where A = mass number (protons + neutrons), Z = atomic number (protons).
- Example: $^{23}_{11}\mathrm{Na}$ has A = 23, Z = 11, net charge of the nucleus $+Z e$ , neutral atom has charge 0 due to $Z$ electrons.
Isotope concept: same element (same Z) with different A due to different N (neutrons).
Atomic weight calculation: weighted average of isotopic masses by their abundances:
- $\bar{A} = \sumi Mi \left(\dfrac{\text{abundance}_i}{100}\right)$
- Example values from the transcript:
- Isotope I: Mass = $61.53\ \mathrm{amu},\; \text{Abundance} = 45.5\%$
- Isotope II: Mass = $74.54\ \mathrm{amu},\; \text{Abundance} = 55.5\%$
- Numerical result: $\bar{A} \approx 69.57\ \mathrm{amu}$